gCD

armonc]
 METHOD
OF

TEACHING HARMONY
BASED UPON

SYSTEMATIC EAR-TRAINING
AND UPON THE

HARMONIZATION OF UNFIGURED BASSES, -FIGURED

AND MELODIES, AND THE CONSTRUCTION
BASSES
OF HARMONIC PROGRESSIONS BY THE PUPIL.

BY

FREDERICK G. S H N N,
I
Mus. Doc., DUNELM, A.R.C.M., F.R.C.O.
PROFESSOR OF THE ART OF TEACHING, OF EAR-TRAINING AND MUSICAL DICTATION, AND OF
HAKMONY AT THE GUILDHALL SCHOOL OF Music.

PART I. DIATONIC HARMONY.

Price 2s. 6d. Cloth boards, QslQ

LONDON :

THE VINCENT MUSIC COMPANY LIMITED,

60, BERNERS STREET, W.
 MUSICAL EDUCATIONAL WORKS
BY

FREDERICK G. SHINN.

ELEMENTARY EAR-TRAINING.
Book I. MELODIC.
Second (enlarged) Edition, with Appendix of 100 Melodies (original and
selected), which include 60 illustrations of old Dance Tunes, taken
from the Fitzwilliam Virginal Book and other sources.
Price Two Shillings.
Book II. HARMONIC AND CONTRAPUNTAL.
PART I. HARMONIC EAR-TRAINING. A method of ear-training in connec-
and progressions of such, supplemented with
tion with intervals, chords
a large number of harmonic dictation exercises carefully graduated in
length and difficulty.
PART II. CONTRAPUNTAL EAR-TRAINING. -A method of ear-training in
connection with musical progressions of a contrapuntal character,
supplemented with a large number of dictation exercises in two, three
and four parts, carefully graduated in length and difficulty, and partly
selected from the works of the greatest composers, from Palestrina to
Schumann. Many of the original exercises in three and four parts
have been written with the object of training the listener to specially
direct his attention towards the inner part or parts.

Price Three Shillings.

A METHOD OF TEACHING HARMONY,

BASED UPON
SYSTEMATIC EAR-TRAINING,
and upon the Harmonization of Unfigured Basses, Figured Basses and Melodies,
and the Construction of Harmonic Progressions by the Pupil.
PART I. DIATONIC HARMONY (including the chord of the Dominant
Seventh, Passing Notes, Suspensions and Simple Modulation).
PART II. CHROMATIC HARMONY AND EXCEPTIONAL PROGRESSION (with
a chapter upon the Harmonization of Ground Basses).

Price of each Part, Two Shillings and Sixpence. In cloth boards, Three Shillings.

MUSICAL MEMORY AND ITS CULTIVATION.

PART I.
- An
investigation into the forms of memory employed in Pianoforte.
Playing, and a theory as to the relative extent of the employment of
such forms.
PART II. The Cultivation of Musical Memory a Guide to the Memori-
zation of Piano Music.

Price Two Shillings and Sixpence,

Press opinions upon the above works will be found at the end of this book.
 AUTHOR'S NOTE.

addition of another text book to the many already published

THE books upon Harmony, seems to call for some explanation.
text

The author believes that an adequate explanation, as well as some

justification for the publication of the present work, may be found
in the plan of the book itself, and that the method of teaching
Harmony herein expounded differs very considerably from any already
published method, at least, so far as the author's knowledge of such
methods extends. Moreover, he believes, that many teachers, whose
number is
increasing every day, will find set forth herein, a complete
and systematic method of teaching Harmony, based upon similar

fundamental principles to those upon which their own teaching has been
based, although, possibly developed in a more complete and comprehen-
sive manner than that which they have been able to employ, owing to
the absence of any book containing suitable graduated exercises. It is

hoped that the present work

supply this very obvious deficiency
will

amongst musical educational works, which no teacher has felt more

keenly than the author himself.
The author wishes to gratefully acknowledge the many valuable
suggestions which he has received from his friends, Dr. H. A. Harding,
Mr. Orlando Morgan, Dr. H. W. Richards, and also to Dr. Hamilton
Robinson who has kindly corrected some of the proof sheets.

SYDENHAM, May 1904.

 TABLE OF CONTENTS.
[The numbers always refer to the Paragraphs, except in those instances in whicn
it is otherwise statedJ\

PAGE.
To THE TEACHER ... vii

PART I.

DIATONIC HARMONY.
CHAPTER.
I. HARMONY AND ITS SUBJECT MAITER I

II. KEY. THE DIATONIC SCALES 3

Key, 4. Scales, 5. The Diatonic Scales, 6. Major Scales and their
key-signatures, 7. Minor Scales and their key-signatures, 8. The
relationship between Major and Minor keys, 9. The names of the degrees
of the Scale, IO. Exercises.

III. INTERVALS THEIR DEFINITION, CLASSIFICATION AND INVERSION ... 8

Intervals, definition, n. "Numerical" definition, 12. "Qualitative"
definition, 13. Classification of Intervals, 14. Consonant and Dissonant
Intervals, 15. Diatonic and Chromatic Intervals, 16. Simple and
Compound Intervals, 17. Inversion of Intervals, 18. Exercises,

IV. THE TONIC TRIAD (MAJOR KEY) 13

The Tonic Triad, 19. Triads and Common Chords, 20. Four-part
Harmony, 21. The doubling of notes, 22. Ear Exercises, 23. Distri-
bution of parts, 24. Overlapping of parts, 25. Crossing of parts, 26.
Mental conception of chords, 27, 28. Exercises.

V. THE DOMINANT TRIAD (MAJOR KEY) 19

The Dominant Triad, 29. Ear Exercises, The mental effect of the
30.
Dominant common chord, 31. The progression and movement of
parts, 32. HARMONIC PROGRESSION Similar, contrary and oblique
motion, 33. The motion between the outside parts, 34. Hidden octaves
and fifths between the outside parts, 35. Consecutive unisons, octaves
and fifths (similar motion), 36. Consecutive octaves and fifths (contrary
motion), 37. MELODIC PROGRESSION Conjunct and disjunct movement,
38. Progression of the Leading-note, and omission of the fifth in a Tonic
common chord, 39. Allowable overlapping of parts, 40. The harmon-
ization of basses and melodies, 41. Exercises.

VI. THE SUBDOMINANT TRIAD (MAJOR KEY) 25

The Subdominant Triad, 42. Hidden octaves and fifths, 43. Exercises.

VII. THE THREE PRIMARY TRIADS (MAJOR KEY) 27

The Three Primary Triads, 44. The selection of chords in the har-
monization of melodies, 45. Ear Exercises, 46. MELODIC PROGRES-
SION Augmented intervals in melody, 47. Diminished intervals in
melody, 48. Large intervals in melody, 49. Progression of the
Subdominant triad to the Dominant triad, 50. Final Cadences, 51.
Ear Exercises, 52. Exercises.
 TABLE OF CONTENTS. V
PAGE.
VIII. THE THREE PRIMARY TRIADS (MINOR KEY) 31
The Primary Triads in the Minor key, 53. THE TONIC TRIAD, 54.
Ear Exercises, 55. The "Tierce de Picardie," 56. THE DOMINANT
TRIAD, 57. Ear Exercises, 58. Melodic Progression, 59- Exercises.
THE SUBDOMINANT TRIAD, 60. Exercises. THE THRKE PRIMARY
TRIADS, 61. Exercises.
IX. THE PRIMARY TRIADS IN THEIR FIRST INVERSION 35
Common Chords and their inversions, 62. THE TONIC AND DOMINANT
TRIADS first inversion, 63. The mental effect of triads in their first
inversion, 64. The doubling of notes, 65. The figuring of chords
Figured basses, 66. Exercises. THE SUBDOMINANT TRIAD first inver-
sion, 67. Exercises. THE THREE PRIMARY TRIADS first inversion, 68.
The doubling of notes in chords of the sixth, 69. The doubling of the
third in Major Common Chords, 70. The Minor Seventh in the Minor
key as a bass note, 71. Exercises.
X. THE SUBMEDIANT TRIAD 42
The Secondary triads, 73. The Submediant triad, 74. Ear Exercises
Progressions formed of the Submediant triad and the Primary triads, 75.
The harmonization of basses and melodies, 76. The doubling of notes, 77.
The "Interrupted Cadence," 78. Exercises. The first inversion of the
Submediant triad, 79. Exercises.
XL THE SUPERTONIC TRIAD 48
The Supertonic triad, 80. Ear Exercises Progressions formed of the
Supertonic triad, and (I) the Tonic triad, (II) the Dominant triad,
(III) the Subdominant triad, (IV) the Submediant Exercises.
triad, 81.
The first inversion of the Supertonic triad, 82. Progressions formed of
a Perfect fifth and a Diminished fifth, 83. Exercises.
XII. THE MEDIANT TRIAD ... 53
The Mediant triad, 84. Ear Exercises, 85. Exercises. The first inver-
sion, 86. Ear Exercises, 87. The harmonization of figured basses, 88.
Exercises.

XIII. THE LEADING-NOTE TRIAD FIRST INVERSION ... ... ... 57

The Leading-note triad, 89. The first inversion, 90. Harmonic progres-
sion, 91. The Minor Seventh as a Melody note in the Minor key, 92.
Exercises.

XIV. THE PRIMARY TRIADS IN THEIR SECOND INVERSION 60

THE TONIC TRIAD second inversion, 94. Ear Exercises, 95. Progres-
sion of the bass when approaching and quitting a six-four chord, 96. The
" Cadential six-four " chord and the " Allowable
Imperfect cadence," 97.
Hidden Octaves, 98. Exercises. THE DOMINANT TRIAD second
inversion, 99. Exercises. THE SUBDOMINANT TRIAD second inversion,
100. Consecutive Perfect fourths with the bass, 101. Exercises.
XV. THE SECONDARY TRIADS IN THEIR SECOND INVERSION ... ... 66
The consonant secondary triads in their second inversion, 102. Exercises.
XVI. THE DISSONANT TRIALS ... 68
The dissonant triads and their second inversion, 103. THE LEADING-
NOTE TRIAD, 104. Consecutive fifths and consecutive fourths with the
bass 105. Exercises. THE SUPERTONIC TRIAD IN THE MINOR KEY,
106. The Major Sixth as a Melody note in the Minor key, 107.
Exercises. THE MEDIANT TRIAD IN THE MINOR KEY, 108. Harmonic
progression, 109. Exercises.

XVII. CADENCES (ALSO THE CONSTRUCTION OF FOUR-BAR EXERCISES TO

ILLUSTRATE THE EMPLOYMENT OF DIFFERENT FORMS OF CADENCK) 73
Cadences, no. Final Cadences, ill. Inverted Cadences, 112. Middle
Cadences, 113. Exercises. Suggestions as to the construction of four-bar
exercises to illustrate the employment of Middle and Final Cadences.
VI TABLE OF CONTENTS.
PAGE.
XVIII. SEQUENCES 78
Sequences, 114. Exceptional progression in Tonal Sequences, 115.
Real Sequences, 116. Exercises.

XIX. THE CHORD OF THE DOMINANT SEVENTH ... ... ... ... 80
Chords of the Seventh, 117. The chord of the Dominant Seventh, 118.
Discords; their nature and
resolution, 119. The resolution of the
Dominant Seventh. Ear Exercises, 120. Harmonic Progression, 1 21.
The repetition of a discord, 122. The figuring of the chord of the
Dominant Seventh, 123. Exercises. FIRST INVERSION, 124-5. Ear
Exercises, 126. Exercises. SECOND INVERSION, 127. Ear Exercises,
128. Exceptional progression of the Seventh, 129. Exercises THIRD
and LAST INVERSION. Ear Exercises, 130. The interval of the Minor
Seventh in Melody, 131. Exercises.

XX. NATURAL MODULATION 91

Modulation, 132, 133. Natural Modulation and Extraneous Modulation,
134. The "connecting link "in a modulation, 135. The triad as the
connecting link, 136. The Tonic triad as the connecting link, 137.
Exercise. The six-four chord as the connecting link, 138. False
Relation, 139. The doubling of notes, 140. Form of Ear Exercises, 141.
MODULATION to the key of the DOMINANT, 142. Exercises. MODU-
LATION to the key of the SUBDOMINANT, 143. Exercises. MODULATION
to the key of the RELATIVE MINOR, 144. Exercises. MODULATION to
RELATIVE MAJOR, 145. Exercises. MODULATION to the
the key of the
RELATIVE MINOR OF THE DOMINANT, 146. Exercises. MODULATION
to the RELATIVE MAJOR OF THE SUBDOMINANT, 147. Exercises.
MODULATION to the RELATIVE MINOR OF THE SUBDOMINANT, 148.
Exercises. MODULATION to the RELATIVE MAJOR OF THE DOMINANT,
149. Exercises.

XXI. THE DIATONIC (OR SECONDARY) CHORDS OF THE SEVENTH ...

105
Diatonic chords of the Seventh, 150. Their preparation and resolution, 151.
Ear Exercises, 152. The figuring of Diatonic sevenths, 153. Exercises.
XXII. UNESSENTIAL NOTES AUXILIARY NOTES, PASSING NOTES AND
ANTICIPATIONS 108
Unessential notes, 154. AUXILIARY NOTES, 155. Their formation, 156.
PASSING NOTES, 157. Chromatic Passing notes, 158. The employment
of the Melodic Minor Scale, 159. Accented Auxiliary notes and Passing
notes, 160. False relation and Unessential notes, 161. Changing notes,
162. Unessential notes in two parts, 163. ANTICIPATIONS, 164.
Harmonic Progression in connection with Unessential notes, 165, 166,
Consecutive Perfect fourths with the Bass, 167. Exercises.

XXIII. SUSPENSIONS 118

Suspensions, 168. Their preparation and resolution, 169. Retardations,
170. The 9 8 SUSPENSION, 171-172. Ornamental Resolutions, 173.
Exceptional Resolutions, 174. The doubling of notes, 175. Harmonic
Progression, 176. Exercises. First inversion, 177. Exercises. Second
inver>ion, 178. Exercises. The inversion with the Suspension in the
bass, 179. Exercises. The 4 3 SUSPKNSIOM, 180. Exercises. First
inversion, 181. Exercises. Second inversion, 182. Exercises. The
inversion with the Suspension in the bass, 183. Exercises. The 6 5
SUSPKNSION, 184. Exercises. The SUSPENDED LEADING-NOTE, 185, 186.
Exercises. DOUBLE SUSPENSIONS, 187. Exercises. TRIPLE SUSPEN-
SIONS and the suspension of complete chords, 188. The figuring of
Suspensions, 189. Suspensions in connection with Discords, 190.
Exercises.

136
 TO THE TEACHER.

possibly help those who make use of this book, if their

may
IT attention is drawn, in a preliminary chapter, to the chief
points in
which this text book differs from other text books upon the same
subject, and, it may also help them to understand the author's point of

view, when he leaves the beaten track, if, to an enumeration of these

differences, is added a brief summary of the reasons which caused them

to be made, and which he believes fully justifies them.

The most characteristic feature of this method, and the feature which,
the author believes, distinguishes it from all other published methods, is,
that it is based upon direct harmonic ear-training. In other words, the
end, which, first of all, it is specially designed to accomplish, is the
training of the pupil's ear to discriminate and to recognize each chord
by its sound, and then, the training of his musical memory to retain the
sound of each individual chord, and to associate such sound with the
correct notational signs. For these purposes Ear Exercises are supplied
in connection with every chord, and they are the first exercises or tests,
to which the pupil is subjected to in connection with any chord. These
exercises are to be played by the teacher upon the piano, or other

keyboard instrument, and then written down by the pupil from their
sound.
Although, the fact that this method is based upon direct ear-training,
is apparently only one amongst several points of difference, which
distinguishes it from other methods, yet, the other differences which
exist are very largely due to this. One of the most important of
these differences is the individual attention which is given to each
chord, and to each inversion of a chord. Especially will this be
noticeable in connection with the diatonic triads and their inversions,
where, with the exception of a few second inversions, each is treated
separately. It must be obvious that to each combination of notes

(whether such is an original position of a chord or an inversion) belongs

a particular musical effect, and also, each has its own special function
and position amongst the chords of a key, and if these characteristic
Vlll TO THE TEACHER.

properties of each chord are to be thoroughly understood, the various

chords must in the first instance be so introduced, that the attention
can be concentrated upon the distinguishing features of each individual
chord. In order to achieve this end, the chords, and their different
inversions, must be presented to the pupil ONE AT A TIME. Starting with a
single chord, the teacher must proceed chord by chord, and inversion
by inversion, until he has completed the whole harmonic fabric. Upon
no other method is it possible to teach Harmony, based on ear-
training, in a thoroughly complete, systematic and satisfactory manner.
Two of the chief objectives which this method has in view, then, are,

(i) the imparting of a knowledge of chords based primarily upon their

sound, and (2) a study of their nature and function, first, individually,
and then, joined with others to form progressions. If, however, we

claim to teach these aspects of the various chords, it is necessary that

the exercises given upon each chord should test the pupil's knowledge,
and exercise his powers in these special directions. That is, the
working of the Exercises, given in connection with the various chords,
must reveal, at least to some extent, how far the pupil can hear,
mentally, the sound of the chords he has written down, and, by his
ability to frame satisfactory progressions of them, how far he under-
stands their individual nature and function. Hitherto, in most Harmony
text books, the Exercises employed have been principally, if not

entirely,in the form of Figured basses, but it only requires a brief

consideration of the nature of such exercises, and of the directions in

which they furnish no test whatever, to show, that, for the above
mentioned purposes, exercises of this kind are quite useless. First of

all, the filling up of Figured basses cannot test the pupil's power of
hearing, mentally, what he is writing down, for it is quite possible to
correctly fill up the parts of an exercise in accordance with the figures,
without having any idea of the musical effect of the resulting harmonic
progressions. Secondly, the filling up of Figured basses neither exercises
nor tests in the slightest degree the pupil's knowledge of the function of
the individual chords, nor his power of selecting chords, which shall be
suitable to join with others, for the formation of satisfactory harmonic

progressions, for all such matters are decided for him. In these two
most essential matters, exercises in the form of Figured basses supply
no test whatever, and, therefore, although the Figured bass has hitherto

been the time-honoured servant, or hack, of every harmony teacher, yet

in this book such exercises have been relegated to a position, more, we

think, in accordance with the small intrinsic value which they possess
as instruments for the teaching of Harmony, than they have hitherto
held.

If, then, the Figured Bass exercise be inadequate for the efficient
 TO THE TEACHER IX

teaching of Harmony, the question arises, what kind of exercise should

take its place? We believe that the matters which we insist should be
tested by Harmony can only be adequately tested, as far as
exercises,
written concerned, by those exercises which leave the
exercises are
selection of the chords almost entirely to the pupil. Apart from the
writing of absolutely original progressions, the only exercises which admit
of this freedom of harmonization are Unfigured basses and Melodies,
and these are the two forms of exercises which we have almost entirely
adopted in this method. In connection with the various discords, in
addition however, to such exercises, the pupil is required to construct
short progressions, similar in form to the Ear Exercises, which shall
illustrate the different resolutions of the special chord under consider-
ation, while in order that the pupil may understand the method of
"
indicating chords by means of figures, which, as a method of musical
"
shorthand has distinct value, a small number of Figured Basses are
included, after the other exercises given in connection with the various
chords.
Before leaving the subject of Harmony exercises, it may not be
inappropriate, to suggest some explanation as to the causes which led to
the almost universal adoption of the Figured Bass as an instrument for
the teaching of Harmony. There can be little doubt that this was
originally due to the custom which prevailed up to the early part of the
nineteenth century, of
indicating instrumental
accompaniments by
means of figured basses. As a general rule, the harpsichord (or organ)
accompaniments to operas and oratorios were written either simply as a
figured bass, or else as a figured bass with the highest part in addition.
This made it necessary for accompanists to understand how to
correctly
supply either the whole of the upper parts, or, at least, the inner parts,
from the figures, and the ability to play with readiness and accuracy
from a figured (or what was frequently called a Thorough) bass became
the indispensable possession of every musician. It was doubtless in

order to acquire this power that many musical students, in the first
instance, entered upon the study of Harmony, and it is therefore not
difficult to understand, how a knowledge of chords, as represented by

figures under a bass part, and the ability to correctly fill up such a bass,
eitherupon paper, or at the keyboard, gradually came to be regarded as
synonymous with a knowledge of Harmony. During the last century,
however, the methods of composers underwent a very considerable
change in the manner of recording their compositions, and the custom
of leaving the details of their works to be filled in by the executant,
from a figured bass, is now never resorted to, whilst even in works in
which was formerly done, the modern editor has stepped in and
this

supplied the deficiency. At the present time, therefore, it is only upon

X TO THE TEACHER.

those exceptional occasions, when an old edition of an old work, is made

use of, that the performer is now called upon to do, what a hundred
years ago was a matter of daily occurrence. This change in the methods
of composers, depreciated, to a very considerable extent, the value of
the figured bass exercise as an instrument for the teaching of Harmony.
While one of the chief objects of the study of Harmony was to acquire
the power of interpreting figured basses, it was necessary that the filling
up of figured basses should enter, very largely, into the study of
Harmony; when, however, facility in interpreting the figures, no
longer remains the prime object, or even an important object in the
study of Harmony, figured bass exercises must be judged according
to the intrinsic merit they possess as instruments for the teaching of

Harmony, and this we believe to be very small. It is a curious fact

that teachers and writers upon Harmony, have, for years, failed to
perceive and hitherto have made few attempts to systematically
this,

supplement figured basses with other and more valuable forms of

exercises. With a conservatism, worthy of a better cause, they have
held on to the beaten track, and finally, have exalted the figured bass
exercise to such a unique position
in the teaching of Harmony,
and in examinations, that the present-day student is still
Harmony
encouraged to cherish the belief, that, upon the successful working of
an unlimited number of figured basses rests his one and only hope of
harmonic salvation.
To one other point only, in connection with this method, generally,
is itnecessary to direct the attention of the teacher, that is, to the order
which has been adopted, in the arrangement of the materials of the
subject, not merely with regard to the chords themselves, but also with
regard to the rules which govern their formation and progression. With
reference to the CHORDS, an order which is suitable for teaching purposes
must be from two points of view: (i), it must show the
satisfactory
chords in the mind can most readily receive and
order in which the
assimilate them as combinations of musical sounds, and (2), it must
also show them in an order which will give to the student clear ideas
as to their systematic formation and classification. The first condition
requires, that the chords, with the sound of which the pupil is familiar
(owing to the influence of his general musical environment) should be
introduced before those, with the sound of which he is less familiar,
and these later ones before those which are comparatively unknown to
him. The second condition requires, that the order employed shall
exemplify the regular and gradual building up of the various chords
upon some intelligible plan. To frame an order in which the require-
ments of both of these conditions should be completely satisfied is

practically impossible ;
it is therefore necessary, that, in every method
 TO THE TEACHER. XT

of teaching Harmony, the order in which the chords are presented, must
represent a compromise between these two conditions, and the nature
of this compromise, that is, the exact order adopted, must be decided

by the author of the method. Whether those using this book feel-

that the order given herein is satisfactory, or prefer to modify it in

some of its details, is
unimportant ; important, what is is, that they
should understand the underlying principles upon which this or any
other suitable order for teaching purposes, must be framed
With regard to the RULES which regulate the progression of the several
chords, or the progression of one or more notes of a chord, generally
"
called the Rules of Melodic and Harmonic Progression," such are
not introduced until the pupil is ready to make immediate use of them ;
"
for instance, the pupil is not informed that consecutive perfect fourths
"
with the bass are forbidden until he is able to use two chords upon
^
consecutive bass notes; neither is he told that "consecutive seconds and
"
sevenths between any two parts are forbidden until he is familiar with
chords which admit of such progressions. As he approaches new tracts
of country where he will require fresh directions, new sign posts are

supplied, but they are not supplied till they are required.
Having reviewed the general principles which underlie the method
employed book, we will now refer quite briefly to a few points of
in this
detail. One
of the most important of these, is the equal attention
which must be given to the various chords in both Major and Minor
keys, in all the different forms of Exercises. The limitations of space
have compelled us to omit all but a few Ear Exercises in the Minor key,
for by employing almost entirely the Major key in such exercises, we
have been enabled to give a far more complete and varied series of
Ear Exercises than would have been possible, had we made equal use
of both keys. It therefore devolves upon the teacher to transpose the

large majority of such exercises from the Major key into the Tonic Minor
key, and this must invariably be done, whenever separate Ear Exercises in
the Minor key are not given* The operation of transposition, which thus
becomes necessary, is not however, otherwise, an entirely useless one, for
it directs the attention of both teacher and pupil to a most important
fact in connection with chords generally, and which is sometimes
overlooked or partly so, namely, that after due allowance has been made
for the characteristic differences between the Major scale and the
Minor the function and progression of most chords, does not
scale,

essentially differ in major and minor keys having the same key-note.

*
This transposition from the key of C major to that 01 C minor should present no
it being merely a mental prefixing of the key signature of C minor with three
difficulty,
flats, while keeping the B's natural.
Xll TO THE TEACHER.

There are of course some exercises which, if transposed from the

Major key to the Tonic Minor key, owing to the differences in the nature
of the two scales, incorrect melodic or harmonic progressions would be
created. Where such incorrect progressions would arise, the exercises
are not marked for transposition. In addition to the Ear Exercises
given, others illustrating the various chords, but showing them in
different keys and with the several notes differently distributed, should
be supplied by the teacher (see note, page 16%*).
Besides those exercises which are specially described as Ear Exercises,
the tea^ her should make it a regular practice to employ as an Ear Exercise

(that is, as an exercise to be written down by the pupil from dictation)

every musical example which illustrates a correct progression, and he
should also employ as an Ear Exercise, although not to be written
down, but carefully listened to, every musical example which illustrates
an incorrect progression. Thus the ear should be trained to dis-
criminate by their sound between progressions which are regarded as
correct, and those which are regarded as incorrect.
The manner of dictating the Ear Exercises, and the number of times
it will be necessary to play them over to a pupil in order that he may

be able to write them down, must of course depend upon the natural
aural capacity of the pupil, both with regard to the discriminative power
or fineness of his ear, and also his retentive power for musical sounds
generally. The average pupil, in the early stages, will probably require
several repetitions for even quite short exercises, and it may be a
considerable time before he will be able to remember progressions of
more than two or three different chords played consecutively, that is to

say, exercises of four or more

different chords, will have to be dictated
in a piece-meal manner. All such matters however can only be decided

by the teacher for each individual pupil.

