Royal Conservatoire The Hague

ASA 1
st
1 semester

Scales

&

Chords
(1st version 2022)

1
 Introduction

This is a little expose about scales and chords in Western Classical music, to be used during
the ASA1 1 semester course at the Royal Conservatoire The Hague.
The idea is that you learn about the variety of scales and chords that was used by composers
in Western Classical music, from approx. the Renaissance till today. You will learn that
different styles use different materials or use materials in different ways.

The best way to deeply learn this as a musician is to actively confront yourself with the
material by playing the examples on your instrument, sing them and see what you can
create with the material itself. You could say that you really know the theory if you can let
others ‘hear’ the theory.

The set-up is that we go from literature examples to the theory and back to the literature
again in which you are challenged to play, sing and create along the way.

September 2022 Patrick van Deurzen

Chapter 1: Scales and modes

1.1 Introduction: What are scales and modes? 3
How are scale/modes used in Western music? 7
Overview of historical periods and type of scales used 7
Intermezzo: Singing/thinking with relative solmization 8
Overview scales and modes: Church modes 11
Major and Minor 13
20thc scales 14
How are scale/modes used in Western music? 15
1.2. Analysis: Recognizing scales in context : a. Bach 19
b. Debussy 23
c. Lassus 28

Chapter 2: Chords
1.1 Introduction: What are chords? 33
How are chords used? 36
Overview of historical periods and type of chords used 37
Overview chords: secudal, tertian, quartal, quintal, mixed 38
Sub-categories Added note, whole tone, polychords 40
Chords and inversions 41
Chord Notation: Figured bass, Roman Numeral, Chord symbols 43
What is the relation between Chords and Scales? 45
2.2 Analysis: Recognising chords in context: a. Mozart 47
b. Lassus 51
c. Debussy 53
d. Stockhausen 56

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 Chapter 1: Scales and modes1

1.1 Introduction:

What are scales and modes?

This first question is relatively easy to answer: a scale or mode is any collection of notes
ordered from low to high, or high to low. This collection of notes is used to create both
melodic and harmonic aspects of a musical work.
If you recognize scales easily, if you can play scales easily on your instrument you will read
scores more easily and you have a better understanding of how the musical language of a
composition works. If you can sing scales easily you will develop your inner hearing which
helps you interpreting a musical work.
Each musical style, or character of a work is partly defined by the type of collection, or type
of scale/mode that is used.

For example, the melody in bar 7-10 from Dvorak’s String Quartet no. 12 played by the first
violin uses just five different notes:

Ex. 1.1a: Dvorak – String Quartet no. 122 (1893) https://youtu.be/_b_rwtDlUXA

If we order these 5-notes from low to high, we will get an F major pentatonic scale which
gives this melody it’s specific ‘Afro-American folky’ character.

Ex. 1.1b: F major pentatonic scale

It is called a pentatonic scale because it uses only five notes, and ‘penta’ means five. It’s
major pentatonic because it has a major third: F – A.

1
In this chapter I will only speak of scales and modes in our well-tempered system which divides the octave in
twelve equal tones, and as used within a limited cultural, mostly European repertoire.
In principle there is not a difference between a scale or a mode, but in certain historical periods one speaks
rather of a mode than a scale and vice versa.

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Minor pentatonic would have a minor third (F – Ab) and is organised like this:

Ex. 1.2a: F minor pentatonic scale

Ex. 1.2b In Gershwin’s song Summertime, from his opera Porgy and Bess (1935), the vocal
line uses the minor pentatonic scale3: (transposed to F min.): https://youtu.be/O7-
Qa92Rzbk4

There is one note in the melody that doesn’t fit the pentatonic scale. Can you find it?

3
The chords, here represented as chord-symbols, do not make use of the pentatonic scale. In the chapter on
chords, we will come back to chord-symbols.
4
Summertime has been performed by numerous Jazz-artists. One of my favorites: Ella Fitzgerald & the Tee
Carson trio: https://youtu.be/u2bigf337aU

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Like in the Dvorak example, the pentatonic scale is used to imitate Afro-American spiritual
music.

Ex. 1.3a In the next example: Messiaen – Chant d'extase (1929) we find eight different notes:
https://youtu.be/z2pwTP7g7xE?t=123

If we order these 8-notes from low to high: we would get a F# octatonic scale, ex. 3b:

It is called an octatonic scale because it uses eight notes, and ‘octa’ means eight.

If you look/listen closely to this scale, you see/hear that it consequently alternates a
half step-whole step.

Another octatonic scale can be created when the scale alternates a whole step-half step.

ex. 1.4a: whole step-half step octatonic scale

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Ex. 1.4b This whole step – half step octatonic scale, transposed to D, is used in Rebikov’s
Une Fete (1907) fourth movement bar 1-16 https://youtu.be/ZpHP48MIRUg?t=106

14

Ex. 1.4c: whole step-half step octatonic scale from D

If we compare the Messiaen and the Rebikov piano pieces we see that not only the scale has
influence on the character of a composition, but also the tempo and dynamic.

Exercises

1. Play the melodies and scales discussed in this chapter on your instrument. Pay
attention to intonation, tempo5, articulation, and dynamics.

5
Important is a steady tempo, not necessarily the exact tempo of the composition.

6
 2. Sing the melodies and scales discussed in this chapter. Pay attention to intonation6,
tempo7, articulation, and dynamics.

How are scale/modes used in Western music?

This question is more difficult to answer than the first