With regard to the written exercises, which involve the harmonization
of a Bass or Melody by the pupil, (and which should also be supple-
mented by others supplied by the teacher whenever additional ones are
required), the note at the top of page 38 ***, referring to the systematic
analysis and figuring of the chords employed in such, should be
carefully attended to, and consistently enforced in connection with every
exercise worked by the pupil. The requirements of all the written
exercises have been designed so as to make the pupil responsible for as
much as possible in the working of them, and yet, not more than he
should be able to successfully accomplish, if he has studied thoroughly,
and really mastered what has preceded any set of exercises. THE VALUE
AND IMPORTANCE OF A PUPIL DOING THINGS HIMSELF, RATHER THAN
MERELY READING ABOUT THEM AND LOOKING AT EXAMPLES WRITTEN
BY OTHERS, CANNOT BE OVERESTIMATED. The author does not hesitate
 TO THE TEACHER. Xlll

to state, that, the working of the numerous construction exercises upon

the model of the Ear Exercises, given in connection with the chord
of the Dominant Seventh, Modulation, Unessential Notes, and Sus-

pensions, in which everything is left for the pupil to do, will teach him
more about these various matters and the way of overcoming their
characteristic difficulties, than reading many text books and filling up
hundreds ot figured basses.
 A METHOD OF TEACHING HARMONY,

PART I.

DIATONIC HARMONY.

CHAPTER I.

HARMONY AND ITS SUBJECT MATTER.

1. HARMONY treats of the nature, classification and treatment of

chords or musical sounds heard in combination. It does not deal with
chords merely in their notational representation, as seems sometimes to
be imagined, but is concerned with them, primarily, as musical effects.
Chords exist quite apart from any form of musical notation by which
they may be represented, just as the objects which surround us exist,
quite apart from the name by which they are known, and the manner
of writing that name in any language. As in everyday life we require
words by which to refer to different things, supplemented by the art of
writing by which we may record facts about them, so, in dealing with
chords, either in connection with Musical Composition, or in the more
elementary studies (such as Harmony and Counterpoint) which lead up
to this, it is necessary that there should be some generally understood
method of bringing them before the mind, through the medium of the
eye (that is, by writing), and also of recording them with some degree
of permanence. This is done by the employment of Musical Notation,
and of the signs belonging thereto. With this notation and its signs
however, Harmony is only indirectly concerned. It is the sounds which
lie behind, and are represented
by the signs, and which the sight of the
signs should instantly recall to the mind, that the study of Harmony is
directly concerned. These sounds, heard in combination, are the essential
things, with the nature, classification, and treatment of which, Harmony
specially concerns itself. To the student of Harmony, there is no fact
of greater importance than this, and upon its due recognition, success
or failure in the mastery of the subject almost entirely depends.
2. It is obvious, therefore, that as the
study of each chord is entered
upon, its musical character must first of all be considered. The rules
referring to the special treatment a chord may require, will doubtless
furnish knowledge of a most valuable kind as to its correct grammatical
employment, but it is knowledge which should follow, and not precede,
knowledge of the sound of the chord itself. It matters not how familiar
the student becomes with the rule* of Harmony, the power he will
acquire of effectively employing; the various chords, in the formation of
2 CHAP. I. HARMONY AND ITS SUBJECT MATTER.

harmonic progressions (and this is the ultimate aim of the study

of Harmony), will almost entirely depend upon the extent to which
he can memorize their sound, and mentally recall this at the sight
of their respective notational signs. Before a chord is employed in
written exercises, its effect in sound, therefore should, to some extent,
have been memorized by the ear. Only when this has been done will
it be possible to create in the mind any clear idea of the sound of the

progressions which are being written down, and unless this can be done,
and is done, systematically, in connection with all written exercises, the
study of Harmony loses its living musical character and becomes merely
a study of lifeless and meaningless signs.
3. In these few remarks we have endeavoured to lead the student
towards the adoption of a correct attitude of mind with regard to the study
of Harmony and the nature of chords in general ; * before proceeding
to a detailed consideration of the different chords, there are, however,
two matters which claim our consideration. The/r^/ of these refers to
the relationship existing between the individual notes which together
make up what is called a Key, and which furnish the material from which
chords are constructed. These and other related matters are treated of
in the following chapter. The second refers to the manner of measuring
and of naming the Intervals formed between the various notes of a key,
and to such matters as the Classification and the Inversion of Intervals.
Chapter III is devoted to a consideration of these.

* "
This aspect of the study of Harmony is further discussed in the author's Musical
Memory and its Cultivation" in chapters VIII and XII of which, it is considered vi h
i;

more completeness than is possible here.

 CHAP. II. THE DIATONIC SCALES.

CHAPTER II.

KEY. THE DIATONIC SCALES.

4. A KEY in music is represented by certain musical sounds, which,

both with regard to their pitch and also to the manner of writing them,
have a definite relation to some one sound or note. This sound or
note is described as the KEY-NOTE, and from it the key takes its
alphabetical name. To each key-note, however, there belongs two
keys, a Major key and a Minor key, both of which take their
alphabetical name from this same note, and the key of a passage is
described as Major or as Minor according to the prominence given to
certain notes of the key.
5. The several notes which together make up a key are twelve in
number. are situated at the distance of a semitone from each
They
other, and are all included within the interval of an octave. Any of
them, however, may be duplicated by being sounded one, or more,
octaves higher or lower, as the compass of musical instruments may
permit. When the notes of a key are heard as a regular succession of
sounds, either ascending or descending, they form what is called a
SCALE. AScale in which all the twelve notes are employed is called a
Chromatic Scale, thus :

Ex. I.

-&
i
Key-note.
The notation of this Scale is explained in Chap. XXIV (Part II).

Scales in which only an alphabetical succession of the notes of the key

are employed, are called Diatonic Scales.
6.The Diatonic Scales. The Diatonic Scales comprise the
Major Scale, and the two forms of the Minor S;ale, the Harmonic forn
and the Melodic or Arbitrary form. The MAJOR SCALE has semitones
between the third and fourth degrees, and the seventh and eighth
degrees, and tones between all the other adjacent degrees, thus :

Ex. 2.

i 2 3^4 5 6 7^8
The HARMONIC MINOR SCALE is so called because it forms the basis of
harmonic combinations in the minor key. It may be formed by lowering
 HARMONY.

the third and sixth degrees of the major scale a semitone. This form of
the minor scale will be found to have semitones between the second and
third, fifth and sixth, and seventh and eighth degrees, an augmented
second (three semitones) between the sixth and seventh degrees, and
tones between all the other adjacent degrees.

Ex. 3.

Aug. 2nd.

The MELODIC OR ARBITRARY MINOR SCALE is so called because

by an
arbitrary alteration of the previous scale, in the employment of the
major sixth and major seventh ascending, and the minor seventh and
minor sixth descending, the interval of the augmented second is
avoided, and the scale is thus made more suitable for employment for
melodic purposes. In this form of the minor scale semitones occur
between the second and third, and seventh and eighth degrees ascending,
and between the fifth and sixth and second and third degrees descending,
and tones between all the other adjacent degrees.

Ex. 4.

7. Major Scales and their Key- Signatures. In the

construction of the Major scales, every scale, with the exception of the
scale of C major, requires the employment of one or more sharps or flats,
in order that the tones and semitones may occur in their proper relative
order. With regard to the scales requiring sharps, the scale which re-
quires the employment of one sharp for its correct formation begins on
the fifth note of the scale of C, that is G, and the note which requires to
be sharpened is F the seventh note from G. The scale which requires
the employment of two sharps begins on D, the fifth note ot the
scale of G, and the notes which require to be sharpened are F and C.
The scale which requires three sharps begins on A the fifth note
of the scale of D and the notes which require to be sharpened are
F, C, and G, and so on until the scale of F sharp with six sharps is
reached. With regard to the scales requiring flats, the scale which requires
the employment of one flat begins on the fifth note of the scale of C
counting downwards, that is F, and the note which requires to be flat-
tened is B, the fifth note from F counting downwards. The scale which
involves the employment of two flats begins on B flat, the fifth note
from F counting down the scale of F, and the note which requires to be
flattened, in addition to B, is E. The scale which has three flats begins
on E flat, the fifth note counting down the scale of B flat, and so on
until the scale of G flat with six flats is reached. A comparison of this
scale (G flat with six flats) with the scale of F sharp with six sharps, will
show that the only difference between these two scales is one of notation;
when played upon keyboard instruments they are absolutely identical.
 CHAP. II. THE DIATONIC SCALES.

The employment of keys requiring more than six sharps or six flats m
the signature is rare, as such keys would have equivalent keys possessing
.a
simpler signature. Thus the key of C sharp with seven sharps would
correspond to that of D
flat with five flats, see Ex. 5 (b) ; and the key
of C flat with seven flats, to that of B with five sharps, see Ex. 5 (a).

MAJOR KEY SIGNATURES.

Ex. 5. SHARP KEYS (a fifth apart counting ujnuards. )

FLAT KEYS (a fifth apart counting downwards.}

8. Minor Scales and their Key- Signatures. The Minor

scales are always written with the key-signature of the Major scale of
their third note. The scale of C
minor (in either form) is therefore
written with the key-signature of E flat major, and has three flats in the
signature, as shown in Exs. 6 and 7. This custom of using the same
key-signature for both major and minor scales involves the employment
of an accidental before the seventh note in all minor scales in their
Harmonic form, and also the employment of accidentals before both
the sixth and the seventh notes in the ascending Melodic form. All
these inflected notes, however, are diatonic notes in the scale or key to
which they belong.
Ex. 6.

HARMONIC MINOR SCALE.

Ex. 7-

MELODIC OR ARBITRARY MINOR SCALE.

-G

The relationship between the key-notes of the Minor scales with

regard to the employment of sharps or flats in regular progression is
similar to that of the key-notes of the Major scales, that is, by ascending
or by descending in fifths respectively. The key-signature of a minor
scale has either three flats more or three sharps less than the key-
signature of the major scale beginning with the same note, or else it has
a signature which is equivalent to this alteration. In Ex. 8 it will be
seen that the last three keys have each an equivalent key.
 HARMONY.
MINOR KEY SIGNATURES.
Ex. 8.

()
9. The Relationship between Major and Minor Keys.
The employment of the same key-signature for two different keys, one
of which is major and the other minor, has given rise to the terms
Relative Major and Relative Minor, which are frequently used to
describe keys having a common key-signature. Thus the key of E flat
major is the Relative Major of the key of C minor, and the key of
C minor is the Relative Minor of the key of E flat major. This so-called
relationship rests entirely upon identity of key-signature, although it
naturally follows from this that many of the notes of one key are also
found in the other. Another form of relationship which may exist
between Major and Minor keys isproduced when such have the same
key-note. They are then described as Tonic Major and Tonic Minor
respectively. Thus, the key of C major is the Tonic Major of the key
of C minor, and the key of C minor the Tonic Minor of the key of
C major.
10. The Names of the Degrees of the Scale. Besides
the ordinary alphabetical names which belong to the notes of a scale,
each degree of a diatonic scale (Major or Minor) has a special name
which defines its relative position in the scale, and by which name it is
usually referred to in the study of Harmony. These names are given
below, and in an order which will help to explain their derivation and
meaning. The different degrees are counted from the first note of the
scale upwards.
FIRST DEGREE. Tonic or Key-note.
FIFTH DEGREE. Dominant
(so called because the chords formed upon
" "
dominate or command the key).
this note
FOURTH DEGREE. Subdominant (the fifth degree below the Tonic ; the
under-dominant).
THIRD DEGREE. Mediant (midway between Tonic and Dominant).
SIXTH DEGREE. Submediant (midway between Tonic and Subdominant
counting downwards).
SECOND DEGREE. Supertonic (the note above the Tonic).
SEVENTH DEGREE. Leading-note (the note which naturally leads to
the Tonic).
Ex. 9. Super- Sub- Sub-
tonic, dominant. mediant. Tonic.

Ill
Dominant. Leading-
Tonic. note.
Sca'e
* Ist and. 3rd. 4th. 5th. 6th. 7th. 8th.
De&ces.
 CHAP. II. THE DIATONIC SCALES.

EXERCISES.
i. Write Major Scales beginning with each of the following notes.
Place the necessary accidentals before the notes of each Scale as they
are required, and the correct key-signature in a separate bar by itself at
the end :

-?<s>-

2. Write, in a similar manner, the Relative Minor Scales (Harmonic

Form) of the above Major Scales.
3. Write the Tonic Minor Scales (Melodic Form) ascending and
descending, of the above Major Scales, except G flat and D flat. In
this Exercise prefix the correct key-signatures in the usual way.
4. Name all the scales (Major and Minor) in which each of the
following pairs of notes are found B and F, B and E sharp, F and
:

C flat, F sharp and C, F sharp and B sharp, C and G flat.

5. Name the scales in which each of the following pairs of notes
are found F sharp and E flat,
: and E sharp, D
and flat, B andA G
C double sharp, F sharp and G double sharp, D and C flat
6. Name the scales in which each of the following pairs of notes
are found B sharp and E, D and G flat, A and D flat, E and A flat,
:

D and A sharp, A and E sharp.

7. Name the Dominants and the Leading notes of the keys of
-

E, F, B and D flat.

Name the Supertonics and the Subdominants of the keys of

8.

A, B C sharp, and G flat.

flat,

9. Name the Mediants and the Submediants of both the Major and
the Minor keys of A flat, F sharp, E flat, and D.
 HARMONY.

CHAPTER III.

INTERVALS THEIR DEFINITION, CLASSIFICATION, AND

INVERSION.
" "
is discussed only from a theoretical
L In this chapter the subject of Intervals
standpoint. The musical -aspect of Intervals, considered with a view to training the
ear to discriminate the different intervals by their sound, has already been dealt with
"
by the author in his Elementary Ear Training" the early chapters of which may
be regarded as complementary to the present chapter.]

11. The difference in pitch between two musical sounds is called an

INTERVAL. The exact nature of an Interval is only accurately known
when it is denned from two different standpoints,
(i) numerically, as a
second, a third, or a fourth, etc.; and (2) qualitatively, as a major interval,
a minor interval, or a perfect interval, etc. When these two forms of
qualification are combined, and such terms as major second, minor
third, or perfect fourth, are employed, the difference in pitch between
the two notes forming the interval is exactly defined \ and, if the name
of one of these notes be given, that of the other may be ascertained by
a matter of simple calculation
12. "Numerical" Definition. Intervals, (which are always
reckoned upwards unless the contrary be specified), are calculated
"numerically" according to the number of notes of different alpha-
betical names included in the interval. In all such calculations both of
the notes which form the interval are counted. Thus in Ex. 10 (a),
both intervals are fourths because there are four different alphabetical
names, C, D, E, and F, included in each interval while in (6), both
;

intervals are fifths because each includes five different names, C, D, E r

F, and G.
Ex. 10.
() W

Although upon all keyboard instruments the notes of the second fourth
and the second fifth are identical, yet for theoretical purposes it is
necessary that intervals should always be defined according to the manner
in which they are represented in musical notation. Speaking then,
"
numerically," C to F sharp is a fourth, and C to G flat a fifth, in spite
of the fact that upon some musical instruments the notes represented
and the sound produced would be exactly the same in both cases.
13. "Qualitative" Definition. In determining the "quality"
of an interval, the intervals between the Key-note of the Major scale and
the several notes of that scale, counted upwards from the Key-note,
 CHAP. III. INTERVALS.

furnish the basis of calculation. All the intervals thus formed are
either Perfect intervals, or Major intervals, as is shown in Ex. 1 1 :

Ex.
-----
ii.

PERFECT. - Unison. - - - - - Octave.

4th. 5th.

MAJOR. - 2nd. - - - - 6th. - 7th.

3rd.

When either Perfect intervals or Major intervals are enlarged by the

addition of a semitone, they become Augmented intervals, as will
be seen by reference to Ex. 12. When Perfect intervals are reduced
by the interval of a semitone they become Diminished intervals, but
when Major intervals are reduced by the interval of a semitone they
become Minor intervals, which Minor intervals being further reduced
by a semitone become Diminished. A Diminished fifth is frequently
" " " "
called an Imperfect fifth, but the term Imperfect is not
similarly
used as an alternative in connection with either the fourth or the octave.
Ex. 12 illustrates the various modifications which intervals undergo:

Ex. 12.
Dim. Perf. Aug. Dim. Minor. Major. Aug.
Unison. Second.

Fourth.

I
,,
H SI
i
<^5
*-*s 1
m$<=3 ri
'{f

Octave.

14. Classification of Intervals. Intervals may be classified

in three different ways (i) as Consonant or Dissonant, (2) as Diatonic
:

or Chromatic, and (3) as Simple or Compound,

15. Consonant and Dissonant Intervals. A Consonant
interval an interval which produces a more or less complete and
is

satisfactory musical effect when heard by itself, as the Perfect fifth (a)
shown below while a Dissonant interval is one which produces an
;

incomplete musical effect when heard by itself, as the Minor seventh

shown at (b).

(a) (i>)
 10 HARMONY.

The CONSONANT INTERVALS comprise all the Perfect intervals (perfect

fourth, perfect fifth perfect octave) and the major and minor thirds
and
and sixths. The Perfect intervals are called Perfect consonances because
x

they cannot be altered in any direction (that is by augmentation or

diminution) without becoming dissonant. The thirds and sixths are
called Imperfect consonances because they have two forms, major and
minor, in both of which they are consonant. The DISSONANT
INTERVALS comprise the major and minor seconds and sevenths and
allAugmented and Diminished intervals.
1 6. Diatonic and Chromatic Intervals. All those intervals
which are found between the notes of the Major scale, or between
the notes of either of the forms of the Minor scale, are described as
Diatonic ; while those intervals which can only be found between the
notes of the Chromatic scale are described as Chromatic. An examination
of the intervals formed between the notes of the Harmonic Minor
scale, see Ex. 13, will show that such intervals as the Augmented second,
the Diminished fourth, the Augmented fifth and the Diminished seventh,
although when used in a major key involve the employment of chromatic
notes, yet under this general form of classification are correctly
described as Diatonic intervals :

Ex. 13.
Dim. 7th. Aug. 2nd.

Dim. 4th. Aug. 5th.

The semitone (the smallest interval employed in music)

interval of the
'
is found Diatonic and Chromatic scales.
in both The Diatonic
semitone, however, is represented by the employment of two notes of
different alphabetical names, as in Ex. 14 (a), while the Chromatic
semitone is represented by the employment of two notes having the
same alphabetical name, one note being inflected by an accidental,
as in (b) :

Ex. 14.
(a) (b)

Of the intervals which are described as Chromatic the most familiar are
the Augmented sixth and the Diminished third.
17. Simple and Compound Intervals. A Simple interval
is one which does not exceed an octave, while a
Compound interval is
larger than an octave, and is made up of an octave added to another
interval. The following interval may be described either as a
major tenth, or as a Compound major third, because it consists of a
major third added to an octave :
 CHAP. III. INTERVALS. 1 I

Intervals of the Ninth, Eleventh and Thirteenth, when forming part

of the chords bearing these names, must be described as Ninths,
Elevenths and Thirteenths, not as Compound seconds, fourths and
sixths.

It is difficult to discover what value this form of classification

possesses, but while
questions referring to it are occasionally to be met with in examination papers, the
prospective examinee should bear it in mind.

1 8. Inversion of Intervals. To "invert" an interval means to

change the relative position of the two notes which form the interval,
by placing the lower note above the higher, or the higher note below
the lower. If the interval does not exceed an octave, it may be inverted

by either note being suitably transposed one octave, as in Ex. 15 (a),

but if the interval exceeds an octave, the note must be transposed two
octaves as in (b).
Ex. 15.
Interval. Inversion. Interval. Inversion.
-*>-
() (b)

In connection with the inversion of intervals, the- chief points to be

noted are: (i) that the numerical value of an interval added to that
of its inversion, together, make 9, therefore, if we subtract the
numerical value of any interval from 9 we obtain the numerical value
of its inversion thus, the inversion of a unison is an octave, the
inversion of a second is a seventh, of a third, a sixth, of a fourth, a
fifth, and so on ; (2) that the inversion of a Perfect interval produces
a Perfect interval; (3) that the inversion of a Major interval produces
a Minor interval, and the inversion of a Minor interval produces a
Major interval; (4) that the inversion of an Augmented interval
produces a Diminished interval, and the inversion of a Diminished
interval produces an Augmented interval ; (5) that the inversion of a
Consonant interval produces a Consonant interval, and the inversion of
a Dissonant Ex. 16, which shows the
interval a Dissonant one.
inversion of intervals not exceeding an
octave, illustrates all these
points. The two intervals shown in each bar, the one above and the
other below, are inversions of one another.
Ex. 16.
Octave. - - - Perfect. - Diminished.

Unison.
iHii
- - Perfect. - -
Augmented.

Seventh. - - - - - - - Minor.
Major.

-&-
Second. - - Minor. - - - - - - -
Major. Augmented.
 Third. - Diminished. - - Minor. - - - -
Major.

- - - - Perfect. - -
'

- Diminished.
Fifth. Augmented.

*=>=
Fourth. - Diminished. - Perfect. - - Augmented.

EXERCISES.
i. Write above each of the following notes a Perfect fourth, a
Perfectfifth, a Major second, a Major third, a Major sixth and a
Major seventh :

2. Write above each of the notes given in the previous exercise,

Diminished and Augmented fourths, fifths and octaves, Minor and
Diminished thirds and sevenths, and Minor and Augmented seconds
and sixths.

3 Write above G sharp in the Treble clef all the Perfect

consonances, and above G flat in the Bass clef all the Imperfect
consonances.
4. Write above middle C all the Diatonic intervals, and classify
them as Consonant and Dissonant.
5. Write above and below each of the notes given in Ex. i a
Chromatic semitone and a Diatonic semitone.
6. Describe the following intervals and classify them as Diatonic
and Chromatic :

^ frg3
frre
I

\fZ
jtcr

7. Invert the intervals given above, describe the intervals produced

by the inversion, and classify these inversions as Diatonic and
Chromatic.
 CHAP. IV. THE TONIC TRIAD.

CHAPTER IV.

THE TONIC TRIAD (MAJOR KEY).

19. The complete chord is made up of three different

simplest
notes, and formed by adding to any note two others, situated
is

respectively a third and a fifth from it, counting upwards, thus :

Ex.17. |3*=
=r?5zgEEEB

The chord thus produced is called a TRIAD. The note from which the
intervals are reckoned, that is, the lowest note, is Root of the
called the
triad,and the chord is named after this root. The chord shown above
is therefore a triad on C. A
diatonic triad may be constructed upon
every degree of the major scale, but the most important triad is that
upon the Tonic or key-note. The above triad is the Tonic Triad in the
key of C major.
20. Triads and Common
Chords. Triads are of various
kinds according to the of the intervals of which they are
nature
composed. Those which the fifth is a perfect fifth are
triads in

generally called COMMON CHORDS, and according as the third from the
root is either a major third or a minor third, they are called Major or
Minor Common Chords respectively. The Tonic Triad in every major
key may therefore be described as a Major Common Chord, because
the third note and the fifth note in every major scale are respectively a
major trjird and a perfect fifth from the Tonic or key-note.
21. Four-part Harmony. In Harmony each note of a chord
represents what is called
"
a part." A part is that which is allotted to
a single voice -in a vocal composition, or to a single instrument in a
composition for several instruments (such as a string quartett).
Harmony may be written in two parts, in three parts, or in any number
of parts up to eight, or even more. For all ordinary purposes, however,
the most useful and convenient number of parts is four, and THIS
BOOK DEALS ENTIRELY WITH FOUR-PART HARMONY. These four parts
will be treated as voice parts, their compass or range corresponding

respectively to the compass of the Soprano, Alto, Tenor and Bass voices.
This may be taken approximately as follows :

Ex. 18.

SOPRANO. ALTO. TENOR. BASS.

 HARMONY.

Music for these four parts or voices may either be written upon the
ordinary Treble and Bass staves, as in Ex. 19, or each part may be
written upon a separate staff with the proper clef belonging to that
particular voice, as in Ex. 20. In Ex. 19 the parts would be described
as being written in "short score," and in Ex. 20 as in "open score."
How far the pupil can advantageously employ "open score" when
working the various exercises which follow must be decided by the
teacher.
Ex. 20.
Ex. 19.
SOPRANO.
SOPRANO.
G clef on 2nd line.

ALTO.
ALTO.
C clef on 3rd line.

TENOR.
TENOR.
BASS. C clef on 4th line.

HASS.
F clef on 4th line.

22. The Doubling of Notes. In four-part harmony, when

dealing with Triads and Common chords, it is necessary, in order to
make up the four parts, that one of the notes of the chord should be
sounded in two of the parts simultaneously, or in other words should be
"'
doubled." Which notes may be doubled depends upon the nature of
the chord. In that under consideration, the Tonic Common Chord in
the major key, and generally in all major common chords, the best
note to double is the root, as in Ex. 21 (a\ after that comes the fifth,
as in (b). The third (major) should rarely be doubled, but when it is

doubled one of the best distributions of the several notes of the chord
is shown at
(c).
It is always possible in a common chord to omit the

fifth, and supply the omission by doubling the root twice, as at (d),
but the omission of the third, as at (e], is not allowed.

Ex. 21.

In all the above chords, the note doubled is always sounded in different
octaves, but a note may also be doubled by both parts sounding it at
the same pitch, that is, by it being "doubled in the unison." If such a
note be a semibreve, this doubling is shown by two semibreves being
made to overlap one another, as in the Tenor and Bass parts in Ex. 22
(a), while in the case of notes other than semibreves, the doubling is
 CHAP. IV. THE TONIC TRIAD.

shown by the employment of two stems turned in opposite directions,

as in (b) :

Ex. 22.

If the above chords are sounded upon a keyboard instrument they

will only produce the effect of three-part Harmony, but this would
not be the case if theywere sung by voices. Although both the Tenor
and Bass voices would sing the same note, yet each would produce a
and their combined effect would amount to a
different musical effect,
distinct doubling of this note.

23. EAR EXERCISES: THE MAJOR COMMON CHORD WITH

THE ROOT DOUBLED. A
presentation of the chord in sound, in various
positions, to be written down by the pupil from dictation, the name of
the bass note onfy, being announced to him beforehand.

Ex. 23.

To the Teacher. Should the pupil find it difficult to discover the notes of which
"
the above chords are composed, they may in the first instance be "spread after the
manner of (a). When hearing them for the first time the pupil's attention should be
specially directed to the different musical effects of the chords ; first, according as the
root, the third, or the fifth is at the top, contrasting (a\, (b) and (c), and, secondly,
according as the several notes are situated closely together or in an extended
position, contrasting (a) with (d] and (b) with (<?). The chords in the above exercise
should be dictated in various orders, and not merely as they are given above.

THE MAJOR COMMON CHORD WITH THE FIFTH DOUBLED.

II
Ex. 24.

These < hords should be contrasted respectively with (c), (e) and (/) of Ex. 23, and
the attention of the pupil directed towards the difference in the musical effect which
is created by the doubling of another note in an inner part.
 HARMONY.

%* THE ABOVE EAR EXERCISES AND ALL WHICH FOLLOW THROUGHOUT THIS
BOOK SHOULD BE TRANSPOSED AND DICTATED IN OTHER KEYS, THE NAME OF
THE KEY BEING ANNOUNCED TO THE PUPIL BEFOREHAND. THEY SHOULD ALSO
BE SUPPLEMENTED BY OTHER SUITABLE EAR EXERCISES To BE SUPPLIED BY THE
TEACHER AS SUCH MAY BE REQUIRED.
24. The Distribution of Parts One of the chief difficulties
in theworking of the Exercises which follow this and subsequent
chapters, will be found in securing a good distribution of the notes of a
chord amongst the various vocal parts. These should as far as possible
be made equi-distant from one another, as in Ex. 25 (a). In any
progression of chords, however, it is only possible to obtain this to an
approximate degree. When an exceptionally large interval between
two of the parts is necessary it should always lie between the two lowest
parts, as at (), and not between two of the inner parts, as at (c), or two
of the upper parts, as at (d). In both (c) and (d) the distribution of
the parts is bad.
() (*) W (d)

Ex. 25.
m
=&=
Good. . . . Bad . . .

When the three upper notes of a chord are situated so that they do not
extend beyond the compass of an octave, as in Ex. 25 (), the chord is
"
said to be in close position," but when they extend beyond an octave,
"
as in the chord is said to be in extended position."
(a),

Although the "close position" and "extended position" of chords is referred to in

nearly every text hook upon Harmony, yet we have been unable to discover what
practical value this classification of the position of chords possesses.

25. The Overlapping of Parts. In any progression of chords,

when passing from one chord to the next, no part should proceed to a
higher note than the note in the first chord which belonged to a higher
part, as the Alto does in Ex. 26 (a), neither should any part proceed
to a lower note than the note in the first chord which belonged to a
lower part, as the Treble does in (b) :

()

Ex. 26.
*y -g-
Not good.
As in (a) the Alto note of thesecond chord is higher than the Treble
note of the first chord, and as in (b) the Treble note of the second
chord is lower than the Alto note of the first chord, these parts are said
"
to overlap." When such overlapping occurs between repetitions of
the same chord it is less objectionable than when it occurs between
different chords, but the pupil would do well in all his early work to
avoid it, except in those instances, hereinafter to be mentioned, in which
it is regarded as unobjectionable (see par. 40).
 CHAP. IV. THE TONIC TRIAD. I
7

26. The Crossing of Parts. When a part passes above a

higher part, as the Alto of the second chord in Ex. 27 (a) passes over
the Treble, or when a part passes under a lower part, as the Treble of
the second chord in (b) passes under the Alto, the parts are said " to
cross."

Ex. 27.
___
"
In the working of Harmony exercises in four parts, crossing of the
parts'" is not allowed. Only when some special musical effect is
required do composers ever cross their parts in four-part writing.
27. Mental Conception of Chords. When working the
Exercises in book, 'the pupil must always endeavour to realise
this

mentally the sound of every chord as he writes it down. At first, this

may require a considerable mental effort on his part, but by making it
a practice never to look at a chord written upon paper without trying
simultaneously to realise its musical effect, this habit will in time have
become so much part of his nature, that such mental conception will
eventually require no effort from him, and the sight of a chord
represented in notation will immediately create in his mind its sound.
In connection with this matter, it may be well also to add a word of
warning to pupils who are tempted to disregard the above suggestion
and to work the exercises in a purely non-musical and mechanical
manner, relying upon their knowledge of rules to avoid any bad errors.
In the early stages of Harmony, when only a few simple chords are under
consideration, it is possible to pursue such a course without revealing
one's entire ignorance of the sound of the chords, but the method
adopted in this book of employing as exercises, almost entirely
unfigured basses and melodies, will soon reveal the deficiencies of the
pupil, and unless he alters his method of study, and by systematic
ear-training develops his power of musical memory and musical thought
up to the level of the chords he is treating upon paper, all real musical
progress in Harmony will be at an end.
28. In the following Exercises the pupil must not forget that the
musical effect of the chords which he is endeavouring mentally to
revive will not be that which specially belongs to the Tonic Triad as a
Tonic chord but that which is the common property of every Major
Common Chord when heard in isolation. What we mean is this, the
special character of a Major Common Chord as a Tonic chord only
becomes evident when it is heard in connection with common chords
upon other degrees of the scale of which this is the Tonic. Its peculiar
function, which is to furnish an effect of final rest or satisfaction, can
neither be illustrated nor realised until common chords, which have a
totally different musical effect such as those upon the Dominant and
Subdominant are heard in contrast with it. Its consideration in
isolation has, however, enabled us to introduce in connection with it
various matters, which, while affecting all common chords, may, we
think, be made simpler by being studied in connection with only one.
i8 HARMDNY.

EXERCISES.
*** All these and similar Exercises are to be written in four Vocal parts,

i.Regard each of the following notes as the root of a Tonic

Common Chord, prefix to each the key-signature of the Major key, and
place over each a Major Common Chord, doubling the root :

- 1^^ -HH=||=
:::1L
-I
|
& II"T~~=II I

2.Regard the following notes (i) as roots, (2) as thirds, and

(3) as fifths, ofTonic Common Chords, prefix in each case the key-
signature of the Major key, and place under each a Major Common
Chord, doubling the root :

3. Regard the following notes as fifths of Tonic Common Chords,

prefix to each the key-signature of the Major key, and place under each
a Major Common Chord, doubling the fifth :

4.Harmonize each note of the following Exercises with the Tonic

Common Chord of the Major key indicated by the key -signature,
treating (a) as Bass parts, (b) as Treble parts, (c) as Alto parts, and
as Tenor parts. Either the root or the fifth may be doubled :

a
__ (b) ,

J .

I J ,

* In
these, and in all Bass parts given to be harmonized, in which the same note is
repeated, the upper parts should not necessarily be repeated in a similar manner. As
a general rule the Soprano, and one of the inner parts, should move to other notes of
the chord.
 CHAP. V. THE DOMINANT TRIAD.

CHAPTER V.

THE DOMINANT TRIAD (MAJOR KEY).

29. After the Tonic triad, the next in importance is the triad upon
the Dominant or fifth degree of the scale.

Ex. 28.

This, like the Tonic triad, is a Major Common Chord. The third of
the Dominant triad being the Leading-Note, this chord is one of
exceptional value for defining the key, especially when it is followed
by the Tonic common chord, as in the first Ear Exercise. In such
cases the Leading-Note, which may never be doubled (except under the
special conditions mentioned in Chap. XVIII on Sequences), almost
invariably rises a step to the Tonic.

30. EAR EXERCISES UPON THE TONIC AND DOMINANT

TRIADS :

Ex. 29.
1
I
e) <d

~ "

fl Vjrl
_2 .Ju
"i r* ii -^-4 ..J- j
F-> CII

The above Exercises may also be dictated in a similar form to that of the first one,
where the first chord (the Tonic Triad) is repeated again as the third and final
chord.

31. The Mental Effect of the Dominant Common

Chord. As the Tonic common chord tends to produce a feeling of
rest,so the Dominant chord tends to produce one of unrest, and when
occurring as the penultimate chord of a musical composition, requires
to be followed by the Tonic chord, in order that a feeling of satisfaction
may be left upon the mind of the listener. If Ex. 30 be played over,
and a long pause be made at the rest, only when the final Tonic chord
is struck will that sense of finality and completeness, which must
characterize the end of a passage, be produced.
20 HARMONY.

fix. 30.

32. The Progression and Movement of Parts. In the

joining of different chords to form harmonic progressions, as is required
in the working of the exercises throughout this book, the progression or
movement of the several parts in connection with one another has to be
carefully considered. It is quite possible for two chords to produce

perfectly satisfactory musical effects when heard singly and in isolation,

yet when the same two chords are sounded one after the other in close
proximity, the progression of the one to the other may produce an
effect which, musically speaking, would be considered as bad. In order
that faulty progressions may be recognized and avoided by the pupil,
rules bearing upon them have been framed from time to time, and the
gaining of a knowledge of these and of their application to different
kinds of progressions, forms an important part of the study of Harmony.
These rules may be divided into two classes, first, those which refer to
the progression of any single part and are called the rules of MELODIC
PROGRESSION; and, secondly, those which refer to the progression of two
or more parts moving together, and are called the rules of HARMONIC
PROGRESSION. The various rules of progression (Melodic and Har-
monic), a knowledge of which is required for the working of the
exercises at the end of this chapter, will now be introduced. These
refer chiefly to Harmonic Progression, and they include many of the
most important rules of this class. The other rules of progression will
be introduced as the matters to which they specially refer come up,
for the first time, for consideration.
33 HARMONIC PROGRESSION -.Similar Motion,
Contrary Motion, and Oblique Motion. Any two parts
may move in one of three different ways with regard to one another.
First, they may both move in the same direction as the Soprano and
Alto parts move in the first two chords in Ex. 31. They are then said
to move in SIMILAR MOTION. Secondly, they may move in opposite
directions as the Tenor and Bass parts move in the same two chords.
They are then said to move in CONTRARY MOTION. Thirdly, one part
may remain stationary while the other part moves, as the Alto, taken
with either of the other parts, does, in the last two chords. In this
case, the motion is called OBLIQUE.

Ex. 31.
 CHAP. V. THE DOMINANT TRIAD. 21

34. The Motion between the Outside Parts. The only

parts,about the general motion of which the pupil need concern himself,
are the outside or extreme parts, that is, the Soprano and the Bass.
As a rule, Contrary Motion employed between these parts, produces
stronger progressions than either Similar Motion or Oblique Motion,
and it is therefore in many cases preferable to these. It is, however,

impossible without misleading the pupil, to further compare the effects

of the employment of different kinds of motion, because either form
may be introduced with the best effect by a skilful writer, or with a bad
effect by an unskilful one. In ordinary progressions it is not possible
to continue any one kind of motion for long, and the best effects are
generally produced by a judicious admixture of all three kinds. In
this, as in many other matters connected with Harmony, experience is
the only safe guide.

35. Hidden Octaves and Fifths between the Outside

Parts. When two parts move by Similar Motion to a Perfect octave
or a Perfect fifth, such octave or fifth is described as a Hidden octave
or a Hidden fifth, respectively. Hidden octaves and fifths when formed
either between two inner parts, or between one inner and one outside
part, are (with one important exception to be referred to later on)
unobjectionable, but as a general rule, hidden octaves and fifths
formed between the outside parts are not allowed. There are, however,
many exceptions to this rule, and these will be stated as a knowledge
of them is required for the correct working of the exercises. Two of
the most important of these exceptions will now follow :

(1) Provided the upper part moves by the step of a second, hidden
octaves and fifths between the Tonic and Dominant Triads are allowed,
see Ex. 32 (a) and (b), and
(2) Hidden octaves and fifths formed by a change in the position of
the same chord as at (c) are allowed.

Hidden octaves and fifths are sometimes described as " exposed "
octavesand fifths, and this term seems to supply a more accurate
"
description of their nature than the traditional one hidden."
Consecutive Unisons, Octaves and Fifths (Similar
36.
Motion). No two parts (whether outside parts or inner parts] may
move in similar motion, in perfect unisons, perfect octaves, or perfect fifths,
see Ex. 33 (a), (b), and (c). Such progressions are generally described
simply as consecutive unisons, consecutive octaves, and consecutive fifths
22 HARMONY.

respectively, and are strictly forbidden. Repetitions of the same notes,

forming between them either of these intervals as at (d) are, however,
perfectly correct :

Ex. 33.
(a) (b) (c) (d)

Bad. Bad. Bad. Good.

37. Consecutive Octaves and Fifths (Contrary Mo-

tion). Consecutive octaves and fifths when employed in contrary
motion, andalso the progression from a unison to an octave, or vice versa,
do not necessarily produce bad musical effects, and such progressions
are not strictly forbidden, but even when musically unobjectionable, as in
Ex. 34, their employment exhibits a freedom of progression which it should
be the prerogative of the advanced student rather than of the beginner
to employ, and in all the following exercises they should be avoided.

Ex. 34.

Not bad.

38 MELODIC PROGRESSION :
Conjunct and Dis-
junct Movement. In theframing of progressions composed
entirely of Tonic and Dominant Triads (as is required in the
immediately following exercises) the opportunities offered for the
construction of faulty melodic progressions are few, and, therefore, the
more important rules belonging to this class will not be introduced
till later, when the pupil's harmonic resources have been increased,
and with them his opportunities for framing incorrect parts. Although
there are no special rules of melodic progression which he is' likely to
infringe in the individual parts of the simple progressions he is now
about to construct, yet it is upon the general nature and flow of
these parts that the smooth movement of one chord to the next, so
desirable in such progressions, almost entirely depends. This smooth-
ness of progression is largely obtained by letting each note forming an
upper part of a chord move to the note in the next chord which is
nearest to it, provided such movement does not infringe any of the
rules ofharmonic progression already mentioned, see Ex. 35 (a). When
the movement is made by the step of the second, as in the Soprano of
Ex. 35, it is called Conjunct Movement, but when a. larger interval is
employed, as in the Bass of the same example, it is called Disjunct
 CHAP. V. THE DOMINANT TRIAD.

Movement. if a note is common to two or

In progressions of chords,
more adjacent chords, the which this note appears should remain
part in
stationary, that is, the note should be repeated, as in the Alto of (a).
In the following examples where the Bass part is assumed as given to be
harmonized, the smoothness of the progression in (a) is unmistakable,
and on that ground alone would make the arrangement of the parts in
(a) preferable to that given in (b) :

(a) (6)

Ex. 35.

Good.
Progression of the Leading-Note, and Omission
39.
of the Fifth in a Tonic Common Chord. In progressions
in which the Tonic Triad is preceded by the Dominant Triad, and
the Soprano part is formed by the fifth of the Dominant (the Supertonic)
falling to the Tonic, as in Ex. 36 (a\ (b\ in order that the Leading-
note may rise to the Tonic, the fifth of the Tonic chord is generally
omitted and the root doubled twice, as in Ex. 36 (a). It is, however,
not incorrect, although less usual, for the Leading-note to fall a third to
the fifth of the Tonic chord, as in (b). The pupil as a general rule should
make all his Leading-notes rise, unless they occur in a descending scale
passage, or in a repetition of the same chord, as in (c).

Ex. 36.

f
40. Allowable Overlapping of Parts. In progressions
formed of Tonic and Dominant Triads, when the root is doubled in
the unison to represent both the Tenor and the Bass parts, as in Ex. 37,
the overlapping of parts caused by the root of the Tonic chord
proceeding to the root and third of the Dominant chord, or vice-versa,
as shown below, is unobjectionable.

Ex. 37.

Good.
24 HARMONY.

41. The Harmonization of Basses and Melodies. In

the working of the Exercises the following points should be borne in
mind :

Every Exercise must end with the Tonic chord.

(i). The large
majority of Exercises also begin with the Tonic chord, but a few later
on will be found to begin with the Dominant chord.
(2). In the
construction of a melody over a given Bass part, the first
note of the melody may be either of the notes of the first chord, but
the last note of the melody should generally be the Tonic itself. A
melody may however end upon the Mediant (the third of the Tonic
chord), but it should not end upon the Dominant (the fifth of the Tonic
chord).
(3). outside parts should, if possible, move in contrary motion,
The
and admit of this a melody (or bass) which begins upon a
in order to

high note and proceeds generally in a downward direction, should be

harmonized with a bass part (or melody) which begins upon a low note
and proceeds generally an upward direction, and vice versa.
in

(4). The fifth of a common

chord may be omitted and the root
doubled twice, whenever the progression of the parts can thereby be
improved.

EXERCISES.

Harmonize the following Bass parts and Treble parts with Tonic and
Dominant Common chords :

"

III .

VI
 CHAP. VI. THE SUBDOMINANT TRIAD.

CHAPTER VI.

THE SUBDOMINANT TRIAD (MAJOR KEY).

42. After the Tonic and Dominant Triads, the next importance ism
the Triad upon the Subdominant or fourth degree of the scale, which
is also a Major Common Chord. r

Ex. 38.
|i

EAR EXERCISES UPON THE TONIC AND SUBDOMINANT

TRIADS :

Ex. 39.

Each of the above progressions may also be dictated in a similar form to that of the
one.
first After the pupil has become somewhat familiar with the sound of them,
they should be contrasted in sound with the corresponding progressions formed by the
Tonic and Dominant Triads, par. 30.

43. Hidden Octaves and Fifths. As in progressions of Tonic

and Dominant Triads, so in progressions of Tonic and Subdominant
Triads, hidden octaves and fifths are freely allowed between the outside
parts, provided the upper part moves Dy the step of a second as in
Ex. 40.

Ex. 40.

Good.
For the working of the following Exercises, with the above exception,
no further rules of progression are required, beyond those which have
already been given in the previous chapters, and which apply to all
chords except where it is otherwise stated.
 26 HARMONY.

EXERCISES.
Harmonize the following Bass parts and Treble parts with Tonic and
Subdominant Common Chords :

s
mn 7 '

r r

..ft r
&=fft=&=*=
! I

^==
 CHAP. VII. THE THREE PRIMARY TRIADS.

CHAPTER VII.

THE THREE PRIMARY TRIADS (MAJOR KEY).

44. The three Triads which we have now considered, the Tonic
Triad, the Dominant Triad, and the Subdominant Triad, are the only
major triads or major common chords which can be formed from the
notes of the major scale, and they are called the PRIMARY TRIADS of
the key. They are so-called because of their great importance in
denning the key, the notes of which they are formed including every
note in the scale, and a knowledge of them therefore supplies the
pupil with sufficient harmonic resources to harmonize the complete
major scale, thus :

Ex. 41.

45. The Selection of Chords in the Harmonization of

Melodies. The above harmonization of the several notes of the scale
is the only possible one with these three triads, when the notes of the

scale are employed in a regular and continuous progression, either

ascending or descending, but in suitable melodic progressions it is also
possible to harmonize the note C the Tonic with the Subdominant
Triad as Ex. 42 (a), and the note G the Dominant with the
Dominant Triad as in (b), instead of harmonizing them with the Tonic
Triad as in the above example :

Ex. 42.

In many of the melodies for harmonization given at the end of this

chapter a choice of two chords will frequently be possible in harmonizing
'the Tonic and the Dominant. In such cases the pupil will have to
23 HARMONY.

decide which is the more suitable chord to employ, and he will only be
able to do so with certainty and success if he can create in his mind the
musical effect which either chord would produce in each particular
instance.

46. EAR EXERCISES:

Ex. 43.

Strictly speaking, the only new feature presented by the employment of

these three triads, is the progression formed by the Subdominant Triad
proceeding to the Dominant Triad, and vice versa, the Dominant Triad
proceeding to the Subdominant Triad. The former of these progressions,
the Subdominant Triad to the Dominant Triad, is a far more useful
and satisfactory progression than the latter, the Dominant Triad to the
Subdominant Triad. This latter must be employed with great care,
otherwise a harsh and unmusical effect will be produced. A good
arrangement of the several notes of the chords is shown in the fourth
Ear Exercise given above. If the progressions formed of these two
chords are to be made correctly, several new and important rules of
Melodic Progression must now be stated.

47. MELODIC PROGRESSION :

Augmented Inter-
vals in Melody. No
part may proceed by an Augmented interval
unless both of the notes forming the interval belong to the same chord.
The only Augmented interval with which we are at present concerned
is the Augmented fourth, formed between the Subdominant and the

Leading-note of the Major scale, reckoned upwards. In the key of C

this would be as follows :

Ex. 44.

These two notes, when forming this interval, may not follow one another
in any part, unless they are both harmonized by the same chord. As
at present they can only be harmonized by two different chords, the
Subdominant by the Subdominant Triad, and the Leading-note by the
Dominant Triad their employment as adjacent notes, so as to form this
;

interval, is strictly forbidden.

48. Diminished Intervals in Melody. When a part

proceeds by a Diminished interval, it must immediately return to a
note
within that interval. The only diminished interval with which we are
at present concerned is the Diminished fifth which lies between the
 CHAP. VII. THE THREE PRIMARY TRIADS.

Leading-note and the Subdominant of the scale, reckoned upwards.

This Diminished fifth is the inversion of the Augmented fourth
mentioned in the previous paragraph. Whenever the two notes which
form this fifth are employed in a part as adjacent notes, the note
which follows must be a note lying within their compass, thus :

Ex. 45.

Good. Not good.

49. Large Intervals in Melody. When an interval larger

than a sixth employed in any part, it should be approached and quitted
is
in the opposite direction to which the leap is made, thus :

Ex. 46.

Good. Not good.

A part should not proceed by the interval of a seventh unless both of the
notes forming the interval belong to the same chord* Until the chord
of the seventh is reached it is therefore not possible to employ the
interval of the seventh between adjacent notes. In connection with
triads, this interval should only be employed in any part when there
are not less than two notes between those forming the seventh, unless
there be a leap of an octave as in (b). Such a Bass part as shown in (a)
must be carefully avoided :

(a)

Not good. Good.

50. Progression of the Subdominant Triad to the

Dominant Triad. When proceeding from the Subdominant Triad
to the Dominant Triad and be required in
vice versa, special care will
order to avoid consecutive octaves and fifths being formed between the
two triads, as in Ex. 48 (a). In progressions of these two chords, the
parts which in the first chord contain the fifth and the octave of the
Root must move in contrary motion to the Bass, as in (b). The hidden
fifth, as illustrated in (<:), is of course incorrect.

Ex. 48.

- Bad. Good. Bad.

* An exception to this rule sometimes occurs in the Minor key in connection with
the Diminished Seventh (see par. 71).
 HARMONY.

'51. Final Cadences. The last two chords in a piece of music

form what is called the CLOSE or FINAL CADENCE, the second of the two
chords being always the Tonic Common Chord in its root position.
Although only three different triads have been considered, yet two of
the most important "final cadences" may be formed from these.
Thus, if the Tonic Triad be preceded by the Dominant Triad to form
the concluding chords, an Authentic or Perfect Cadence is formed, while
if the Tonic Triad be preceded
by the Subdominant Triad, a Plagal
Cadence is formed. Of the Ear Exercises in Ex. 43, the first three end
with Perfect Cadences and the last with a Plagal Cadence.
52. Ear Exercises. The teacher should test the pupil's power
of discriminating these different forms of cadence by playing such in
various keys.

EXERCISES.
Harmonize the following Basses and Melodies employing the three
Primary Triads :

I.

ik S
LO

^
^=r^-^=B
 CHAP. VIII. THE PRIMARY TRIADS (MINOR KEY)

CHAPTER VIII.

THE THREE PRIMARY TRIADS (MINOR KEY).

53. As in the major key, the Primary Triads in the minor key are
those formed upon the Tonic, the Dominant and the Subdominant,
and we shall consider them in the same order as we did in the
major key.
54. The TONIC TRIAD in the Minor key is made up
of a Minor third and a Perfect fifth from the root, as shown below,
and is therefore a Minor Common Chord (see par. 20) :

In this chord the best note to double is the root, but in this and in all

Minor Common Chords, either the third or the fifth may be doubled
instead of the root, if desired.

55. Ear Exercises :

THE MINOR COMMON CHORD WITH THE ROOT DOUBLED.

Ex. 49.

WITH THE FIFTH DOUBLED. WITH THE THIRD DOUBLED.

The above chords should be severally contrasted in sound with corresponding major
common chords (par. 23), so that the pupil may learn to recognise, readily, either
major or minor chords by their sound.

56. The "Tierce de Picardie." In former times it was the

custom to bring a composition in a Minor key to a close, by employing
as the final chord, the Major Common Chord upon the key-note, instead
32 HARMONY

of the Minor Common

Chord, which Major chord was called the
"^Titrcc de Picardie"This practice is not a common one amongst
modern composers, and it is now almost entirely confined to church
music.

57. The DOMINANT TRIAD in the Minor key is

composed of exactly the same notes as that in the major key and is

therefore a Maior Common Chord.

Ex. 50.

As the third of the Dominant Triad is the Leading-note, it must always

be modified by an accidental in a similar manner to the Leading-note
of the key to which it belongs. The conditions as to the doubling of
the notes of the Dominant Triad in the Minor key are the same as
those which apply to the notes of the Dominant chord in the Major
key. The root is the best note to double. The third may never be
doubled.

58. Ear Exercises UPON THE TONIC AND DOMINANT TRIADS.

Before proceeding to the following Exercises, the Ear Exercises upon
the same chords in the Major key (Ex. 29) should be transposed and
dictated in the key of C minor, and also in other Minor keys :

Ex. 51.

59. Melodic Progression. In progressions of these two triads

in the Minor
key, the formation, in the same part, of the interval of an
Augmented fifth or of its inversion, the Diminished fourth, becomes
possible, The Augmented fifth, which is formed between the third of
the Tonic chord and the third of the Dominant chord, Ex. 52 (a\ must
be avoided altogether. When the Diminished fourth (the inversion of
the same notes)occurs, the next note in that part must return to a
note within the fourth, as in (b\ and not proceed to a note outside the
interval, as in (c) :

Ex. 52.
(*) W)
td*
fe
Bad. Good. Bad.

As in the Major key, the Leading-note almost invariably rises a step to

the Tonic.
 CHAP. VIII. THE PRIMARY TRIADS (MINOR KEY). 33

EXERCISES.
Harmonize the following with Tonic and Dominant Common
Chords :

*.
I.
&
II.
2* - m
III.
:|^ 3
^ ^
te
 HARMONY.

6i. The THREE PRIMARY TRIADS in the Minor

Key.
Ear Exercises:
Ex. 55-

The chief difficulties presented by the employment in the Minor key

of the three Primary Triads are those of melodic progression. In addi-
tion to the Augmented fourth formed between the Subdominant and
Leading-note, Ex. 56 (a) (as in the Major key), there are two other
Augmented intervals which can be formed by the progression of the
Subdominant Triad to the Dominant Triad. One is the Augmented
second between the sixth and seventh degrees of the Harmonic Minor
Scale, shown at (^), and the other is the Augmented fourth between
the sixth degree and the second degree of the same scale, reckoning
upwards as shown at (c) :

Ex. 56.
() (*) )

Bad. Bad. Bad.

At the present stage of advancement all such melodic progressions must

be carefully avoided.

EXERCISES.
Harmonize the following, employing the three Primary Triads :

VII.

VIII

'

' g=^=^~1 I
'

I
T
m$
 CHAP. IX, THE PRIMARY TRIADS IN THEIR FIRST INVERSION. 35

CHAPTER IX.

THE PRIMARY TRIADS IN THEIR FIRST INVERSION.

62. Common Chords and their Inversions. A common

chord which is heard with
root as the lowest note is said to be in its
its

original position or its root position. All the chords we have hitherto
considered have been heard, only in their root position. When,
however, the notes of a chord are so arranged that the root is not
sounded as the lowest note but appears only in the upper parts, the
chord is said to be in an inverted form, or merely an inversion. Thus,
in the following example the first chord is the common chord of C in
its original or root
position, while the second and third chords are
inversions of it :

() (*) W
Ex. 57- &==; Ill
A chord has the same number of inversions as the number of
notes which make up the chord, omitting the root, and they are
generally described as first inversion, second inversion, and so on,
according to the position of their bass note in the original position of
the chord. Thus, the first inversion is that which has the third of the
original chord as its bass note, as in Ex. 57 (b), and the second inversion
is that which has the fifth of the
original chord as its bass note, as in (c).

63. The TONIC and DOMINANT TRIADS First

Inversion.
Ear Exercises:
Ex. 58. .

r '

i i \

The above Ear Exercises should be transposed into the key of

C minor, and dictated in that key as well as in the Major key.
 HARMONY.

64 The Mental Effect of Triads in their First

Inversion. The upon the mind by the first inversion of a
effect left
triad, compared with the effect of the same triad heard in its original
position, is one of much less strength and firmness. Whilst retaining
its own special musical character (that is, as a Tonic, Dominant,
Subdominant, or whatever chord it may be) that character is less
strongly defined. Yet it is because of the existence of such differences
of musical effect between the root position and the inversions of a
triad, thatwe are able by a judicious employment of different positions
of the same chord to obtain a varied and pleasing harmonization of a
melody without too frequently changing the chord. The two harmoni-
zations of the same phrase, shown in Ex. 59, will illustrate this point.
In (a) the effect is one of strength but also of monotony, the chords
being in their strongest position upon both the strong and the weak
beats of the bar. In (b) the variety and interest of the musical effect
has been largely increased by the employment of first inversions upon
the weaker beats of the bar :

Ear Exercises:
(a) (*)
L_
=^^=E!SlE3E^
=F=F=r^^ =y
^-F=FE^
Ex. 59.
J.J..J.
r-t
c=* :t:

It must not be inferred from this that the inversions of triads are always
most effective when employed upon the weak beats of a bar. and the
root position of triads when employed upon the strong beats. No
general rule of this kind is possible, for it is quite easy to give examples
in which such would not be the case. The only guides to an effective
employment of the different positions of a chord are, first, a knowledge
of their respective musical effects, and, secondly, the experience gained
by the framing of many progressions in which such are included.
65. The
Doubling of Notes. In the first inversion of common
chords, the same notes may be doubled as in the original position. In
both major and minor common chords, therefore, either the root mav
be doubled, as in Ex 60 (a) and (<:), or the fifth from the root, as in
(k) and (d). These in a first inversion are the sixth and the third from
the bass note respectively. In the first inversion of a minor common
chord, the bass note, the third of the chord in its original position
may also be doubled, as in (<?)
:

(a)

Ex. 60,

Root C
 CHAP. IX. THE PRIMARY TRIADS IN THEIR FIRST INVERSION. 37

66. The Figuring of Chords: Figured Basses. In the

study of Harmony a method of indicating the various chords in a more
concise manner than by writing them in full upon a staff, is frequently
a great convenience, if not an absolute necessity. For this purpose a
system has been gradually built up, by which the notes of a chord may
be indicated by figures placed one above another, under the bass note
of the chord, showing numerically the intervals at which the several
notes of the chord are distant from this bass note. A bass part under
which the chords by which it is to be harmonised are indicated in this
manner, is called a Figured Bass. In Figured Basses, notes which are
to be harmonized by triads in their original position are left unfigured.
The only exception to this rule is when either of the notes of a triad

require an accidental, as, for instance, the third of the Dominant chord
in the Minor key. In such cases a i,,fe whichever is necessary
orjj,
to effect the required change, should be placed under the bass note, as
in Ex. 6 1. This means that the third of the triad upon this note is to
be modified in accordance with the accidental.

Ex. 61.

When it is required to modify any other interval, an accidental

indicating the nature of the inflection must be placed before the figure
representing the note to be inflected, as 12 5 or \ 6, which mean
respectively, that the fifth from the bass should be flattened, or the sixth
from the bass sharpened. A line drawn through a figure, thus 0,
indicates that the note represented by the figure is to be raised a
semitone. The first inversion of triads, having a third and a sixth from
the bass note, would if completely figured be represented by J, this
however is abbreviated to 6, the 3 being implied, as illustrated in Ex. 62,
and these chords are frequently described as "chords of the sixth."

Ex. 62.

The figuring of the various chords, where this requires further

explanation, will be considered as each chord is introduced for study.
38 HARMONY.

EXERCISES.
%* AND IN ALL SIMILAR EXERCISES WHICH FOLLOW, THE PUPIL
IN THESE,
SHOULD, AFTER HE HAS WORKED AN EXERCISE, FIGURE THE BASS IN ACCORDANCE
WITH THE CHORDS (ROOT POSITION OR INVERSION) WHICH HE HAS EMPLOYED. HE
SHOULD ALSO WRITE THE R.OOT OF EACH CHORD UPON A SEPARATE STAFF (UNDER
THE BASS STAFF), LEFT BLANK FOR THIS SPECIAL PURPOSE.
Harmonize the following, employing Tonic and Dominant Triads in
their root position and first inversion :

ii.

ig^gpas
i

td*

*_=
iv. >:!

67.The SUBDOMINANT TRIAD. First Inversion.

Ear Exercises:
Ex. 63.
_L
I I
, J
4-J-

f
J-J-J-. ^-J-J-J-
==rJttzfac: *z
H E=f

*-* To be dictated also in C minor.

EXERCISES.
Harmonize the following, employing Tonic and Subdominant Triads
in their root position and first inversion :

SE
 CHAP. IX. THE PRIMARY TRIADS IN THEIR FIRST INVERSION. 39

68 The THREE PRIMARY TRIADS. First In-

version.

Ear Exercises:
Ex. 64.

U-*=g=?=*=q=Q::
=fE*^to^3E^E
r-r-TT
(Also in C minor).

69. The Doubling of Notes in Chords of the Sixth.

In progressions of chords of the sixth upon adjacent bass notes, as
illustrated by the progression of the first inversion of the Subdominant
Triad to the first inversion of the Dominant Triad, care must be taken
to avoid the formation of such consecutive fifths or octaves between
the upper parts as are shown in Ex. 65 (a). Thus, when the fifth
of the original chord is placed above the root, as in the treble and
alto of the first chord of (a), the parts containing these notes must not
move conjunctly to the fifth and root of the next chord respectively,
otherwise consecutive fifths will be formed; neither must the corres-
ponding note in both chords (the fifth or the root), be doubled in the
same parts, as in the Treble and Tenor of (a), otherwise consecutive
octaves will be formed. Such incorrect progressions may be avoided
by doubling different notes in each chord, that is, the root in one
chord and the fifth in the other, as in (), and also by the employment
of contrary motion, as in (c) :

(a)

Ex. 65.

^=r=fMW=F=M=
70. The Doubling of the Third in Major Common
Chords. Although as a general rule the third of a Major Common
Chord should not be doubled (whether such chord be in its Root
position or in an inverted form), yet such doubling is allowed provided
both notes are approached and quitted by step in opposite directions,
as is the third of the Subdominant Triad in Ex. 66.
 HARMONY.

Ex. 66.

Good

71. The Minor Seventh in the Minor key as a Bass

note. In the minor key the progression of the first inversion of the
Dominant Triad to either the first inversion of the Subdominant Triad,
or the root position of the Submediant Triad (or vice versa\ is inad-
missible, because of the interval of the Augmented Second which would
be formed between the two bass notes thus :

Ex. 67.

In order to avoid this interval, when the bass part descends stepwise
from the Tonic to the Submediant, the descending form^oTthe Melodic
Minor Scale may be employed, that is, the Minor Seventh (B flat in the
key of C minor) may be substituted for the Major Seventh (B natural)
and like that note, harmonized with a 3 chord, as in Ex. 68.

Ear Exercise:

Ex. 68.

The Minor Seventh is available as a bass note only in passages which

descend from the Tonic to the Submediant. It is not available in cor-

responding passages which ascend. A chord upon the Leading-note

sometimes follows one upon the Submediant by the bass leaping a
Diminished Seventh downwards as in Ex. 69, but such a progression
should not be employed at this early stage.

Ear Exerciser-

Ex. 69.
 CHAP. IX. THE PRIMARY TRIADS IN THEIR FIRST INVERSION. 41

EXERCISES.
Harmonize the following, employing the three Primary Triads in their
root position and first inversion :

VII.

ix. be

X.

In the following Exercises the "chord of the sixth" upon the Minor
Seventh of the scale is to be introduced at each of the places indicated *.

* -

-
,,..
42 HARMONY.

CHAPTER X.

THE SUBMEDIANT TRIAD.

73. There yet remain four diatonic triads to be considered, those

upon the Submediant, the Super tonic, the Mediant and the Leading-note.
To distinguish these from the Primary Triads, they are sometimes called
SECONDARY TRIADS. The most useful and familiar of the Secondary
Triads the Submediant Triad, which we shall consider next.
is

74. In
the Major key, the triad upon the Submediant, or sixth degree
of the scale, isaMinor Common Chord, see Ex. 70 (a). It is therefore
unlike other triads in that key which we have yet con-
eithe^olyftie
sidered, all having been Major Common Chords. In the Minor key, the
Submediant Triad is a Major Common Chord, see Ex. (b\

() (*)

Ex.70. bt==H=: 1:bfc=^= :

75. EAR EXERCISES (Root Position). In connection

with the study of the following Ear Exercises, the pupil, after endeavour-
ing to write down from dictation each series, should carefully read the
statement which follows, and which has been added for his guidance
when harmonizing the basses and melodies upon this chord. It will be
excellent practice for him to test the accuracy of these several statements,
by a further study of the same chords placed in a different order and
with the parts differently arranged :

Ex. 71.
(a)
<^/r^ ~m

~^=&a$^
I
^ : i II II __

f if ^ '
' rr

*** To be dictated also in C minor.

,-
;<

Progressions formed of the Submediant Triad and citktr bf the

I.

Primary Triads (or vice versa}, both chords being in their root position,
are almost invariably good. The least satisfactory is that formed by the
Submediant Triad proceeding to the Tonic Triad, thus :
 CHAP. X. THE SUBMEDIANT TRIAD.

I I

Ex. 72. I I

^~J J-
ry

Weak.

When either the Tonic Triad or the Subdominant Triad is followed

by the Submediant Triad, as indicated by the bass parts given in Ex. 73,
it better for the bass to leap a third, as in (), than a sixth, as in (&).
is
The leap of a sixth in a bass which is harmonized by triads in their root
position, frequently produces a weak effect :

(a)

J.J. j. j. ,
e . *.-. -f-.j-*.

( Also in C minor.) #

II. Progressions formed of the Submediant Triad in its root position,

and either of the Pritnary Triads in their first inversion, are mosth good.
Such progressions naturally lack the strength of the last mentioned ones,
in which chords in their root position only, were employed. This will be
specially noticeable in progressions formed of the Submediant Triad and
the first inversion of the Subdominant Triad, where both chords have the
same bass note. In and in most progressions of triads and their
this,
inversions where the t>ass note is repeated, it is better for the second
'chord to be upon a weaker beat (as in Ex. 75) or upon the weaker part of
aHBeat (as in Ex. 74*), than the first chord, and also for the treble part
to move, that is, not to repeat the same note.

Ex. 75.
 44 HARMONY.

76. The Harmonization of Basses and Melodies.

The introduction of the Submediant Triad, adds very considerably to
the pupil's harmonic resources in both major and minor keys. In the
Major key it brings within his range an entirely new element of contrast
in the form of a Minor Common Chord, and either of the three notes
of which it is composed, and which he has hitherto been compelled to
harmonize with a major chord, he is now able to harmonize with either
a major chord or a minor chord, as in Ex. 76 (a). In the Minor key it is
capable of similar employment, but with an opposite musical effect, for
it enables the pupil to harmonize either of its three n o tes, which have

hitherto been necessarily harmonized with a minor chord) with either a

minor chord or a major chord, as in (b) :

Ex. 76.
I

Major Triads. Minor Triad. Minor Triads. Major Triad.

"With increased resources however comes increased responsibility, for

as there are now two and sometimes three different chords, either of
which it may be possible to employ, to harmonize a note in a given
bass or melody, such harmonization requires a constant exercise of the
pupil's taste and judgment, in order that the most suitable chord may
be employed in each particular instance. This selection of suitable
chords will naturally tend to become more difficult, as the resources of
the pupil are enlarged, by the introduction to him of further new chords,
but, provided he memorizes the sound of each chord before he makes use of
in written exercises, and is able to hear, mentally, the musical effect
M\t Df what he is writing down, the difficulties of selection will gradually
I
disappear.

77. The Doubling of Notes. In the Major key, the Submediant

Triad being a Minor Common Chord, either the root, the third, or the fifth
may be doubled. It will frequently be found that a better arrangement
of the parts may be obtained by doubling the third, and this may be done
without any hesitation, see Ex. 71 (b] and (c). In the Minor key., this Triad
being a Major Common Chord, according to the general rule, either the
root or the fifth should be doubled; when, howeve^ it is either preceded
*o <-v.; c mi/* or>r>
orjollowed by the Dorr^^^^f:d^^it
L fnrT^g_gjjjgyrppi-inn
the third is usually doubled. The reasons for this exceptional course
are not difficult to discover. Assuming, for example, that the Dominant
Triad precedes the Submediant Triad, as in Ex. 77, the third of the
Dominant Triad (the Leading-note) naturally rises a step to the third of
the Submediant Triad (the Tonic) ; if, then, the fifth of the Dominant
Triad also rises a step to the fifth of the Submediant, as in (a), consecu-
 CHAP. X. THE SUBMEDIANT TRIAD. 45

tive fifths are formed with the bass, or if the fifth of the Dominant chord
leapsdownward to the root of the Submediant chord, as in (), an
augmented fourth is formed in that part. Both of these progressions are
incorrect It only remains then for the fifth of the Dominant chord to
fall a second to the third of the Submediant chord, thus doubling the

third, as in (c). This is by far the best, as well as the most familiar
arrangement of the parts. The exceptional leaping of the Leading-note
a diminished fourth, as in (d\ provided the next Tenor note is a note
within this interval, is a possible progression, but it will be found a far
less useful one than that shown in (^).

Ex. 77.

Bad. Bad, Good. Possible.

78. The "Interrupted Cadence." The progression of the

Dominant Triad Submediant Triad is frequently employed to form
to the
what is called the "Interrupted Cadence" The Interrupted Cadence is
one of the most important of the MIDDLE CADENCES, so called, because
they can only occur during the progress of a composition and never at
the end. In the following exercises, an Interrupted Cadence should be
introduced at each of the places marked (a).

Ear Exercises. The teacher should test the pupil's power of

discriminating by their sound, Perfect, Plagal, and Interrupted Cadences,
by playing such in various keys.

EXERCISES.
Harmonize the following, introducing the Submediant Triad at each
of the places indicated :

I. *

II.
46 HARMONY.

\m
ii
> n jyS^frj.
'

79. The FIRST INVERSION of the SUBMEDIANT

TRIAD.
Ear Exercises:

~i ^ n Ji fj M , i
'

n~j i n ii

ill' I
'

(Also in C
i

minor.)
i

(Also in
T C minor.)

In this inversion, the Bass note is generally the best note to double,
although either of the other notes may be doubled, if desired.
The progressions formed of the first inversion of the Submediant
Triad and either of the Primary Triads are, taken as a whole, far less
useful than those formed when the Submediant Triad is in its root
position. Progressions formed of the first inversion of the Submediant
Triad and either of the Primary Triads in their root position, are, in
general, less satisfactory than progressions in which the Primary Triads
are present in their first inversion. In progressions of the former class,
when the Tonic Triad is employed, as in Ex. 78 (a\ the pupil should
remember what was said in par. 75, with reference to a repeated bass
note. *
 CHAP. X. THE SUBMEDIANT TRIAD. 47

EXERCISES,
Harmonize the following, introducing the first inversion of the
Submediant Triad at each of the places indicated :

VII. #
=+=^=^ -Hs>-FTi^t
EEF
l
'

i *r
EEE
VIII.

IX.

pa
X. *

XII.

^ElE
 HARMONY.

CHAPTER XL
THE SUPERTONIC TRIAD.

80. In the Major key, the triad on the Supertonic or second degree of
the scale is a Minor Common Chord, see Ex. 79 (a). In the Minor key,
the fifth from the Supertonic being a Diminished fifth and the third a
Minor third, the triad which is formed upon this note is called a
Diminished triad, see Ex. 79 (b) :

Ex. 79.

As a Diminished triad is what is called a "discord," and its pro-

gression is subject to certain consideration will be
restrictions, its

postponed until after all the concords have been introduced (Chap.
XVI), and we shall confine our attention (so far as the root position of
the Supertonic triad is concerned), to the Supertonic Triad in the Major
key. Either of the notes of this chord may be doubled when it is
employed in the Major key, but a better progression of parts will often
be obtained by doubling the third instead of the root or the fifth.
81 EAR EXERCISES (Root Position):

The progressions formed of the Supertonic Triad and either of the

other triads of the key which have already been considered, differ so
greatly, both in usefulness and musical effect, that they require to be
referred to separately.
 CHAP. XI. THE SUPERTONIC TRIAD. 49

I. THE SUPERTONIC TRIAD USED IN CONNECTION WITH THE TONIC

TRIAD OR ITS FIRST INVERSION. As there is no note which is common
to these two chords (Tonic and Supertonic Triads), such progressions
are characterised by an absence of smoothness, which, if care be not
exercised in the arrangement of the several parts, may amount to defi-
nite harshness. At the same time, provided the parts be judiciously
distributed and the outside parts move in contrary motion, such pro-
gressions may, with one exception, be employed with good effect, see
Ex. 80 (a] and (d). The exception is the progression of the Supertonic
Triad to the Tonic Triad, when both chords are in their root position,
thus :

^ J J_

Ex. 81.

^
This progression should be avoided.
II. THE DOMINANT TRIAD OR ITS FIRST INVERSION. The effect of
progressions formed of Supertonic and Dominant Triads is almost in-
variably excellent. The roots of these triads being situated a fourth
apart (or a fifth apart, whichever chord comes first), the chords stand
in a somewhat similar relationship to one another as the Tonic Triad
to the Subdominant Triad (or the Dominant Triad), and this is the
strongest relative position which any two triads can occupy. In pro-
gressions formed of these two chords, even when such hidden fifths
occur as are shown below, the musical effect is nearly always good.

Ex. 82.
&

Good.

One of the most familiar positions of the Supertonic Triad, is when it

precedes the Dominant chord (or the second inversion of the Tonic
chord) in leading up to a Cadence, see Ex. 80 (), (c) and (*/), also
Ex. 95 (c).
III. THE SUBDOMINANT TRIAD OR ITS FIRST INVERSION. Of pro-
gressions which may be formed of Supertonic and Subdominant Triads,
the strongest is that in which the Subdominant Triad precedes the
Supertonic Triad, both chords being in their root position and the bass
leaping a third downwards, as in Ex. 80 (b). Other progressions formed
of these chords may be used, but with the exception of the one shown
'in
(<?),
none of them are very strong.
 HARMONY.

IV. THE SUBMEDIANT TRIAD OR ITS FIRST INVERSION. The roots

of these two triads (Supertonic and Submediant) being situated a fifth
apart (or a fourth apart, whichever chord comes first) the musical effect
of progressions formed of these chords is almost invariably good, see
Ex. 80 (c) and (<?).

EXERCISES.
Harmonize the following, introducing the Supertonic Triad at each of
the places indicated :

III.

ET-IZ*=E|==
t r

=m^
IV.

V.

82. The FIRST INVERSION of the SUPERTONIC

TRIAD. Although the Supertonic Triad in its root position in the
minor key, having a dissonant interval (a diminished fifth) from the
bass, unavailable for employment as a common chord, yet in its first
is

inversion, when the dissonant interval (the augmented fourth or its in-
version the diminished fifth) occurs only between two of the upper parts,
as in Ex. 83 (b) and (c), it may be employed with the same freedom as
the first inversion in the major key :

w (*)
 CHAP. XI. THE SUPERTONIC TRIAD.

Ear Exercises (To be dictated also in C minor) :

Ex. 83.
{a)
J , I I
w; '

Progressions formed of the first inversion of the Supertonic Triad and

either of the triads previously considered, in their root position, are
generally good (see (a), (c) and (d)) except that in which the Sub-
t

dominant triad is employed, when, the bass being repeated, the musical
effect is weak. Progressions in which both the chords are employed in
their first inversion lack strength, but if judiciously introduced, may
produce good, and even excellent effects, see (b).
83. Progressions formed of a Perfect Fifth and a
Diminished Fifth. In the minor key, the progression of a
common chord (root position or inversion) to the first inversion of the
diminished triad upon the Supertonic (or vice versa), makes the pro-
gression of a perfect fifth, followed or preceded by a diminished fifth,

possible, as shown in Ex. 84. Progressions like these, formed of fifths

of two different kinds, obviously do not produce the same effect as pro-
gressions formed of two perfect fifths, and are not, like them, universally
prohibited. When a progression formed of a perfect fifth and a dimin-
ished fifth occurs between two upper parts, (as such fifths only can
occur at the present stage), provided the perfect fifth comes first, as
shown in (a), it is freely allowed ; while, when the diminished fifth comes
it is also allowed, if either of the parts
first, as in (b), forming the fifths
move by the step of a semitone. A much better progression, however,
is formed when the lower part rises a semitone, as will be shown in con-

nection with the first inversion of the Leading-note Triad, Ex. 92 (b), than
when the higher part falls a semitone, as in Ex. 84 (b). It will be better
for the pupil to avoid such a progression as (b) in his early exercises :

() ! W
{=z=F=nq
|

_C2~

Jl
'

Ex. 84.
<"? __
52 HARMONY.

EXERCISES.
Harmonize the following, introducing the first inversion of the
Supertonic Triad at each of the places indicated :

VII. *

VIII.
111. I

*
IX.

x.
 CHAP. XII. THE MEDIANT TRIAD 53

CHAPTER XIL

THE MEDIANT TRIAD.

84. In Major key, the triad on the Mediant or third degree of the
the
scale, isMinor Common Chord, see Ex. 85 (a). In the Minor key^
a
the fifth from the Mediant being an augmented fifth, and the third a
major third, the triad which is formed upon this note is called an
Augmented triad, see Ex. 85 (b) :

(a)

Ex. 85.

The Augmented triad is a discord and will be considered with the

other dissonant triads in Chap. XVI. In this chapter we shall confine
our attention, so far as the root position of this triad is concerned, to
the Mediant triad in the Major key. Either the root or the third of the
chord may be doubled, but the fifth (the Leading-note) may not be
doubled.

85. Ear Exercises (Root Position):

Ex. 86.

The upon the Mediant is the least useful of the common

triad
chords the Major key, and, unless great care be exercised in its
in

employment, unsatisfactory and harsh progressions will be produced.

Some of the progressions formed of this triad and the Subdominant
Triad in its root position being amongst the most unsatisfactory of
these. When the Mediant Triad is used in connection with the Sub-
mediant Triad or its first inversion, the effect is generally excellent, and
there are a few other chords, (some of which are shown above), with
which it may be employed, also with good effect. Its employment,
however, should be rare, except in those exercises in which it is
specially indicated.
54 HARMONY.

EXERCISES.
Harmonize the following, introducing the Mediant Triad at each of
the places indicated :

I. * *

n.

*
in. *

86 The FIRST INYERSION of the MEDIANT

TRIAD. As in the first inversion of the Mediant Triad in the Minor
key, the dissonant interval (the diminished fourth, or its inversion,
the augmented fifth) occurs only between two of the upper parts, see
Ex. 87 (b) and (c), this chord, in its first inversion, is available for
unrestricted employment in both major and minor keys.

Ex. 87.

87. Ear Exercises (to be dictated also in C minor) :

Ex. 88.

This inversion, like the root position of the same chord, -is not frequently
used, but it may be employed with excellent effect when followed either
by the Dominant, Tonic, or Submediant Triad, as shown above. The
best effect is produced when the root of the chord is in the highest part
 CHAP. XII. THE MEDIANT TRIAD. 55

and the bass note is doubled, as in the last four Ear Exercises. When
employed in this form in Cadences, it is frequently described as a chord
of the Dominant Thirteenth, and as such it will be fully considered in
the chapter upon the Chord of the Dominant Thirteenth (Part II).

88. The Harmonization of Figured Basses. In the

harmonization of Exercises XI and XII, and of all subsequent figured
basses, the pupil should bear in mind the two following points :

(i) When a line is placed immediately under a bass note, it means that
the chord over the previous bass note is to be either repeated or sus-
tained over this bass note, as in Ex. 89 (a). (2) When a line is used
in connection with a figure, as in (), it means that the note indicated

by the figure or accidental which immediately precedes the line, is to

be repeated or sustained to the end of the line. Thus, the B 'of the f

second chord is continued through the third chord, as indicated by the

line placed after the natural.

(a) (*)
I I
I

Ex. 89.
'.
^=&=i
6
fl

EXERCISES.
Harmonize the following, introducing the first inversion of the
Mediant Triad at each of the places indicated :

V. * * *

VII.
rfcfc :
F==
VIII.
 HARMONY.

IX.

-*

X.

^==
* *

Harmonize the following basses in accordance with the figuring

XI.

666 6 6

XII.

6 6
 CHAP. XIII. THE LEADING-NOTE TRIAD (FIRST INVERSION). 57

CHAPTER XIII.

THE LEADING-NOTE TRIAD FIRST INVERSION.

89. In both Major and Minor keys, the fifth from the Leading-note
or seventh degree of the scale, being a diminished fifth, the triad which
is formed upon this note is a Diminished Triad, thus :

This triad is a discord and will be considered with the other dissonant
triads in Chapter XVI.
90. First Inversion. As in the first inversion of this triad, the
dissonant interval (the augmented fourth or its inversion, the diminished
fifth) occurs only between two of the upper parts. This inversion of the
chord may be freely employed in both Major and Minor keys, thus :

Ex. 90. ^f=

91. Ear Exercises be dictated also in C minor):

!,l,i
(to
Ex. 91. , I

1 '
r r
I

j.j. .;..;.
-U3r

This chord is employed with the best effect when it is preceded or

followed by the Tonic Triad or its first inversion, as shown above.

Either the bass note or the third from the bass may be doubled, but not
the sixth, which is the Leading-note. Provided the Leading-note rises,
the progression of the chord is unrestricted.
92. Harmonic Progression. The progression of a perfect
fifth to a diminished fifth, as shown in Ex. 92 (a), as well as the reverse
of this, the progression of a diminished fifth to a perfect fifth, as in (),
both of which may be formed between this chord and the Tonic Triad
or its first inversion, are allowed (see par. 83). Progressions formed of
two diminished fifths, such as may be formed in the Minor key between
the first inversions of the triads upon the Supertonic and the Leading-
note, as in (<r), are also allowed.
 HARMONY.
() I

-rjr
-6>_;

Ex. 92.

t
Good. Good. r:rl
Good.

93. The Minor Seventh as a Melody Note in the

Minor Key. When a melody in the Minor key takes the
descending form of the Melodic Minor scale, and proceeds stepwise
from the Tonic down to the Submediant by the employment of the
minor seventh, this latter note is frequently harmonized by a chord of
the sixth upon the Supertonic, the minor seventh taking the place of the
major seventh or Leading-note, as in Ex. 93 (a). The minor seventh
may also be harmonized by a chord of the sixth upon the Dominant, in
which case it becomes the third from the bass, as in Ex. 93 (b\ but this
is a less familiar harmonization than the previous one.
Ear Exercises:
>
"^M:
*-J-

Ex. 93.

EXERCISES.
Harmonize the following, introducing the first inversion of the
Leading-note triad at each of the places indicated :

I. * * *

'
r r i

in.
 CHAP. XIII. -THE LEADING-NOTE TRIAD (FIRST INVERSION). 59

In the following melodies the Minor Seventh is to be harmonized by a

chord of the sixth either upon the Supertonic or upon the Dominant :

n VIIL I
I
I

* *
Harmonize the following Basses in accordance with the figuring
IX.
?T3

p
66
-=|

EtE
\=*=.
66 66
X.

6 6 6 5 6 6
3

6 6
XL
lfe=E'E^;
P ^_CI_i_ZJ i ^_j* i

I^EgiiS^^jg^^E
6o HARMONY.

CHAPTER XIV.

THE PRIMARY TRIADS IN THEIR SECOND INVERSION

94. The TONIC TRIAD Second Inversion. The second

inversion of a triad has the fifth of the original chord in the bass. The
second inversion of the Tonic Triad is shown in Ex. Q4 ().

Ex. 94.

The rootand the third of the original chord have now become the
fourth and the sixth from the bass respectively, and the figuring of the
chord is 2- / the second inversion of all consonant triads, the best note
to double (with one exception) is the bass note, that is, the fifth of the
chord in its original position. It is possible, however, to double either
of the other notes, provided such note be not the Leading-note.

95. Ear Exercises (also in C minor, except (e) ):

Ex. 95.

-. JT]
r;
-. ...g .g. .. .. .. & .

n
.
i

s ^ r ii
..g.
^-ir i
* -
~^-f-
 CHAP. XIV. PRIMARY TRIADS IN THEIR SECOND INVERSION. 61

96. The Progression of the Bass WHEN APPROACHING AND

QUITTING A SIX-FOUR CHORD The second inversion of a common
:

chord, owing to the fact that one of its notes stands at the distance
of a Perfect fourth from the bass, is always subject to special rules
of progression. The interval of the Perfect fourth as an inversion
of the Perfect fifth, is included amongst the perfect consonances, and
when it is heard in a chord, between two of the upper parts, it produces
no dissonant effect. When, however, it is heard as the fourth from the
bass, it loses to some extent its perfectly consonant character and the
chord of which it forms part is not allowed that free and unrestricted
progression which belongs to the root position and first inversion of
common chords. The rules to which the second inversion of
common chords are subject, refer entirely to the progression of the
bass part, both as to the approaching and the quitting of the bass note
of the 4 chord. They are as follows :

I. When a chord is both preceded and followed by other positions

of the same chord, the bass note of the f chord may be approached
and quitted by any interval, see Ex.
95 (a),
II. When a J chord
preceded by another chord in its root position'
is

the bass part is free to move to the bass note of the $ chord either by a
step, as in (b\ or by a leap, as in (c).
III. When a $ chord is preceded by an inversion of another chord,
the bass part must move to the bass note of the chord by a step, as in
(d) and (<?).
IV. A chord may be preceded or followed by a different chord
(root position or inversion) upon the same bass note, see Ex. 99 (a).
V. When a J chord is followed by a different chord (that is, except
when the same chord is repeated in another position, as in Ex. 95 (a) ),
the bass must either remain stationary, as in (b) and (^), leap an octave,
as in (c), or move by the step of a second, either upwards or downwards,
as in (e).
VI. When a f chord, which is preceded by a different chord, is
followed by another position of the same chord, the bass part, when the
harmony changes, should return to a note, to which a correct progression
from the f chord could have been made, as in (/).

97. The "Cadential Six-four" Chord, and the "Im-

perfect Cadence." In examples (), (c\ and (d\ given above, it
will be seen that the second inversion of the Tonic Chord is employed
immediately before the two chords which form the final cadence. In
this position, this 2 chord is both familiar and valuable. There is
however another position which it frequently occupies, and in which it
is hardly less familiar or less valuable, that is, as the first chord of one

form of the "Imperfect Cadence" or "half-close on the Dominant" one of

the MIDDLE CADENCES referred to in par. 78. In the following example
this chord is seen in both positions, at (a) forming part of a half close
on the Dominant and at (b] as leading to a Perfect Cadence :
62 HARMONY.
Ex. 96.

J. J. J. -J i

f-
I
-+-
!

-m- -G>-

EEEE
6 65
43 65
43
When a J chord is employed in either of these positions it is called a
\" A "cadential |" nearly always occurs upon a stronger
" cadential
beat of the bar, or upon a stronger portion of a beat, than the chord
which immediately follows it, and as a general rule the sixth and the
fourth of the first chord move respectively to the fifth and the third of
the second chord. The single exception to this rule, as to the position
of the cadential chord, occurs when the 4 chord is both preceded
and followed by chords upon the same bass note, as in Ex. 99 (a). In
connection with the figuring of the above example, it should be noticed
that when a triad is preceded hy a different chord upo?i the same bass note,
(as is the case in both the second and third bars above), the Iriad requires
to be figured, otherwise it would be understood that the figuring of the
first bass note applied also to the second bass note. Sometimes both
chords are sounded over one sustained note, as shown below. The
two sets of figures are then placed under this one note. In such cases,
each chord either takes half the value of the note, as in (c), or in the case
of a dotted note, the first chord takes two-thirds of the value, as in (d).
(d)
|

The employment
43 43
of a | chord, not cadentially, but as a passing J
"
is
"

shown in Ex. 95 (e), and when so employed it may be upon either an

accented or an unaccented beat of the bar.
98. Allowable Hidden Octaves. Hidden octaves which are
formed between the outside parts when proceeding to the second
inversion of a common chord, are allowed, provided either the bass
moves a fourth and the highest part a second, as in Ex. 97 (a), or the
bass moves a second and the highest part a fourth, as in (b) :

(a) (b)

Ex. 97.
 CHAP. XIV. PRIMARY TRIADS IN THEIR SECOND INVERSION. 6j

EXERCISES.
Harmonize the following, introducing the second inversion of the
Tonic Triad at each of the places indicated :

*
in.

IV.
, ,

V.

VI.

%* Some further exercises upon the employment of the second

inversion of the Tonic Triad, used cadentially, will be found at the end
of Chap. XVII on Cadences.

99.The DOMINANT TRIAD Second Inversion.

Ear Exercises (also in C minor) :

" Ladhd^^^5^=
;=^=j:|=ftrQ=^-^- ~^~&
-^Qrj =j=:Jr^g^-
z---=: ^=f?
.J^L* _j_ .J- J J.

The second inversion of the Dominant Triad is used almost entirely

"
as a passing j," either between repetitions of the Tonic Triad or between
the Tonic Triad and its first inversion as shown above.
 HARMONY.

EXERCISES.
Harmonize the following, introducing the second inversion of the
Dominant Triad at each of the places indicated :

VII. *

ioo. The SUBDOMINANT TRIAD-Second Inversion.

Ear Exercises (also in C minor) :

Ex. 99. (a)

The second inversion of the Subdominant Triad is used chiefly

cadentially, as one of the forms of the Plagal Cadence in the manner
shown in.
(a).

101. Consecutive Perfect Fourths with the Bass.

Now that it is
possible to employ two | chords upon adjacent bass
notes (the second inversions of the Dominant and Subdominant Triads),
.although such a progression would neither be a very familiar nor useful
one, yet the following rule must be brought to the pupil's notice. In
any progression of\ chords, no part may proceed in perfect fourths with
the bass. When two | chords are employed upon adjacent bass notes,
.as in Ex. ioo, the fourths in the two chords, if they are both perfect

fourths, must not appear in the same part, as in (a) but in different
parts, as in (/>).
 CHAP XIV. PRIMARY TRIADS IN THEIR SECOND INVERSION.

Ex. 100.

?-
4 4
Bad. Good.

EXERCISES.
Harmonize the following, introducing the second inversion of the
Subdominant Triad at each of the places indicated :

*
XII.

Harmonize the following, introducing the second inversion of one of

the Primary Triads at each of the places indicated :

m
XIV.

?E=*
7=r
*

XV.

'M I

a, V

i
* * *
66 HARMONY

CHAPTER XV.

THE SECONDARY TRIADS IN THEIR SECOND INVERSION.

102. The second inversions of the consonant Secondary Triads, are

the second inversion of the Submediant Triad in both major and minor
keys, see Ex. 101 (a), and the second inversions of the Supertonic and
the Mediant Triads in the major key, see (b} and (c). Neither of these
second inversions are very useful nor very familiar. They are rarely to
be met with, and the occasions when the pupil will wish to use either
of them in preference to any other chord will be few and far between.
For the sake of completeness, however, it is necessary that they should
be mentioned, and a few exercises upon them should be given. As
in the following exercises, when they are employed it is generally as
" "
In the
passing \ chords, the bass moving in stepwise progression.
second inversion of the Mediant Triad, the bass note, being the
Leading-note, may not be doubled. With this exception the rule as to
the doubling of notes, given in par. 94, applies also to these chords.

(also in C minor).

EXERCISES.
Harmonize the following, introducing the second inversion of a Triad
at each of the places indicated :

I. * * *

i
 CHAP. XV. SECONDARY TRIADS IN THEIR SECOND INVERSION. 67

Harmonize the following basses in accordance with the figuring :

__II.
MFJF=== -
- ~r^

* 7-' ? '6 '5

4 U

66 6
4
^
6 $6 6
4 4

III.

=]
*i _ m
II -
56
'

6
6 6 6 6
4 3
4

SE
666
66656
4
443 4343

-
68 HARMONY.

CHAPTER XVI.

THE DISSONANT TRIADS.

103. We
have now to consider those triads which on account of
their dissonant character require special treatment. These comprise
the Diminished Triad upon the Leading-note in both Major and Minor
keys, as shown in Ex. 102 (a) and ()), the Diminished Triad upon the
Supertonic in the Minor key> as in (c),
and the Augmented Triad upon
the Mediant in the Minor key> as in (d ), as well as the second inversion

of each of these triads.

Ex. 102.
(a) (6) (c)
t?

In each of these triads and their second inversion a dissonant interval

is formed between the bass note and one of the other notes of the
chord, and the notes which form this dissonant interval must proceed
in such a manner that a satisfactory musical effect shall be left upoi.
the mind of the listener, in other words, the dissonant interval must bt
resolved. The subject of Discords and their Resolution can only be
touched upon quite incidentally in this chapter, but it will be more
fully dealt with in connection with the chord of the Dominant Seventh
(Chapter XIX).
104. The LEADING-NOTE TRIAD (DIMINISHED TRIAD).
Ear Exercises (also in C minor) :

Ex. 103.
(a) (*) (c)

J. J.

n 3EE
In the original position of this triad, which is the same in both Major
and Minor keys, the dissonant interval, the Diminished fifth from the
bass, may either fall a second to the third of the Tonic chord, as in (a\
or it may remain to be a note of the next chord, as in
(b). The bass
note always rises a step to the Tonic, unless the chord be repeated in
another position. The third of the chord should be doubled. This
triad is frequently regarded as an incomplete form of the chord of the
 CHAP. XVI THE DISSONANT TRIADS. 69

Dominant Seventh, of which it forms the three highest notes. When

it so described the root, of course, is the Dominant.
is The second
inversion of this triad resolves upon the first inversion of the Tonic
Triad, as in (c), and the progression of the two notes which form the
dissonant interval (the Augmented fourth) is the same, as in (a), except
that their relative position is now reversed. In neither of these forms
is this chord often to be met with, and the pupil should rarely make

use of it except in exercises where it is specially indicated.

105. Consecutive Fifths and Consecutive Fourths
with the Bass. The progression of a Perfect fifth to a Diminished
formed between the bass and an upper part, as shown between the
fifth,
altoand bass parts of the first two chords in Ex. 03 (a), is freely allowed,
1

but the reverse of this, a Diminished fifth followed by a Perfect fifth

between the bass and an upper part is not allowed. In Ex. 103 (c),
where the second inversion of this triad is preceded by the second
inversion of the Tonic triad, the tenor part moves in fourths with the
bass. It should, however, be noticed, that although the first fourth is a
Perfect fourth, the second is an Augmented fourth. The progression of
a Perfect fourth to an Augmented fourth, formed between the bass and an
upper part (provided the parts move by step) is freely allowed. Such
consecutive fourths will be frequently met with in connection with
the last inversion of the chord of the Dominant seventh (Chapter XIX).
The reverse of this progression, an Augmented fourth followed by a
Perfect fourth, is not incorrect, but it is a far less familiar progression
and in these early stages should be avoided.

EXERCISES.
Harmonize the following, introducing the Leading-note Triad or its
second inversion at each of the places indicated :

ISIS^IgiB

106 The SUPERTONIC TRIAD in the MINOR

KEY (DIMINISHED TRIAD). Although this triad in the minor key,
and also that upon the Mediant in the same key (par. 108), owing to the
fact that they are both discords (and the progression of some of their
notes therefore restricted), differ, in their nature from the corresponding
triads in the major key, which are concords, yet, the function of each of
these triads, in both major and minor keys, is not essentially different ;
that is, allowing for the limitations of correct resolution and progression,
the chords to which each can most effectively proceed are the same in
both keys. This will be seen by a comparison of Ex. 80 (d] and Ex. 95 (c)
with Ex. 104 (a) and (b) respectively, and in connection with the Mediant
Triad, a comparison of the last two exercises in Ex. 86 with Ex. 106 (a)
 HARMONY.

and In the resolution of both of these dissonant triads, it will be

(b).
seen the best progression is formed when the root of the next
that
chord is a fourth above that of the discord, as in Ex. 104 (a] and
Ex. 1 06 (a). Later on it will be seen that this is the most familiar
progression of roots formed by discords and their resolution.
Ear Exercises:
Ex. 104.
(a) (b) (c) (d)
(

In the original position of this triad, the Diminished fifth from the
bass is resolved either by falling a second, as in Ex. 104 (a) and (b), or
by remaining stationary and becoming a note of the next chord, as in
(c).
The progression of the bass note is not restricted, and either this
note or the third may be doubled. When this triad is preceded by the
Tonic Triad in its root position, the fifth from the Tonic (a Perfect
fifth) may proceed to the fifth of the Supertonic (a Diminished fifth), as
at (c), (see par. 105). In the second inversion, the bass note (which
was the Diminished fifth in the original chord) falls a second, as in (d}.
This inversion is rarely to be met with.
107. The Major Sixth as a Melody Note in the Minor
Key. When
melody in the Minor key takes the ascending form of
a
the Melodic Minor scale, and proceeds stepwise from the Dominant to
the Leading-note by the employment of the Major sixth, the Major
sixth may be harmonized by a Minor Common Chord upon the
Supertonic, as in Ex. 105 (a) and (b). When the Minor Common
Chord on the Supertonic is so employed, it is generally followed by a
chord of the sixth upon the same bass note, as in (a), but it may also
be followed by a Dominant chord, as in (b). A chord of the sixth upon
the Tonic is also sometimes employed to harmonize this note, as
shown in (c).
Ear Exercises:
Ex. 105.

n 1-

* ii
i
-*- *
I
i

I
f
il 1

The harmonization
7 ~T
of this Major sixth in the Minor key by a Major
triad upon the Subdominant, although occasionally to be met with in the
works of old composers, is very rarely employed by modern composers.
 CHAP. XVI. THE DISSONANT TRIADS.

EXERCISES.
Harmonize the following, introducing the Supertonic Triad or its

second inversion at each of the places indicated :

III. * -2- ,

**=F=F=E:

M^
4-ZZZtzni

In the following, the Major sixth (*) is to be harmonized by a Minor

Common Chord on the Supertonic:
IV.

i
108. The MEDIANT TRIAD in the MINOR KEY
(AUGMENTED TRIAD).
Ear Exercises:
Kx. 106.

(*)J J J
-* .

In the resolution of this triad / //r original position, the bass

nearly always rises a fourth (or falls a fifth) to the Submediant, and the
chord resolves either upon the Submediant triad, as in (a), or the first
inversion of the Subdominant triad, as in (b). The Augmented fifth is
resolved by rising a semitone to the Tonic, and either the bass note
or the third of the chord is doubled. In the second inversion this chord
resolves upon a Tonic triad, as in (c), the sixth from the bass being
doubled.
109. Harmonic Progression. The progression of an Augmented
fifth to a Perfect fifth (or vice versa], which may be formed in the Minor
key between the triad upon the Mediant and one of the common chords
of the key, or an inversion of such, as shown below, is not allowed :

Bad. I
 HARMONY.

EXERCISES.
Harmonize the following, introducing the Mediant Triad, or its second
inversion, at each of the places indicated :

V. *

Harmonize the following Basses in accordance with the figuring :

VII.

6 6 666 66 6
6 5
4 3
VIII.
(foV b u
 CHAP. XVII. CADENCES. 73

CHAPTER XVII.

CADENCES.*
(ALSO THE CONSTRUCTION OF FOUR-BAR EXERCISES TO ILLUSTRATE THE
EMPLOYMENT OF DIFFERENT FORMS OF CADENCE).

1 10. When a succession of chords

is brought to a final termination in
a musically satisfactory manner, or progress is temporarily arrested, or
its
we might say punctuated, (as in the second bar of the following example),
a CADENCE is said to be formed thus :

Ex. 107.

Cadence. Cadence.

A Cadence means a close, and cadences mark the close or completion

of such portions of a musical composition as phrases, sentences or
sections, as well as the close of the entire composition. It naturally

follows, therefore, that there are different varieties of cadence, which

produce different degrees of finality in their musical effect, and cadences
are described and classified according to the nature of this effect. The
simplest form of classification is to divide cadences into two classes,
namely I. FINAL CADENCES, or cadences which can be employed to
:

terminate a composition ; and II. MIDDLE CADENCES, or cadences

which can be employed only during the progress of a composition.
in. I. Final Cadences. In these, the Tonic chord in its root

position is always the second and final chord, and it is generally preceded
either by the Dominant chord (triad or discord) or the Subdominant
chord When both the chords forming the cadence are in their root
position, it is called a Full Close or a Full Cadence, thus :

(a] (b) (c)

Ex. 108.

*
Although some forms of Cadence have already been briefly referred to, yet, in
order that the nature and classification of cadences may be considered with as much
completeness as possible, in the present chapter, reference to such cadences will be
included even at the cost of some small amount of repetition.
74 HARMONY.

A Full Cadence which is formed by the progression of the Dominant

chord to the Tonic chord, as Ex. 108 (a) or (b), is called an Authentic
or Perfect Cadence, and one which is formed by the progression of the
Subdominant chord to the Tonic chord, as (c), is called a Plagal
Cadence. In Perfect cadences the effect of finality is most completely
attained when the highest part is formed either by the Leading-note or
the Supertonic proceeding to the Tonic, as in (a) and (b} respectively ;
while in Plagal cadences it is best to repeat the Tonic in the highest
part, as in (c). The Plagal Cadence is found chiefly in old music and in
church music generally, while the Autnentic Cadence belongs specially
to modern music, and represents the feeling for modern tonality

ii2. Inverted Cadences. If either or both of the chords of a

Full Cadence be an inverted form, an Inverted Cadence is formed.
in
When only the first chord of the cadence is inverted, as in Ex. 109
(a) and (6), the cadence still remains a Final cadence ; but should the
final Tonic chord be inverted, as in (c\ the cadence ceases to be a Final
cadence and becomes a Middle cadence. Another form of inverted
cadence is formed by the first inversion of the Leading-note triad as
in (d).

(a) (b) (c) (d)

Ex. 109.
_

In all the cadences in Ex. 108 and 109, it will be noticed that, with
one exception, the second chord is upon a stronger beat of the bar than
the first chord. This is generally the case in Final cadences. The
exception shown in Ex. 109 (b) is due to the fact that both chords have
the same bass note, and therefore the first one may be upon the stronger
beat. Compare Ex. 99 (a).
113. II. Middle Cadences. Middle Cadences may be subdivided
into Imperfect Cadences (which are also called Half Cadences or Half
Closes], and Interrupted Cadences.
IMPERFECT or HALF CADENCES have the Dominant Triad in its root
position for their final chord, and it may be preceded by almost any
other triad, or inversion ot such. Some of the most useful forms are
given below :

Ex. no.
J

4A J
 CHAP. XVII. CADENCES. 75

In INTERRUPTED CADENCES the Dominant chord, instead of being

followed by the Tonic chord, as in a Perfect Cadence, is followed by
another chord, generally that upon the Submediant, and the effect of
finality which would have been produced is interrupted, hence the
name :< Interrupted Cadence." Such cadences are also called false or
Deceptive Cadences. Ex. 1 1 1 shows two forms of such cadences.

Ex. in.

For Ear
Exercises, to test the pupil's power of discriminating
the various cadences by their sound, the teacher should play different
cadences for the pupil to name, after hearing the key-chord sounded
beforehand.

EXERCISES.
I. Write examples of the following Cadences in the keys of B flat
major and F sharp minor A Perfect cadence, a Plagal cadence, an
:

Inverted Perfect cadence, and an Inverted Plagal cadence, all to be

Final cadences ; also the following Middle cadences, two different forms of
the Interrupted cadence, six different forms of Half cadences, and an
Inverted Middle cadence.
Harmonize the following, introducing some suitable form of cadence
at each of the places indicated. Describe each cadence you employ :

II. # # * * * * * *

rr
III. ** ** * *

v -

K i
m1

* * * * * *
76 HARMONY.

VI. Taking Ex. 96 as your model, construct passages of four bars in

length (consisting of triads and their inversions) in the keys of G, E flat,
and B major, and D, C sharp, and F minor. Each passage must
illustrate the employment of the second inversion of the Tonic Triad
used cadentially in two different ways, (i) as forming an Imperfect
Cadence in the second bar, and (2) as leading to a Final Cadence in
the third bar (see Model worked below).
VII. Taking Ex. 107 as your model, construct similar passages of
four bars in length in the keys of F, A, and D
flat major, and E, G, and
F sharp minor. In these, the cadence in the second bar must be an
Interrupted Cadence to the Submediant.

TO ILLUSTRATE THE EMPLOYMENT OF MlDDLE AND FlNAL CADENCES.

FIRST STEP. Write down in the key of the Exercise everything

which is already determined, thus :

Model in C minor for Ex. VI.

\^2^.^li
_
 CHAP. XVII. CADENCES. 77

If the pupil is sufficiently musical to conceive both melody and

harmony together, this step and the next one will practically merge into
one mental operation, but if he is unable to do this, he must consciously
proceed to the next step.

FOURTH STEP Supply suitable harmonies to the above melody, and

indicate such by means of a figured bass, thus :

*
i I i iii
-B- *-
jgrgh
 HARMONY.

CHAPTER :r

SEQUENCES.

114. When a melody or a progression of chords is repeated not less

than twice, each repetition starting upon a different degree of the
scale, but the whole series proceeding in some regular manner, either
ascending or descending, a SEQUENCE is said to be formed, thus :

Ex. 112.

A Sequence in which the repetitions of the original progression occur

only in one part, the other parts present moving in an independent
manner, as in Ex. 1 12, is called a MELODIC SEQUENCE; while one in which
two or more parts move as in the original progression, as in Ex. 113,
where all the four parts so move, is called a HARMONIC SEQUENCE. An
examination of the above Sequences will show that the intervals and
chords which correspond with one another in the original progression,
and in the different repetitions, only agree with one another numerically
and not qualitatively. Thus, the interval of a Perfect fourth which is
formed between the first and second treble notes of the original
progression in Ex. 113 is represented in the first repetition by an
Augmented fourth, and in the second by a Diminished fourth, and only
in the third by another Perfect fourth ;
while the first chord, which in
the original progression is a Minor triad, is represented in the first
repetition by a Diminished triad, and in the second by an Augmented
triad. Sequences of this kind are called Tonal Sequences.
115. Exceptional Progression in Tonal Sequences
In Tonal Sequences exceptional freedom of treatment and progression is
allowed in the formation of the repetitions of the sequence. Thus,
 CHAP. XVIII. SEQUENCES. 79

provided there is no fault in the original progression or text of the

sequence, and also that no faulty progression occurs between the last
chord of this initialprogression and the first chord of the first repetition,
then, no account need be taken of faulty Melodic or Harmonic
progressions which may be formed by the parts forming the repetitions
of the sequence. It may be helpful to the pupil, if we indicate the
directions in which, under these special circumstances, the ordinary rules
of progression are relaxed. In the repetitions of a Sequence
(1) An Augmented interval may occur in any part;
(2) The Leading-note may be doubled, and it may either rise or fall ;
(3) Dissonant triads may be employed with the same freedom as
Common chords, that is, the dissonant note may be doubled and its
progression is unrestricted.
The pupil will now understand that all of the apparently incorrect
progressions in Ex. 113 are justified by their occurring in one of the
repetitions of a sequence.
1 1 6. Real Sequences. Besides Tonal sequences, in which, as
we stated above, the repetitions are not the real counterparts of the
original progression, there are sequences of another kind, in which
the several intervals and chords of the various repetitions do exactly
correspond qualitatively as well as numerically with those of the original
progression. Such are called Real Sequences, and the following is an.
example of this kind of sequence :

Ex. 114.
-J- J
(S:
-I i
*F=
As will be seen from this example, Real Sequences generally involve
modulation to extreme keys. Their formation is quite simple but they
are rarely employed for many repetitions.

EXERCISES.
Harmonize the following Basses in accordance with the figuring.
Where the bass part progresses sequentially, the upper parts should also
move sequentially :

I.

31=5:

6 5
6 '
6 66 66
4 3
II.
80 HARMONY.

CHAPTER XIX.

THE CHORD OF THE DOMINANT SEVENTH.

117. The chords which come next to the Triads in simplicity of

construction are those of the seventh. A chord of the seventh is
formed by adding to a triad a note which is a seventh from the root of
the triad, thus :

Ex. 115.

1 1 8. A
chord of the seventh may be formed upon every note of the
diatonic scale, but the most important as well as the most familiar and
useful chord of the seventh is that which is formed upon the Dominant,
and is called the CHORD OF THE DOMINANT SEVENTH, thus :

The notes of this chord are exactly the same in both a Major key and
itsTonic Minor key, and the intervals of which it is composed are, a
Major third, a Perfect fifth, and a Minor seventh, reckoning, of course,
from the root. The interval of the seventh being a dissonant interval,
the chord of the Dominant seventh and all chords of the sevenths are
"
what are called discords"
119. Discords, their Nature and Resolution. The
term "discord," as employed music, has not the same meaning
in
as when it is employed in connection with non-musical matters.
Musical discords are not only neither necessarily disagreeable nor
unpleasant, but in the majority of instances are distinctly agreeable and
pleasant. It is no exaggeration to say, that most of the charm which
music possesses is due to the skilful employment of discords. When
applied to a chord in music, the term "discord" simply means that
the effect of such a chord is to leave the listener, musically speaking,
unsatisfied. If the above chords be sounded, one cannot fail to recog-
nize their unsatisfying nature, while if either chord be repeated several
times, it seems to become more unsatisfying after each repetition.
The fact is, that EVERY DISCORD REQUIRES TO BE FOLLOWED BY SOME
OTHER CHORD, WHICH SHALL SUPPLY THAT FEELING OF MUSICAL
SATISFACTION OR REST, FOR WHICH THE DISCORD HAS CREATED THE
DESIRE, and this feeling of satisfaction is only completely produced
when the notes which form the dissonant interval move in some special
 CHAP. XIX.- :HORD OF THE DOMINANT SEVENTH. 81

manner to certain of the notes of the next chord, thus effecting what is

called THE RESOLUTION OF THE DISCORD.

120. The Resolution of the Dominant Seventh. In the
chord of the Dominant seventh, the notes whose progression is restricted
so that a satisfactory resolution of the discord may be obtained are the
third and the seventh, which between them form either a Diminished
fifth or its inversion, an Augmented fourth, according to their relative

position. As will be seen from the following Ear Exercises, the seventh
must either fall a second, as in Ex. 117 (a) and (b\ gr_remain_stationary,
as in (c}, while tJie third, the Leading-note of the key, must always rise
a second to the Tonic.

EAR EXERCISES (Root Position) :

Ex. 117.
(a) (b) (c\ (d)

*+* All the above, except (d), should be dictated also in C minor.
In doing^so, it should not be forgotten, that in the chord of the seventh,
" "
as in the Dominant triad, the B's are natural (not flat).

The most familiar resolution of the chord of the Dominant seventh is

upon the Tonic Triad in its root position, as shown in (a). The seventh
of the Dominant chord then falls to the third of the Tonic chord, and
the third of the Dominant chord rises to the root of the Tonic chord.
In this resolution the fifth of the Tonic chord is generally omitted.
The chord of the Dominant seventh followed by the Tonic Triad in this
manner absolutely defines the key of a passage, and is the most familiar
form of the Perfect Cadence, see (^)f. Another familiar resolution is
upon the tsubmediant Triad in its root position, as shown in (b). Here,
the seventh and the- third proceed as in the previous resolution, but
to the fifth and the third of the Submediant Triad, respectively. This
resolution is often employed to form an Interrupted Cadence, as in (<?)*.
A less familiar resolution is upon the first inversion of the Subdominant
Triad, as shown in (c], where the seventh r^mair^s, stationary fro h^^.Q^ne
a note of the next chord. The seventh occasionally moves to another
82 HARMONY.

note of the chord before proceeding to its proper resolution, as shown

in (f). A
resolution of this kind is called an "ornamental resolution."
The progression of the fifth of the Dominant chord is unrestricted, and
if desired, it may be omitted, as in the first chord of Ex. 119. In such
cases the root is doubled, and it is the only note which may be doubled.
It is possible to omit the third of the chord the root, fifth and seventh
only being present but this is rarely done.*
121. Harmonic Progression. In the resolution of this chord,
such progressions as the following, where the intervals of the seventh
and ninth proceed by similar motion to an octave, as in Ex. 118 (a) and
(b) respectively, and where the interval of a second proceeds similarly to
a unison, as in (<:), are strictly forbidden :

(>

Ex. 118.

Bad.

(a) and (b) illustrate "hidden octaves" in a form, which, whether

between outside or inner parts, is equally bad. These, and all similar
progressions which it may be possible to form in connection with
chords to be studied later on, infringe the following important rule of
harmonic progression :

No two notes next to one another in alphabetical order, and being

sounded together\ may proceed by similar motion to an octave or a unison.
122. The Repetition of a Discord, The chord of the
Dominant seventh (or any other discord) may be repeated any number
of times before proceeding to its resolution, this being delayed until
after the final repetition, as in Ex 119. When a discord is repeated in
this manner, the dissonant note or notes may be transferred from one

part to any other part, their resolution eventually taking place in those
parts in which they last appear, thus :

Ex. 119.

The Augmented fourth formed in the treble part between the third
and fourth chords, is not incorrect, as both notes belong to the same
chord (see par. 47).
* The chromatic resolutions of the chord of the Dominant seventh will be explained
in Pa*t II., in connection with the chromatic chords upon which such resolutions are
made.
 CHAP. XIX. CHORD OF THE DOMINANT SEVENTH.

123. Tne Figuring of the Chord of the Dominant

Seventh. The complete figuring of this chord would naturally be 5 ,

but unless either the or the third require modification by means of

fifth
an accidental, this is abbreviated to the single figure, 7. In the figuring
in the Minor key, the third of the chord being the Leading-note, the
employment of an accidental to indicate the inflection required by this
note is always necessary. The figuring in the keys of C major and of
C minor would therefore be as follows :

Ex. 1 20. sat

EXERCISES.
I. Regard each of the following notes as the third of a Dominant

chord, prefix the correct key-signature of the major key, and place
under each, the chord of the Dominant Seventh, resolving it (a) upon
the Tonic Triad, (b) upon the Submediant Triad and (c) upon the first
inversion of the Subdominant Triad :

II. Regard each of the above notes as the seventh of a Dominant

chord, prefix the correct key -signature of the major key, and place
under each the chord of the Dominant Seventh, resolving it in the three
ways mentioned in Ex. I.
III. Regard each of the following notes as the fifth of a Dominant
chord, prefix the correct key-signature of the minor key, and place under
each the chord of the Dominant Seventh, resolving it in the three ways
mentioned in Ex. I :

Harmonize the following, introducing a chord of the Dominant

Seventh each of the places indicated, and correctly resolving it upon
at
the next chord :

IV. * *
BS1E 1^5-Ff*
84

VI.
|
 CHAP. XIX. CHORD OF THE DOMINANT SEVENTH. 85

the Tonic, and that should help the pupil to recognize this position of
the chord by its sound.
The resolution of this inversion upon the Tonic Triad in its root
position, as shown in (a), is by far the most familiar and useful resolution.
The resolutions upon the first inversion of the Submediant Triad, as
shown in (b}, and upon the second inversion of the Subdomiuant Triad, as
shown in (c), are very much rarer than the corresponding resolutions of
this discord in its root position.

EXERCISES.
VIII Regard each of the following notes as the seventh of a
Dominant chord, prefix the correct key - signature of the major key
and place under each the first inversion of the chord of the Dominant
Seventh, resolving it (a) upon the Tonic Triad, (b} upon the first
inversion of the Submediant Triad, and (c] upon the second inversion
of the Subdominant Triad. In thetwo latter resolutions take as models
for your exercises, Ex. 122 (b} and (c) :

IX. Regard each of the last four notes of the above Exercise as the
root of a Dominant chord, prefix the correct key-signature of the minor
key, and place under each the first inversion of a chord of the
Dominant Seventh, resolving it in the three above mentioned ways.
Take Ex. 122 (b) and (c) as your models also in this exercise.
Harmonize the following, introducing the chord of the Dominant
Seventh or its first inversion (whichever is
suitable) at each of the
places indicated :

X.

XL * *

18

Harmonize the following, introducing the first inversion of the chord

of the Dominant Seventh at each of the places indicated :
86 HARMONY

SECOND INVERSION.
127. This inversion has the fifth of the original chord for its bass
note, thus :

Ex., 23 .

The seventh of the original chord is now a third, the root a fourth, and
the third a sixth from the bass note, which is the Supertonic of the key.
s*

The complete figuring of this inversion would be 4 but it is abbreviated

,

to 3 unless, as in the Minor key, the sixth requires to be modified by an

accidental. The full figuring is then necessary.

128. Ear Exercises (also in C minor):

Ex. 124.

*** Contrast this inversion, in sound, both with the root position and
first inversion.

This inversion rarely resolves upon any other chord than that of the
Tonic, but it may resolve upon the Tonic chord either in its root position^
as shown above, or in its first inversion, as shown in Ex. 125.

129. Exceptional Progression of the Seventh. When

this inversion resolves upon the inversion of the Tonic chord, the
first

seventh falling a second, as in Ex. 125 (#), the third of the Tonic chord
(the bass note of its first inversion)
is inevitably doubled. Under these
circumstances, although in the Major key this is not desirable, it is
allowed. In order, however, to avoid doubling the third of the Tonic
chord, when the bass of the second inversion of the chord of the Dominant
seventh rises a second to the third of the Tonic chord, the seventh may also
rise a second to the fifth of the Tonic chord^ as in (b). In this form of
resolution, when the root and the seventh are situated as adjacent
notes, that is, at the interval of a second apart, as in (c) and (d), they
must not proceed by oblique motion to an unison, as in (d), but the
root of the Dominant chord must leap to the root of the Tonic chord,
as in (c\ (see par. 166).
 CHAP. XIX. CHORD OF THE DOMINANT SEVENTH.

Ear Exercises (also in C minor) :

Ex. 125.
J-J

Bad.

EXERCISES.
XIV. Regard each of the following notes the seventh of a
as
Dominant chord, prefix the correct key-signature of the major key, and
place under each the second inversion of the chord of the Dominant
Seventh, resolving it (a) upon the Tonic Triad in its root position and
(b) upCH> the Tonic Triad in its first inversion, the seventh resolving
upwards :

XV. Regard each of the above notes as the root of a Dominant

chord, prefix the correct key - signature of the minor key, and place
under each the second inversion of the chord of the Dominant Seventh,
resolving it in the two above mentioned ways.
Harmonize the following, introducing the chord of the Dominant
Seventh, either in its root position, or in its first, or second inversion
(whichever is suitable), at each of the places indicated :

XVI. # * * * * **

Harmonize the following, introducing the second inversion of the

chord of the Dominant Seventh at each of the places indicated
:

XVIII.
 HARMONY.

THIRD AND LAST INVERSION.

130. This inversion has the seventh of the original chord for its bass
note, thus :

Ex. 126.

The root of the chord is now a second from the bass, and the third and
of the original chord are now respectively a fourth and a sixth from
fifth
the bass note, which is the Subdominant of the key. The complete
figuring would be 4 ,
but this is abbreviated to ^ . In the Minor key
the 4 always require"s some form of modification, as illustrated above.

Ear Exercises (also in C minor) :

*** Contrast this inversion, in sound, with the root position, and the
firstand second inversions.
As the seventh of the original chord, which is now in the bass, must
fall a second, this inversion almost invariably resolves upon the first
inversion of the Tonic chord. When the bass note of this inversion is
approached by leap, it is better if the leap be made in an upward
direction, as in (b\ than in a downward one. The progression of fourths
with the bass, in (c\ the first fourth being a Perfect fourth, and the
second, an Augmented fourth, is perfectly correct (see par. 105).
131. The Interval of the Minor Seventh in Melody.
Now that the interval of the Minor seventh may be formed by two notes
belonging to the same chord (the chord of the Dominant seventh), it is
possible to make use of it in a melody or part, at the same time it is not
an interval which should be frequently employed for melodic purposes.
When it is used in the bass part, it is less usual for both notes forming
the interval to be harmonized by the chord of the Dominant seventh,
than for the first note to be harmonized either by the Dominant Triad,
as in Ex. 128 (a), or by the second inversion of the Tonic Triad, as in (b},
and the second note by the last inversion of the Dominant seventh.
The progression of the bass in (), is not an infringement of the rules
referring to the progression of the bass part when quitting a J chord
(par. 96), as F, in one sense, is next to G.
 CHAP. XIX. CHORD OF THE DOMINANT SEVENTH. 89

Ear Exercises (also in

M)
9 HARMONY.

XXV.

r-^cr
XXVI.

(Imp. Cad.)

(Imp. Cad.)

Harmonize the following in accordance with the figures : A

XXVIII. &

|^fc *r-E L uT-

 CHAP. XX. NATURAL MODULATION. 91

CHAPTER XX.

NATURAL MODULATION.

132. MODULATION is the process of passing from one key to

another. The first four chords in Ex. 129 illustrate a modulation from
the key of C to the key of G, which is effected by means of the chord
of the Dominant Seventh in the key of G,* (the key to which the
modulation is made), resolving upon the Tonic triad in that key.
Similarly, the last three chords illustrate another modulation, this time
from the key of G
back to the key of C, which is effected by tne chord
of the Dominant Seventh in the key of C,f (the key to which the modu-
lation is
made), resolving upon the Tonic triad in that key.

A g
I

Ex. 129.
J. J. JL A. JL.

are very frequently effected in the above manner, that is,

chord of the Dominant Seventh (or an inversion of it) in
the key to which the modulation is to be made, and resolving it upon
the Tonic triad (or an inversion of it) in this new key

133. Amodulation, or change of key, only takes place when there

are at least two chords, which definitely leave one key and proceed to
another. Thus, in Ex. 129, the third and fourth chords, taken together,
belong to the key of G
major, and cannot belong to any other key, but
either taken singly couldbe employed in other keys and therefore would
not define the key of major. G The same may be said with reference
to the fifth and sixth chords, as representing the key of C major.
Taken together, they effectually define this key, but taken singly they
cannot do so. Modulations in which the new key prevails for only
two or three chords, as in the above example, are sometimes called
Transitions or Transitory Modulations. \Vhen a new key is definitely
established in the mind of the listener, by the two chords which effect
the modulation being immediately followed by other chords, characteristic
of the new key, the modulation is sometimes described as permanent.
In the following paragraphs, however, every change, of key, whether of
two or more chords, will be described simply as " a modulation."
92 HARMONY.

134. Natural Modulation and Extraneous Modula-

tion. To every key there are certain other keys, which, because of
their nearness in tonality, and the relationship which exists between
their respective key-notes, are called related (or attendant) keys. The
related keys to any major key are, the major keys of the Dominant
and Subdominant, its own relative minor key, and the relative minor
keys of the Dominant and Subdominant. The following shows the keys
related to C major :

F major. C HiajOP. G major.

D minor. A minor. E minor

The related any minor key are, the minor keys of the
keys to
Dominant and Subdominant, its own relative major key, and the relative
major keys of the Dominant and Subdominant. The following shows
the keys related to A minor, and it will be seen that they correspond
with those given above as related to C major, the relative major of
A minor :

D minor. A minor. E minor.

F major. C major. G major.

should be noted that the keys of C major and C minor, are not, in
It
this sense, related keys. When a modulation is made from a key to
one of its related keys it is called a NATURAL MODULATION, and when
it is made to an unrelated key it is called an EXTRANEOUS MODULATION.

The present chapter treats only of Natural Modulation, the subject of

Extraneous Modulation being reserved for a later one (see Part II).

135.The " Link" in a Modulation. In

Connecting every
modulation there is present some " connecting link which forms a bond
"

of union between the key from which the modulation is made, and that
to which the modulation is made. This link may take the form of a
complete chord which can be employed in either key, as in Ex. 130 (a),
where the second chord could be the first inversion of either the
Supertonic triad in C or of the Subdominant triad in A minor, or the
link may be merely a single note which is common to th". two chords repre-
senting both keys, as in Ex. 130 (), where the note E is common both
to the chord of C, and to the first inversion of the chord of the
Dominant Seventh in A minor.

Ex. 130.

136. TheTriad as the Connecting Link.

The following
table of triads in C major and
related keys, will show the pupil, at a
its

glance, the chords which are common to the different keys in any set
of related keys, and which may be employed as connecting links in
 CHAP. XX. NATURAL MODULATION. 93

modulation between these keys. The various triads in the related Keys
are placed below the triad upon the corresponding bass note in the
original key, and those triads which are identical with that in the original
key are written entirely in semibreves, while, in those which differ, the
particular notes which differ are written in black notes.

TABLE FOR COMPARING THE TRIADS IN A SET OF RELATED KEYS.

Ex. 131.

C MAJOR.

- i I
i t
^-, OHHEZHZ P
A minor.

G major.

E minor.

F major.

D minor.
Ete feE=j3g=E3BJ^^=
5 1Q CJ I
ziB t :t

The above table will show that there are four triads in common
between the keys of C and G, C and F, and C and A minor, three
triads between C and E minor and one between C and D minor. Every
major key has then at least one diatonic triad, which is common to
that key and to any key which is related to it, and it is always possible
therefore, when modulating to a related key, to employ a chord as the
connecting link between the two keys. Most related keys, however,
have several of such chords in common, and when modulating between
these keys, it is possible, by the employment of the chords which are
common to both keys, and the avoidance of those chords which belong
" "
only to one key, to, as it were, gradually lean towards the new key,
and thereby effect a modulation with greater smoothness, than would
otherwise be the case. Thus, in the following example, it would have
been possible to have modulated from C major to A minor by the
employment of the first chord and the last two chords only, this
would have been what is sometimes described as a Sudden or Direct
Modulation, but the abruptness of such a progression has been avoided
by placing between the chord of C and the Dominant Seventh in
A minor four other chords, all of which might belong either to the key
of C major or that of A minor. In this example they belong to the key
 HARMONY.

of C major, because a key prevails until a chord appears which effects a

modulation from that key, and as the first chord which definitely
modulates out of C is the chord of the Dominant Seventh upon E,
only this chord and the last one are in A minor, all the previous being
in C major. A modulation which is gradually led up to by chords
common to both keys, is sometimes called a Gradual Modulation.

/L *

Ex. 132.
 CHAP. XX. NATURAL MODULATION. 95
Ex. 133.

139. False Relation. In the construction of modulations, it

frequently happens that two chords are present, situated either next to-
one another, or with only one chord between, in which the same note
(alphabetically) is employed, but inflected differently in each chord, as,
for instance, the B natural and B flat in Ex. 134 (a). In such cases,
the note which is so inflected should, if possible, be kept in the same
part in both chords, as in (^), otherwise what is called a FALSE RELATION
is produced. When the altered note has been correctly introduced, as
in (b), it may then appear in any other part immediately afterwards, as
at*, without creating any bad effect.

^j=J= 5t

1 r-7t f-
Ex. 134.
J. jAL
^/ J- J-

Bad. Good.

The employment of notes standing in false relation to one another

does not always produce a bad musical effect, and it is therefore only in.
those special circumstances in which a bad effect is produced, that
false relation is regarded as a fault. The worst form of false relation
(and the only form which is universally condemned) is that which is
produced between two notes belonging to Common Chords
or inversions of
Common Chords, derived from the same root, as illustrated in Ex. 1 34 (a).
This kind offalse relation is strictly forbidden.
It may help the pupil to understand the full significance of this rule,
if we supplement it by examples of false relation which are allowed.

FALSE RELATION is ALLOWED

(1) Between the notes
of two Common Chords, (or inversions of
first chord is either the root or the fifth
such), when the third of the
of the second, as in Ex. 135 (a) and (b\ respectively.
(2) Between the notes of a Common Chord, (or
an inversion of such),
and the first inversion of a Diminished triad, as in (c).
(3) Between the notes
of a Common Chord, (or an inversion of such),
and a Dominant discord (or other Fundamental discord, see Part II), as
in (d).
(4) Between the minor seventh
of the key, in the Minor key, and
the third of the Dominant chord, when there is one chord between,
as in (<?).
96 HARMONY.
Ex. 135.
()
(a) (*) , (')
,
(*)
,
W ,

'J I

Although none of the above are incorrect, yet a smoother progression

would have been produced, both in (a) and (), by keeping the inflected
note in the same part, as shown below :

Ex. 135. PT m'' -j- ^

j. -&

i i

140. The Doubling of Notes. In passages which modulate,

the rules which regulate the doubling of notes apply to the several notes
of a chord, regarded in that key to which it belongs at any particular
moment. Thus, in the second chord of Ex. 140, the Bass note being
the Dominant of E minor, and not the Leading-note of C, the doubling
of it is perfectly correct.

141. Form of Ear Exercises. Each of the Ear Exercises

which are given in connection with the different modulations, illustrate
two different modulations. Thus, in the first series, which are given as
illustrations of modulations to the key of the Dominant, assuming
that the Tonic chord in C represents the key of C, there is first a
modulation from the key of C to the key of G, the Dominant, and then
a modulation from the key of G back to the key of C. This latter
modulation, regarding G for the moment as the Tonic, is a modulation to
the Subdominant of G. In the second series of Ear Exercises, which are
given as illustrations of modulations to the key of the Subdominant, the
reverse takes place, that is, the first modulation is from the key of C to
that of F, the Subdominant, while the second is from the key of F back
to that of C, which, regarding F for the moment as the Tonic, is a
modulation to the Dominant of F. All the Ear Exercises in this
chapter, which now follow, are constructed upon a similar plan, that is,
each one two different modulations,^^/, a modulation from
illustrates
the key of Cone of its related keys, and, secondly, a modulation
to

(which we call a complementary one), which returns from this related

key back to the original key of C.
 CHAP. XX. NATURAL MODULATION. 97

142. Modulation to the key of the Dominant (by means of

the chord uf the Dominant Seventh and its inversions) with complementary
return to the original key.
Ear Exercises (b) to (e) also in C minor :

*+* BEFORE DICTATING EITHER OF THE EAR EXERCISES GIVEN UPON

MODULATIONS, THE TEACHER SHOULD INVARIABLY ESTABLISH IN THE
MIND OF THE PUPIL THE KEY OF C IN A MORE COMPLETE MANNER THAN
IS DONE IN THE EAR EXERCISES, WHICH ARE MADE AS SHORT AS

POSSIBLE, AND MERELY ILLUSTRATE I HE ESSENTIAL POINTS OF THE

MODULATION. THE PLAYING OF A FULL CADENCE CONSISTING OF THE
CHORD OF THE DOMINANT SEVENTH RESOLVING UPON THE TONIC
CHORD WOULD BE SUFFICIENT.

* &-* * Q H
3^5^-liEEEi
EXERCISE. Taking the above as your models, construct four complete
series ofmodulations to the key of the Dominant, by means of the
chord of the Dominant Seventh and its inversions, starting from, and
returning to, the keys of and G A
flat major, and F and sharp minor. D
In the major keys, the modulations should be made to the major key of
the Dominant, and in the minor keys to the minor key of the Dominant,
as shown in (a) and (f) respectively.
*+* In this, and in all similar exercises in connection with other
modulations, the employment of the root position and every inversion
of the chord of the Dominant seventh should be illustrated in separate
exercises.
Harmonize the following, modulating to the key of the Dominant
at the places marked iand returning to the original key
1
,

immediately afterwards. A chord of the Dominant Seventh, or one of

its inversions, should be employed both in modulating to the Dominant

key and also in returning to the original key, as in the above Ear
Exercises. In figuring the following after they have been harmonized,
it should not be forgotten that all chords in which accidentals are
employed, require those accidentals to be fully indicated in the figuring.
 HARMONY.

ii.

I
I

m. j i

^ Q 1
<--''
II

IV.

v.
Si^
VI.

VII.

VIII.

143. Modulation to the key of the Subdominant, with

complementary return to the original key.

Ear Exercises:

Ex. 137.

EXERCISE. Taking the above as your models, construct two com-

plete series of modulations to the key
of the Subdominant, employing
the chord of the Dominant Seventh and all its inversions, starting from,
and returning to, the keys of A major and B flat minor.
Harmonize the following, modulating to the key of the Subdominant
at the places marked and returning to the original key immediately
afterwards :
 CHAP. XX. NATUKAL MODULATION. 99
IX. , ,

X.

XI.
&
XII.

Harmonize the following, modulating to the keys of the Dominant

and Subdominant, respectively, at the places indicated :

* * It will be noticed in these

# Exercises, that the modulation to the
key of the Dominant always comes before that to the Subdominant. In
passages which modulate to both of these keys, this is the order in which
these two modulations generally occur.
Half close. D. S.D.
XIII

144. Modulation from a Major key to the key of the

Relative Minor, with complementary return to the original key (that
is, a modulation from a Minor key to the key of the Relative Major).
Ear Exercises:
Ex. 138.

r r [
!

. i i
r i i
100 HARMONY.

EXERCISE. Taking the above (Ex. 138) as your models, construct

two series of modulations to the key of the Relative Minor, employing
the chord of the Dominant Seventh and all its inversions, starting from,
and returning to, the keys of B flat and E major.
Harmonize the following, modulating to the key of the Relative
Minor at each of the places indicated :

XVII. ,
,

XVIII.
I-

*E=3E 3t3:
I .

145. Modulation from a Minor key to the key of the

Relative Major, with complementary return to the original key.

Ear Exercises:

V -G>- I ! ^\
I I

=M-'-M^-^aEE
EXERCISE. Taking the above as your models, construct two series
of modulations to the key of the Relative Major, employing the chord
of the Dominant Seventh and all its inversions, starting from, and
returning to, the keys of G minor and C sharp minor.
Harmonize the following, modulating to the key of the Relative
Major at each of the places indicated :

XIX. ,
,

EEEsE

Harmonize the following, making a suitable modulation at each of

the places indicated. It should be noticed that after a modulation, the
new key is sometimes employed for one or more bars, and also that
when the line is extended thus, it should be followed \
by a ,

modulation to another related key :

XXI. ,
, , ,

T r
 CHAP. XX. NATURAL MODULATION. 101
XXII.

146. Modulation from a Major key to the Relative

Minor key of the Dominant, with complementary return to the
original key (that is, a modulation from a Minor key to the Relative
Major of the Subdominani}.
Ear Exercises:
Ex. 140.

EXERCISE Taking the above as your models, construct two series of

modulations to the Relative Minor key of the Dominant, starting from,
and returning to, the keys of E flat and B major.

-
Harmonize the following, modulating to the Relative Minor key of
the Dominant at each of the places indicated
XXV.
:

XXVI.

147. Modulation from a Minor key to the Relative

Major of the Subdominant, with complementary return to the
original key.
Ear Exercises :-

Ex. 141.
102 HARMONY.

EXERCISE. Taking the above (Ex. 141) as your models, construct

modulations to the Relative Major key of the Subdominant, starting
from, and returning to, the keys of E minor and F minor.
Harmonize the following, modulating to the Relative Major key of
the Subdominant at each of the places indicated :

XXVII. , ,

XXVIII.
ja
-^:
Harmonize the following, making a suitable modulation at each of
the places indicated :

XXIX.

XXXII. ,

_LJ
^-'-r^-H '

. .#*

148. Modulation from a Major key to the Relative

Minor of the Subdominant, with complementary return to the
original key, (that is, a modulation from a Minor key to the Relative
Major of the Dominant}.
Ear Exercises:
I I

-
Ex. 142.

EXERCISE. Taking the above as your models, construct modulations

to Relative Minor key of the Subdominant, starting from, and
the
returning to, the keys of A
flat and F sharp major.
 CHAP, XX. NATURAL MODULATION. 103

Harmonize the following, modulating to the Relative Minor key of

the Subdominant at each of the places indicated :

XXXIII.

i49- Modulation from a Minor key to the Relative

Major of the Dominant, with complementary return to the
original key.
Ear Exercises:
'

~ , ! I I I I
i*^n. j

Ex. 143.
J. J. J

EXERCISE. Taking the above as your models, construct modulations

to the Relative Major key of the Dominant, starting from, and returning
to, the keys of D minor and G sharp minor.

Harmonize the following, modulating to the Relative Major key of

the Dominant at each of the places indicated :

XXXV. ,
,

Harmonize the following, making a suitable modulation at each of

the places indicated :

XXXVII.

XXXVIII.
J
fil-T:

"^MT"
m
104 HARMONY.

XXXIX.

XLI. Taking Exercises XIII to XVI as your models, construct

passages of eight bars in length, in the keys of A and E flat major, and
B and F minor, illustrating the employment of a half cadence in the
second bar, a modulation to the Dominant at the fourth bar, and to the
Subdominant at the fifth or sixth bar.
* * In this and the two following exercises, the pupil may proceed
#
upon very similar lines to those suggested in connection with four-bar
passages in Chap. XVII, starting thus :

Model framework in A major.

iPr-j- e ^ i
E
 CHAP. XXI. DIATONIC CHORDS OF THE SEVENTH.

CHAPTER XXI.

THE DIATONIC (OR SECONDARY) CHORDS OF THE SEVENTH.

150. In addition to the chord of the seventh upon the Dominant, a

chord of the seventh, formed of the diatonic notes of the scale, may be
employed upon any other degree of the major or minor scales.
Ex. 144.

An examination of the nature of these different chords, will show that

they differ considerably with regard to the quality of the intervals of
which they are composed, and not one of them, in this respect,
corresponds exactly with the chord of the Dominant seventh.
151. In former times, when these chords were employed, they were
subject to very strict treatment. It was necessary that the seventh
should be prepared, by being present as a concord in the previous chord
and in the same part, and that it should be resolved^ falling a second to
the third of a chord whose root was a fourth above, or a fifth below, that
of the discord, thus :

Ex. 145.

These restrictions never had universal acceptance and are

have
practically disregarded by modern composers. As, however, in some
of the more dissonant forms of these chords, such preparation and
resolution greatly add to the smoothness of the musical effect which is
produced, in the present chapter, the above chords will be treated in
the strict manner, and in the Exercises which follow, they must always
be prepared and resolved according to the above mentioned conditions.
It must be borne in mind, that the special treatment of the seventh,
when it is employed in connection with the Leading-note Triad in both
Major and Minor keys, and the Supertonic and Mediant Triads in the
Minor key, in no way interferes with the special treatment required by
other dissonant notes of the same chord (see Chap. XVI).
to6 HARMONY.

152. EarExercises. The most useful of these chords of the

seventh, is that upon the Supertonic, and the following Exercises show
the employment of this chord, correctly prepared and resolved, in its
root position and inversions :

Ex. 146.
* *
i
I

-r'-rr -vrPV
I J..
-S-ji.pl.

r 1 r

Ex. 147 shows a progression of Diatonic chords of the seventh,

employed sequentially. Except in such progressions, a chord of the
seventh upon the Subdominant resolving upon a chord of the seventh
upon the Leading-note triad, as at (a), is rarely employed. The
sequential nature of the progression also explains the doubled Leading-
note, at (a). It will be noticed that in every other chord of the seventh,
the fifth is omitted. This is necessary to avoid a progression of
consecutive fifths :

()
=?S^
,

I
*-i+
v ' '
i i
r r
Ex. 147.
J J
+
] I !

-
<^s M\ b f m~~ +
p=^=t=p=n 7 7
^

153. The figuring of diatonic chords of the seventh and their

inversions is the same as the figuring of the chord of the Dominant
seventh and its inversions, both being made up of a note with its third,
fifth, and seventh. The difference between the various chords of the
seventh is determined solely by the quality of the several intervals, and
of this the figuring takes no account, unless it is necessary to express it
by means of accidentals.

EXERCISES.
I. Construct progressions similar to those in Ex. 146, showing the
employment of a diatonic chord of the seventh upon the Supertonic,
and all its inversions, correctly prepared and resolved, in the keys of
A major and F minor.
Harmonize the following, introducing a diatonic chord of the seventh
at each of the places indicated. The root position to be employed in
(II), the first inversion in (III), the second inversion in (IV), and the
 CHAP. XXI. DIATONIC CHORDS OF THE SEVENTH. 107

last inversion in (V). Note carefully the places where modulations

occur :

II. * * *

1 P

i
I

m.

i
i

iv. *i

V.

Harmonize the following, in accordance with the figuring

VI.
lLTl
~

7 7 7 6 6
5

6464 6466 I
| |

111
io8 HARMONY.

CHAPTER XXII.

UNESSENTIAL NOTES. AUXILIARY NOTES, PASSING NOTES, AND

ANTICIPATIONS.

\Thtre are no separate Ear Exercises given in connection with this

chapter,but most of the musical examples will be found suitable for
employment as such^ having been constructed with this end in view.']

154. Notes which are sounded in connection with chords of which

they do not form a real or essential part, are called UNESSENTIAL NOTES.
Thus, in the following example, in which the common chord of C is
repeated throughout three bars, the notes, (indicated by asterisks), which
do not form part of this chord, but which are employed in connection
with the several notes of the chord to elaborate the treble part in the
first bar, and the bass part in the second bar, are Unessential Notes.

Ex. 148.

As unessential notes are always dissonant against the prevailing

harmony, they are also frequently described as UNESSENTIAL DISCORDS.
Two of the most important, as well as the most useful kinds of
unessential notes, are AUXILIARY NOTES and PASSING NOTES, both of
which will be considered in the present chapter, while another kind,
almost equally important, called SUSPENSIONS, will be considered in the
next chapter.

155. AUXILIARY NOTES. Auxiliary notes are unessential

notes formed at the distance of a second, either above or below the
harmony notes to which they proceed, and which form their Resolution.
An auxiliary note may be approached either by step, as in Ex. 149 (a),
or by leap, as in (b) ; or it may be preceded by a rest, as in (<:). When
an auxiliary, note is approached by step, as in (a), it is always preceded
and followed by the same harmony note.
 CHAP. XXII. UNESSENTIAL NOTES. 109-
Ex. 1 49.
(a) '"
*

w =
I 10 HARMONY.

III. An auxiliary note formed below the harmony note upon

which it resolves, when approached
by leap, is almost invariably at the
distance of a semitone below, see Ex. 153. An auxiliary note so
formed, may be approached by the leap of an Augmented interval, if
desired.

Ex. 153.

IV. An
auxiliary note which is formed a semitone below a harmony
note, almost invariably written as a Diatonic semitone below, as in
is

Ex. 153, and not as a Chromatic semitone below, as in Ex. 154.

Ex. 154

157. PASSING NOTES. A Passing note is an unessential

note approached by step from a harmony note, but which, instead of
returning to the same harmony note (as in the case of an Auxiliary note
approached by step) continues or "passes" on in the same direction, and
resolves upon another harmony note, as in Ex. 155. The harmony
notes upon either side of a Passing note may be harmonized by the
same chord, as in (a), or by different chords, as in (ft).

* *

fir-

Ex. 155.
 CHAP. XXII. UNESSENTIAL NOTES. Ill

&f=
112 HARMONY.

individual beats, yet they may also be employed upon the strong beats,
or upon the stronger portion of individual beats. In such positions they
are similar in nature to appoggiaturas, thus :

* *

1
Ex. 160.
N
I
1 6 1. False Relation and Unessential Notes. In the
above example, there is no incorrect False Relation created between the
F sharp in the Treble part and the F natural in the Alto and Bass parts
of the previous chord. The following rule refers to this and all similar
passages. Chromatic unessential notes, when correctly formed and resolved,
do not create incorrect False Relation with the harmony notes of their own
chord or of adjacent chords (see also Ex. 157).
162. Changing Notes. Either an Auxiliary note or a Passing
note may, instead of immediately resolving upon a harmony note, leap
a third to another unessential note beyond this harmony note, the
second unessential note then proceeding to the harmony note, which
would have been the resolution of the first unessential note. The
elaboration of (a) to form (b) illustrates these points :

(*)

The two unessential

A
m
notes so formed next to one another, are called
CHANGING NOTES.
"
Auxiliary notes, having some resemblance to changing notes," may
be formed by the elaboration of a series of two or more adjacent
harmony notes, the auxiliary notes leaping a third to their resolution,
thus :

* * # *

Ex. 162.
 CHAP. XXII. UNESSENTIAL NOTES.

163. Unessential Notes in two parts. Unessential notes

may move together in two parts, or one part may be formed of
unessential notes and the other of harmony notes, while some of the
essential notes of the chord are sustained, as shown in Ex. 163, where
the unessential notes are indicated by asterisks. In such cases the
progression formed by the joint movement of these two parts must be
correct, quite apart from their relation to the notes of the chord which
are remaining stationary, thus :

Bad.

Passing notes proceeding in two parts by contrary motion, may

continue on in the same direction, irrespective of the dissonances which
are created by their progression, until they simultaneously reach harmony
notes, thus :

J J
Ex. 164.

When auxiliary notes proceed in two parts in thirds or sixths,

they may be situated at the distance of either a tone or a semitone
from their resolution, provided both parts move diatonically, as in
Ex. 165 (a), but if either part move a semitone which is produced by
chromatic alteration, the other part must also move a semitone as at (b)

^
and f :

(a) (b) (c)

Ex. 165.
4J.4 .j. j j

164. Anticipations. When one or more notes of a chord are

proceeded to previously to the other notes of the same chord, such notes
are said to be anticipated, and the note or notes which form the
anticipation, and which are always upon a weaker beat, or a weaker
part of a beat, than the note or notes which they anticipate, are
called ANTICIPATIONS, thus :
114 HARMONY.
* *

J^V^

m
Ex. 166.

165. HARMONIC PROGRESSION in connection with

Unessential Notes. Most of the rules of progression which have
already been given in connection with harmony notes, apply also to
progressions into the formation of which Auxiliary notes or Passing notes
enter.* All such faulty progressions as those illustrated below, although
entirely due to the introduction of Auxiliary notes, are forbidden :

5-5

Ex. 167.

5
- 5 (see par. 121.)

Although, as shown above, the introduction of unessential notes may

easily change a correct progression into an incorrect one, yet their
introduction will never change an incorrect progression into a correct
one. Thus, the forbidden consecutives between the harmony notes in
the following are bad, in spite of the passing notes which come between
them :

8 8

Ex. 1 68. r

i i

5 5

1 66. The
following rules of progression must be borne in mind
when working the Exercises at the end of this chapter. No two parts
may proceed by oblique motion from a second to a unison, as in Ex. 169 (#),
but the reverse of this progression, to proceed from a unison to a second,
as in (b\ is perfectly good :

* This from the composers point of view,

is not strictly accurate, but as
statement,
far as the student of concerned, in matters of progression, no "exceptional
Harmony is

progressions," such as those mentioned in the chapter upon Exceptional Progression

(Part II). should be allowed in these early stages.
 CHAP. XXII. UNESSENTIAL NOTES.

(a) (6)
2 I 2 I I 2

Ex. 169.
-I 1-
-h-i

Bad.
F
Good.

This rule applies both to essential (or harmony notes) and unessential
notes (see par. 129).
No two parts may proceed in seconds, (or ninths], or sevenths,
with one another. Such progressions as the following, in which
consecutive seconds and sevenths are formed by the employment of
unessential notes proceeding to notes belonging to inversions of the
Dominant Seventh, should be avoided :

f G> m """"
*-
n6 HARMONY.

III. Show the formation of Passing Notes, both ascending and

descending, between each of the notes of the Tonic triad in the keys of
D major and F minor (see Ex. 155 (a) ).
IV. the formation of Passing Notes, both ascending and
Show
descending, between notes of the Tonic and Subdominant triads, and
between notes of the Tonic and Submediant Triads, in the keys of B flat
major and E minor (see Ex. 155 ()).
V. Show the formation of Changing Notes in connection with each
of the notes of the Tonic triad, in the keys of D
flat major and B minor

(see Ex. 161).

VI. Show the formation of Anticipations in the treble part, in
connection with Perfect cadences in the keys of E major and D minor.
VII. Show the formation of unessential notes in two parts, in
connection with the Tonic triad in the keys of G major and B minor
(see Ex. 163).

Harmonize the following, treating the notes indicated, as unessential

notes :

VIII. # r
i^l

* *
 CHAP. XXII. UNESSENTIAL NOTES.

44-

J3.

* *

XIII.

Harmonize the following in accordance with the figuring. Any

figuring which may seem unfamiliar to the pupil, will, when the passage
is filled up, be found due to the employment of Passing notes :

XIV.

- 6 - 6 - 16

XV.

p^-p-u gg^pc
nS HARMONY.

CHAPTER XXIII.

SUSPENSIONS.

1 68. A a note tied or suspended over a chord of which

SUSPENSION is

it forms no essential but to one of the notes of which it can pass

part,
by moving the step of a second. Thus, in Ex. 172, the notes in the
treble part, which are sustained from the previous chord over the chord
of C (indicated by asterisks), and then proceed to a note of that chord
by moving the step of a second, are called SUSPENSIONS.
<"'

Ex. 172.

169.A suspension must be present as an essential or harmony note

in the immediately preceding chord to that in which it is suspended, and
it must be heard in the same part as that in which it appears as a suspen-

sion. The harmony note in the preceding chord which is identical with
it, and
to which it is generally tied, is called THE NOTE CF PREPARATION
or simply THE PREPARATION, and this note should be at least equal
in length to the suspension itself. The note to which the suspension
proceeds, is called THE NOTE OF RESOLUTION or simply THE RESOLUTION.
A suspension always occurs either upon a stronger beat, or upon the
stronger portion of a beat, than the note upon which it resolves. The
most useful suspensions are, the suspension of the note above the root
of a triad, shown in Ex. 72 (a), called the 9 8 SUSPENSION, and the
suspension of the note above the third of a triad, shown in (b\ and called
the 4 3 SUSPENSION. The suspension of the note above the fifth of a
triad, shown in (<:), and called the 6 5 SUSPENSION, is less useful than either
of the others, and its character as a suspension is somewhat ambiguous.
It is more frequently met with in an inverted form than in its root

position.
170. Retardations. It is possible for some suspensions to resolve

by second instead of falling one, they are then frequently called

rising a
RETARDATIONS. The most important of these is the suspended or
retarded Leading-note. This is generally suspended over the Tonic
 CHAP. XXIII. SUSPENSIONS.

triad, as in Ex. 173 (a), whenit becomes a 7 8 SUSPENSION OR RETARDA-

TION. It may also be employed over the Submediant (see par. 186).
The suspended ninth is
occasionally resolved by rising to the tenth, (or
third), as in (), but this form of resolution is rare.

Ex. 173.
120 HARMONY.

172. In this suspension the suspended note, which may appear in

either of the upper parts, must always be not less than a ninth above the
root of the chord, whether the root be present only in the bass or
doubled in one of the inner parts. That is to say, the ninth may never
be employed at the interval of a second from the root when this is
sounded simultaneously with the ninth, as in the following example
(see par. 166) :

Ex. 176.

173- Ornamental Resolutions. A suspension, before pro-

ceeding to its regular resolution, may first of all move to some other note
of the chord, from which it may proceed either direct to its regular
resolution, as in Ex. 177 (a), or by means of one or more intermediate
notes, as in (&} and (c). In these cases, what are called "ornamental
resolutions" of the suspension are formed. Another, and even more
familiar form of ornamental resolution, is shown in (d).

Ear Exercises (also in C minor) :

Ex. 177.

\i cj ^
 CHAP. XXIII. SUSPENSIONS. I2t

is for a change of chord to take

place at the resolution, as in (b\ where
the suspended note appears as a ninth above C, but is resolved upon
the third of the triad of A. In such resolutions the figuring must be
modified according.
() (*)

* 1

'

Ex. 178. I

'"
I I I

9 6 9 3

175. TheDoubling of Notes. In a suspension, the notes of

the chord which may be doubled are the same as if the suspension
were not present, such doubling however is subject to the following
special condition When the note upon which a suspension resolves is
:

sounded in one of the upper parts simultaneously with the suspension

itself, (not of course at the same pitch, but at the distance of one or more

octaves), it must be approached by step in the contrary direction to which

the suspension resolves, thus :

Ex. 179.

Good. Not good.

1 76. Harmonic Progression. As a suspension is an unessential

note which only temporarily takes the place of a harmony note,
progressions which are incorrect without a suspension cannot
be corrected

by the introduction of a suspension, thus :

Ex. 1 80.
I

-- i
r'i j
-*- j&_

\
i

8 8 8 8
Bad. Bad.

Paragraphs 173 to 176 refer to ALL suspensions and inversions of such.

122 HARMONY.

EXERCISES.
Taking the Ear Exercises, Ex. 175, as your models, construct a series
of progressions showing the 9 8 suspension correctly prepared and
resolved, and employed in connection with all the available common
chords and triads in the keys of E major and F minor.
*** The Augmented second between the sixth and seventh degrees
of the Harmonic Minor Scale, prevents the suspension of the Leading-
note in the Minor key, in suspensions which resolve d(nunward. This
should be borne in mind when woiking the above, and all Exercises of
a similar nature.
Harmonize the -following, introducing a 9 8 suspension, correctly
prepared and resolved, at each of the places indicated :

I. I
* * |

11
i
i
i

^E JTUTr
* I
* I
* i
*_J *
Taking the Ear Exercises, Ex. 177, as your models, construct a series
of progressions, showing different ornamental resolutions of the 9 8 sus-
pension in connection with (a) the Tonic Triad, and (b} the Subdominant
Triad, in the keys of E major and minor. G
177. First Inversion:

Ex. 181.

7 6
The third of the original chord now being in the bass, the suspended
ninth has become a suspended seventh
resolving upon the sixth, both
being accompanied by the third from the bass, that is, the fifth of the
original chord. The figuring of this Suspension, which is simply 7 6,
must not be confused with the figuring of the chords of the seventh, in
which the figure 7 includes a 5 as well as a 3. In the filling up of
figured basses, an examination of the chord upon which the 7 resolves,
will show conclusively whether the chord indicated by the 7 is an
essential discord or a suspension.
Ear Exercises:
Ex. 182.

J- J
K J J- i J- A
(Also in C minor.) (Also in C minor.)
 CHAP. XXIII. SUSPENSIONS.

As a chord of the sixth may be employed upon every degree of both

major and minor scales, this suspension may also be employed upon

every degree upon which it can be correctly prepared and resolved.

EXERCISES.
Construct a series of progressions showing the first inversion of the
9 8 suspension (7 6) correctly prepared and resolved, and employed in
connection with all the available chords of the sixth in the keys of
A flat major and F sharp minor. (Models, Ex 182.)
Harmonize the following, introducing the first inversion of the 9 8
suspension at each of the places indicated :

III,. * * *l * I
*

IV. fX
*
t3t

Ifh r"^
124 HARMONY.

EXERCISES.
Construct a series of progressions showing the second inversion of the

9 8 suspension ( s ~) correctly prepared and resolved, and employed in

connection with each of the Primary triads in the keys of B major and
G minor. (Models, Ex. 184.)
Harmonize the following, introducing the second inversion of the 9 8
suspension at each of the places indicated
*':'*'*
:

V. *

&=r***^=3&
^ cT n*
LJ i

179. The Inversion with the Suspension in the Bass:

Ex. 185. ^==l^t^~^

7
4
2
The suspended ninth of the original chord being now in the lowest part,
the other notes of the chord are a second, a fourth, and a seventh above
the suspended note, and become, respectively, a third, a fifth and an
octave from the note upon which the suspension resolves. When the
root is heard simultaneously with the suspension, as in the above
example, it must be approached by step in the opposite direction to the
resolution of the suspension (see par. 175). When the root is not present
the figuring of the chord is * ~ This
~ must not be confused
simply .
J
with the same figures when representing the last inversion of a chord of
the seventh.
Ear Exercises (also in C minor) :

Ex. 1 86.

o j-J-J < : L!_L_.

^ 1=
J- J- -J-

(see par. 71.)

 CHAP. XXIII. SUSPENSIONS. I2 5

In this inversion, progressions like the following, which are incorrect

without the suspension, must be carefully avoided (see par. 176) :

Ex. 187.
r.26 HARMONY.

THE 4 3 SUSPENSION.
1 80. When a note which is suspended over a chord is resolved by
falling a second to the third of that chord, it is called a 4 3 SUSPEN-
SION OR A SUSPENDED FOURTH :

Ex. 1 88.

4 3

In root position, this suspension being generally accompanied by the

its

perfect fifth from the bass, is rarely employed except over those degrees
of the scale upon which common chords can be formed, and the figures
4 3 imply the fifth, which is always present with the fourth. When
employed over the Dominant it is frequently accompanied by the
chord of the Dominant seventh. The figuring is then J ^ .

Ear Exercises (also in C minor) :

Ex. 189. | ,_ , I
K-S ,^

In suspension either the root or the fifth should be doubled.

this
The third, when a minor third,
however, and when approached by step,
is sometimes heard
as in the third exercise above, simultaneously with
the suspended fourth at the distance of a ninth, but never at the
distance of a second.

EXERCISES.
Taking the above Ear Exercises as your models, construct a series of
progressions showing the 4 3 suspension, correctly prepared and resolved,
and employed in connection with all the available common chords in
the keys of E flat major and sharp minor. G
Harmonize the following, introducing a 4 3 suspension, correctly
prepared and resolved, at each of the places indicated :

XI. . * * * *

XII.
 CHAP. XXIII. SUSPENSIONS. 127

Construct a series of progressions, showing different ornamental

resolutions of the 4 3 suspension in connection with (a) the Tonic
Triad, and (b) the Dominant Triad, in the keys of A flat major and
F sharp minor (see Ex. 177).

1 8 is First Inversion:

Ex. 190.
HI
The third being in the bass, the suspended fourth has now become a.
suspended ninth resolving upon the octave, both being accompanied by
the third and sixth from the bass. This inversion cannot be employed
upon the Leading-note as it would involve the doubling of this note.
Ear Exercises (also in C minor):

^.bj^^
?= I

m
Ex. 191.
J.

it=daJ:

EXERCISES.
Construct a series of progressions, showing the first inversion of the
4 3 suspension (^ ) correctly prepared and resolved, in connection with
all the available first inversions of triads, in the keys of flat major A
and C sharp minor. (Models, Ex. 191.)
Harmonize the following, introducing the first inversion of the 4 3.

suspension at each of the places indicated :

XIII. * *

182. Second Inversion:

Ex. 192.

The fifth of the original chord being in the bass, the suspended fourth
has now become a suspended seventh resolving upon the sixth, both.
128 HARMONY.

being accompanied by the fourth from the bass, which is the root of
the chord. The progression of the bass note of this inversion, is of
course subject to the same rules as those which govern the progression
of the bass notes of % chords generally. (See par. 96.)
Ear Exercises (also in C minor) :

rj"j_r- '

K^I

Ex. 193.

EXERCISES.
Construct a series of progressions showing the second inversion of the
4 3 suspension (J _.), correctly prepared and resolved, in connection
with the second inversion of each of the Primary triads, in the keys of
A major and E flat minor. (Models, Ex. 193.)
Harmonize the following, introducing the second inversion of the
4 3 suspension at each of the places indicated :
 CHAP. XXIII. SUSPENSIONS. 12Q

EXERCISES.
Construct a series of progressions showing the 4 3 suspension
employed in the correctly prepared and resolved, in
bass (2 T),
connection with all the available first inversions of triads in the keys of
E major and B flat minor. (Models, Ex. 195.)
Harmonize the following, introducing the 4 3 suspension with the
suspension in the bass at each of the places indicated :

XVII.

Harmonize the following in accordance with the figures :

XIX.

643 I

643'
I

986
6-
7656
4- 3 5

5 5
- 7687 6 6 7 4 3
2- 2 4-43
XX.
1^1 jy-t
 HARMONY.

the same bass note. Only when the suspension and its resolution are
sounded simultaneously, is the character of the chord as a suspension
clearly defined. In this form, it is perhaps most useful in its second
inversion, as shown in Ex. 197 (c), although it is not a very familiar
chord in any form, or in any inversion. The figuring of the different
inversions is given below.
Ear Exercises (also in C minor) :

Ex. 197.
(a) Root pos. (6) ist Inv, (c) 2nd Inv. (of) Susp. in bass.

EXERCISES.
Taking the above Ear Exercises as your models, construct similar
series of progressions showing the 6 5 suspension, and its inversions,
correctly prepared and resolved, in connection with the Tonic triad, in
the keys of B flat major and E minor.
Harmonize the following, introducing the 6 5 suspension, or one of its
inversions, at each of the places indicated. The letters refer to the
different positions of the chord as illustrated in the Ear Exercises :

XXI. (a) . (f) (c) (a) (b) , ,(</)

f@t

Harmonize the following in accordance with the figures :-

XXIII.
i
/W\ w
hSyy
 CHAP. XXIII. SUSPENSIONS. 131

THE SUSPENDED (OR RETARDED)

LEADING-NOTE.
185. All the suspensions which fall a second to their resolution have
now been considered, and there only remains one other suspension
to be referred to, that is, THE SUSPENDED (OR RETARDED) LEADING-NOTE,
when resolves by rising a second to the Tonic.
it When the Leading-
note is suspended in this manner over the Tonic chord, it forms a 7 8
suspension, the 7 in this suspension including both a 5 and a 3, thus :

Ex. 198*.
I
3
This suspension may be employed in any of its inversions, but like the
6 5 suspension, its character as a suspension is only clearly denned
when the suspended note and its resolution are sounded simultaneously,
as in the first and last examples given below. The figuring of the
suspension in the different positions in which it is generally employed,
is shown below.

Ear Exercises (also in C minor) :

* *""
Kb

Ex. 199.
132 HARMONY.

EXERCISES.
Taking the Ear Exercises, Exs. 199 and 200, as your models, construct
similar series of progressions showing the employment of the suspended
Leading-note in connection with (i) the Tonic chord in its root position
and inversions, (2) the Submediant triad, and (3) the first inversion of
the Subdominant triad, in the keys of F sharp major and Gminor.

Harmonize the following, introducing the suspended Leading-note in

connection with the Tonic triad, or an inversion of it, at each of the
places indicated:

XXIV. *

XXV. I I

1 I- icJ:

Harmonize the following in accordance with the figuring :

XXVI.
"6^$i
 CHAP. XXIII. SUSPENSIONS, 133

Ear Exercises (also in C minor) :

Ex. 201.
(*) M <<O
|
Ypj |^ J skE
I I I/-N 1 1 I

'
,
I
^ _-
^ I

I
I ^ 1

J^J^^T; -J, i!

ist Inv.

EXERCISES.
Taking the above Ear Exercises as your models construct similar
series of progressionsshowing the employment of the various forms of
double suspensions, correctly prepared and resolved, in connection with
the Tonic triad in the keys of G major and F minor.

Harmonize the following, introducing a double suspension at each of

the places indicated :

XXVII. * *l
*erwe

XXVIII. *l

XXIX.
Pi

r ^ ,-
 J
34 HARMONY.

Harmonize the following in accordance with the figures :

XXX.
I

^_ | fj__
:
^ 1
Q __
a
 CHAP. XXIII. SUSPENSIONS. 135

190. Suspensions in connection with Discords. Suspen-

sions are generally employed in connection with triads and their
inversions, but, provided they are correctly prepared and resolved, they
may be also employed in connection with discords, the only suspension
however, which is at all frequently employed in connection with such, is
the 4 3 suspension. This suspension has already been shown in con-
nection with the chord of the Dominant seventh.

EXERCISES.
Taking Ex. 202 (a) and (&) as your models, construct similar pro-
gressions showing the employment of triple suspensions in connection
with the Tonic and Submediant triads, in the keys of E major and B flat
minor.
Harmonize the following, introducing a triple suspension at each of
the places indicated:

XXXI. * I * I
* I
* I
* I

XXXII.

^
^ ^ m
Harmonize the following in accordance with the figures :

XXXIII.
(?*)" \J *
136 INDEX.

INDEX.
[ The numbers always refer to the Paragraphs except in those instances in which it i$

otherwise stated}.

Accented auxiliary notes and passing notes, 160.

Accidentals in figuring, 66, 88,
Analysis of chords, page 38 # % .

Anticipations, 164.
Augmented intervals in melody, 47, 59, 61, 122; in Sequences, 115.
Augmented triad on Mediant, 84, 103, 108 ; first inversion, 86 ; second
inversion, 108 ; as Minor thirteenth, 87.
Authentic cadence, 51, in.
Auxiliary notes, 154, 155; accented, 160 ; employment of Melodic Minor Scale, 159 ;

False relation, 161. Harmonic progression, 165 ; in two parts, 163.

Bass figured, 66, 88.

Bass part, harmonization of, 41, 76 ; progression of, 75 ; repeated notes, 75 ?
with six-four chords, 96, 131-

Cadences, no; Authentic or Perfect, in, 120; False or Deceptive, 113^

Final, 51, no, in ; Full, in; Half, 97, 113; Imperfect, 97, 113;
Interrupted, 78, 113, 120;
Inverted, 112; Middle, 78, 97, no, 112, 113;
Plagal, 51, in with cadential six-four, 97.
;

Cadential six-four chord, 97.

Changing notes, 162.
Chromatic intervals, 16.
Chromatic scale, 5.
Close (see Cadences).
Close position of chords, 24.
Common chords, 20 figuring
; of, 66 ; inversions of, 62.
Compass of voices, 21.
Compound interval, 17*
Conjunct and disjunct movement, 38.
Connecting link in a modulation, 135; the triad as, 136; the Tonic triad, 137;
the six-four chord, 138.
Consonant and dissonant intervals, 15.
Consecutive fifths, 36 ; by contrary motion, 37 diminished fifths, 92 ; perfect and
;

diminished, 83, 91 ; with the bass, 105 augmented and perfect, 109.
;

Consecutive fourths with the bass, perfect, 101 perfect and augmented, 105 ; \.

with unessential notes, 167.

Consecutive octaves and unisons, 36 ; by contrary motion, 37.
Consecutive seconds (or ninths) and sevenths, 166.
Contrary motion, 33.
Crossing of parts, 26.

Deceptive cadence, 113.

Degrees of scale, names of, 10.
Diatonic chords of the seventh, 150.
Diatonic intervals, 16
Diatonic scales, 5, 6.
Diminished interval in melody, 48, 59 ; leap of seventh in bass, 71.
 INDEX. 137

Diminished triad on supertonic of minor key, 80, 103, 106 first inversion, 82
; ;

second inversion, 103, 106.

Discords, 103, 119; diatonic, 150; repetition of, 122; unessential, 154.
Disjunct movement, 38.
Dissonant interval, 15.
Dissonant triads, 103, 115.
Dominant Seventh, chord of, 118; with 4 3 suspension, 180; figuring compared
with that of 9 8 suspension, 177, 178, 179; suspended over Tonic or Sub-
mediant, 188.
Dominant triad, major key, 29 ; minor key, 57 ; first inversion, 63 ; to Sub-
dominant triad, 50 ; to Submediant triad, 75, 77 ; to Supertonic triad, 81 II,
82 ; second inversion, 99.
Double Suspensions, 187.
Doubling of the Leading-note, 29; in Sequences, 115, 152.
Doubling of notes, in major triads, 22 in minor triads, 54
; ; in the Dominant
triad, 29, 57 ; inversion of triads, 65, 69
in the first in the Leading-note triad,
;

90, 104 ; the major third, 70; in the Submediant triad, 77 ; in Sequences, 115 ;
in Modulations, 140; in Suspensions, 175.

Exceptional progression, in Tonal Sequence, 115 ; of Dominant Seventh, 129.

Exceptional resolution of Dominant Seventh, 129; of suspensions, 174.
Exposed octaves and fifths, 35.
Extended position of chords, 24.

False cadence, 113.

False Relation, 139 in connection with unessential notes, 161.
;

Fifth, omission of, in common chords, 22; in the Tonic triad, 39; in the chord of
the Dominant Seventh, 120.
Figured basses, 66, 88, 97.
Figuring of chords, 66, 88, 97, page 38 # ; %
of Dominant Seventh, 123 ; compared
with 9 8 suspension, 177, 178, 179; of suspensions, 189.
Final cadences, 51, III.
Four-part harmony, 21.
Full cadence, ill.

Half cadence or half close, 97, 113.

Harmonic Progression, 32, 33, 50, 83. 91, 98, 101, 105, 109, 121 ; in connection
with suspensions, 176 ; unessential notes, 165-7.
Harmonization of basses and melodies, 41, 45, 76.
Harmony and its
subject matter, I.
Hidden fifths, 35
; allowable, 43, 81 (II).
Hidden octaves, 35 ; allowable, 43, 98 ; forbidden form of, 1 21.

Imperfect consonances, 15.

Imperfect cadence, 97, 113.
Interrupted cadence, 78, 113; with Dominant Seventh, 120.
Intervals, ii; defined, 12, 13; classified, 14; inversion of, 18.
Inversions of common chords, 62.
Inverted cadences, 112.

Key, 4 ; major keys, 7 ; minor keys, 8 ; relative major and minor, 9 ; related or
attendant, 134.

Large intervals in melody, 49.

Leading-note, progression of, 39 in minor key, 59 ; in Sequences, 115, 152.
;

Leading-note triad, 89, 103, 104 first inversion, 90 ; second inversion, 104.
;

Line, through a figure, 66 ; following a figure or accidental, 88 under a note, 88.

;
138 INDEX.

Major scale, 6, 7, 9.
Major sixth in the minor key, harmonized, 107.
Mediant triad, 84 first;inversion, 86 ; second inversion, 102 ; in minor
1 08.
key, 103,
Melodic Minor Scale, harmonization of, major sixth, 107; minor seventh, 71, 92;
as unessential notes, 159.
Melodic progression, 32, 38, 47, 59, 61, 115 ; seventh in melody, 71, 131.
Melody, harmonization of, 41, 45, 76.
Mental conception of chords, 27.
Mental effect, of the Dominant common chord, 31 ; 01 triads in their first
inversion, 64.
Middle cadences, 78, 97, no, 112, 113.
Minor Scale, 6, 8, 9.
Minor Seventh in minor key as a bass note, 71 ; as a melody note, 93.
Modulation, 132; transitory, 133; permanent, 133; natural, 134; extraneous, 134;
sudden or direct, 136; gradual, 136.
Motion, between outside parts, 34 ; similar, contrary, or oblique, 33 ; conjunct and
disjunct, 38.
Movement of parts, 32.

Oblique motion, 33.

Omission of the fifth in common chords, 22; in the Tonic triad, 39; in the chord
of the Dominant Seventh, 120.
Omission of the third in the chord of the Dominant Seventh, 120.
Open score and short score, 21.
Ornamental resolutions of Dominant Seventh, 120; of suspensions, 173.
Overlapping of parts, 25 ; allowable overlapping, 40.

Parts, defined, 21; distribution of, 24; crossing of, 26 ; general progression of, 32 ;
overlapping, 25 ; allowable overlapping, 40; vocal, 21.
Passing notes, 154, 157; chromatic, 158; in Melodic Minor Scale, 159; accented,
160 ; in two parts, 163.
Passing six-four chord, 97, 99, 102.
Perfect cadence, in; with Dominant Seventh, 120.
Plagal cadence, 51, in.
Preparation of Diatonic Sevenths, 151; of Suspensions, 169.
Primary triads in major key, 44; in Minor key, 53, 61 ; first inversion of, 68;
with Submediant triad, 75, 79 ; with Supertonic triad, 81, 82.
Progression of parts, 32 (see also Harmonic progression and Melodic progression).
Progression of the bass, 75 (see also bass part).

Real Sequence, 116.

Related or attendant keys, 134, 136.
Relative major and minor keys, 9.
Repeated notes in bass part, 75.
Repetition of a discord, 122.
Resolution of discord, 119; of the Dominant Seventh, 120; exceptional resolu-
tion, 129; of Diatonic Seventh, 151; of Auxiliary notes, 155; of Passing
notes, 157; of Suspensions, 169; exceptional resolution, 174; ornamental
resolutions, 173-
Retardations, 170.
Retarded Leading-note, 185.
Root of chord, 19 ; upon a separate staff, page 38 *% .

Root progression, 81 (II).

Scale, 5.
Second inversion ot triads, progression of bass, 06, 131.
Second to a unison. 166.
Secondary Sevenths, 150.
 INDEX. 139

Secondary triads, 73 ; second inversion of, 102.

Selection of chords in the harmonization of melodies, 45, 76,
Sequences, 114.
Seventh in melody, 49, 131 ; diminished, 71.
Short score, 21.
Similar motion, 33.
Six-four chord, progression of bass, 96 cadential, 97 ; passing, 97, 99, 102.
;

Sixth, chords of, doubling of notes, 65, 69 ; figuring of, 66.

Subdominant triad, major key, 42 ; minor key, 60 ; first inversion, 67 ; second
inversion, 100; with Submediant triad, 75, 79; with Supertonic triad,
81 (III), 82 ; with Mediant triad, 85.
Submediant triad, 74 ; first inversion, 79 second inversion, 102 ; with Supertonic
;

triad, 81 (IV), 82 with Mediant triad, 85.

;

Supertonic triad, 80, 106 ; first inversion, 82 ; second inversion, 102, 106 ; minor
triad in minor key, 107.
Suspensions, 154, 168 doubling of notes, 175;
; exceptional resolution, 174;
harmonic progression, 176; ornamental resolution, 173; in connection with
discords, 190; figuring of, 189.
Suspensions, Nine-eight, 171; Four-three, 180; Six-five, 184; Leading-note, 170,
185 ; Double, 187 ; Triple and of complete chords, 188,

Tierce de Picardie, 56.

Tonal Sequence, 114, 115.
Tonic triad, major key, 19; minor key, 54; first inversion, 63.; second
inversion, 94; with Submediant triad, 75, 79 with Supertonic triad, 81 (I), 82 ;
;

with Leading-note triad, first inversion, 90.

Transition, 133.
Triad, 20 (see also Tonic triad, &c.).
Triple suspensions, 188.

Unessential discords, 154.

Unessential notes, 154; False Relation, 161 ; Harmonic progression, 164;
in two parts, 163.

Vocal compass, 21.

END OF PART I.
 BY THE SAME AUTHOR.

MUSICAL
AND
MEMORY ITS CULTIVATION,
ALSO AN
INVESTIGATION INTO THE FORMS OF MEMORY EMPLOYED IN PIANO-
FORTE PLAYING, AND A THEORY AS TO THE RELATIVE
EXTENT OF THE EMPLOYMENT OF SUCH FORMS.

A GUIDE TO THE llSoRIZING^oFpIANOFORTE MUSIC.

Price Two Shillings and Sixpence.

"THE
TIMES" says:
" Of books on the technique of music, none lately published has been executed
with more skill and certainty than Musical Memory,' a small treatise that will be of
'

the utmost service to the many who must find what is called the * memorizing of
'

music a formidable task. The soundness of the methods recommended, and the
practical experience which appears on every page, call for nothing but praise."
" THE DAILY GRAPHIC" says:
"An interesting little book on musical memory. It is clearly written, and
many
of the hints and suggestions with regard to memorizations will be valuable to
students."
" THE SUNDAY TIMES" says:
" commend
I to the perusal of musicians generally young and old, professional
and amateur Dr. Shinn's clever little book. Fascinating as the subject is, it has
never before been treated by a writer from a scientific standpoint or reduced to a
a system upon lines definite enough to be followed and utilized by either teacher or
student."

"
"THE OBSERVER" says :

Hehas treated his subject in a thoroughly scientific and therefore practical

manner, and has at the same time so worded his remarks that the least scientifically-
minded reader may understand them."
"
THE GUARDIAN" says:
" Dr. Shinn has
evidently made a deep study of the subject, and his little essay is

extremely able and interesting."

"THE MUSICAL TIMES" says:
"Dr. Shinn not merely theorizes on a subject about which no literature seems to
exist, but by copious musical examples gives practical proof of the truth that is in him.
We unhesitatingly commend this excellent treatise."
" THE MUSICAL NEWS" says:
"The author has laid the musical world under a debt by the publication of a capital
little book upon a subject far too long left unstudied. His book will amply repay the
most careful and thoughtful perusal."
"THE I.S.M. JOURNAL" says :
" An able and extensive and one which has evidently been the outcome of
treatise,
much experimental research."
" THE MUSICAL HERALD" says :
" An excellent work, in which the subject is treated by its author in a truly
philosophic spirit. We heartily recommend it to all pianoforte teachers."

THE VINCENT MUSIC CO., Ltd.,60,BERNERS ST., LONDON, W.

 BY THE SAME AUTHOR.

Elementary Ear-Training,
BOOK I. MELODIC.

A Method of Training- the Ear to Perceive and to Dis-

criminate Relations of Pitch, Relations of Strength,
and Relations of Length,in so far as these constitute
the Elements of Musical Sounds, and on the Writing
of the same from Dictation ;

WITH

Over 750 Graduated Ear-Tests and Dictation Exercises,

Price Two Shillings.

The Times says : "A thoughtful little treatise."

The Sunday Times says :

"
A valuable addition to the select store of musical text
books published by Mr. Vincent. Teachers of the young especially, will appreciate
the practical form in which the author has here embodied his hints for training the
untutored mind to grasp the various relations of pitch, strength and length."

The Musical News says " A

crystallisation into convenient form, of the many
:

appeals which have been recently made on behalf of a broader and deeper considera-
tion of this vital part of the music teacher's duty, and a handy guide in the discharge
of that duty. . . suitable for immediate introduction into classes as a text book."
.

The Musical Courier says " As a contribution to the

:
systematic training of that
organ upon which music makes special demands, Dr. Shinn's book deserves high
commendation, the subject being treated in a practical manner, and presented in a
form useful to the teacher and easily comprehensible to the learner."

The I.S.M. Journal says " It

presents a thoroughly practical and well considered
:

system, and one, moreover, which can only be the result of considerable practical
experience. We recommend it
very heartily to all teachers of music."

THE VINCENT MUSIC CO., Ltd., 60, BERNERS STREET, LONDON, W.

 Theoretical Works and Music Text Books.
Net.
Elementary Ear-Training ..........
....... Fred. G. Shinn
s.
2
d.

Rudiments of Musical Knowledge . C. W. Pearce 1

Rudiments of Music for Choirs and Schools . . . .
Harvey Lohr 6
Manual of Sight Singing, Part I. Paper Cover, Is. , Cloth, Is. 6d. F.J. Sawyer
,, Part II. Paper Cover, Is., Cloth, Is. 6d.
Graded School Song-Book,
Designed for use with The Manual of Sight Singing, ten parts,
each 2d. Complete
....... Vincent
in
Choral Instructor for Treble Voices
Paper Cover,

..........
Is. 4d., in Cloth, 2s.
C.
,, ,.

8
New-Century Pianoforte Method 2
School of Arpeggio Fingering ...... S. 3
Harmony, Diatonic and Chromatic ........A. Myerscough
............
(Practical)
C.Vincent 3
and Roots 6
Students' Counterpoint ............
Tonality Greenish J. 1
W. Pearce 2
Composers' Counterpoint
Form
..........
............
C.
,, 2
Music 3 O
in
Scoring for an Orchestra ............ Humfrey Anger
The Reading of Music ............ M. E. P. Zeper
Vincent
/.
C. 1 6
6
Combined ..............
Rhythms R. Rowe
......
/.
1
8
Musical Memory and 6
On Organ Playing ................Guido A. Page
its Cultivation

..............
Fred. G. Shinn 2
2
Voice Culture
Hints to Singers ..............
300 Examination Questions
Porpora
.......... A. R. White T.
3
3
6
Mangehdorff 1
Score Reading in the various Clefs, 48 Fugues, 2 Vols. /. S. Bach each 4
HOW we Hear (A Treatise on Sound) F. C. Baker 1 6
Vocal Exercises for Choir Boys F. N. Baxter 1
Practical Suggestions for Training Choir Boys E.G. Bentall 6
Voice Exercises for Boys ..........
........
.

2
On Mendelssohn's Organ Sonatas C. W. Pearce 2
Scales and Arpeggios
The Art of Violin Bowing
............
.......... 6". Midgley 3
3
O
PaulStoeving
Choir Training based on Voice Production A. Madeley Richardson 2 6
The Psalms, their Structure and Musical Rendering ,, 3
Training of Men's Voices ..........
......
.,
R. T. White 6
Memorizing Major and Minor Scales F.A.Clarke 3
Rudiments of Vocal Music .......... T. L. Southgate 2
Vocal Exercises on the Old Italian System E.G. White 2 6
......
. . . .

The Brass Band and how to Write for 6

A History Of Music ..............
Studies in Musical Graces ............
It C. Vincent
E. Duncan
2
2
3
6
Ditto ..................
E. Fowles
Key to 1 6
Melodies and How to Harmonize Them ...... E.Duncan 3
Key to Ditto .................. 2
What Music ............ Duncan Hume 6
Plain-Song and Gregorian Music ..........
is 1
2 6
Singing ..............
Burgess F.
Words in C.J.Brenn 1 6
Organ Accompaniment to the Psalms .. W. C. Pearce 2
Dictionary of Organ Stops .. .. Wedgwood J. 1. 5
A Treatise on Harmony, Part I & Part II /. Humfrey Anger each 3
Voiee Training Exercises and Studies . . F. C. Field Hyde
. . 4
The First Principles of Voiee Production Thomas Kelly 6
Practical Points for Choral Singers .. Robert Simmons 1

The Organist's Directory C. W. Pearce 3

The Indispensible Theory Book Woodrow Rudd & \ O
Graded Score Reading (C and G Clefs) . . F. J. Sawyer 2 6
Primer of Part-Singing, Two Books F. J. Satvyer each 1
A Method of Teaching Harmony .. Fred. G Shinn
Part I Diatonic Harmony. Cloth boards, 3s.; Limp covers, 2s. 6d.
,, II Chromatic Harmony. ,, 3s.; ,, 2s. 6d.

The VINCENT MUSIC CO. Ltd., 60, Berners St., London, W.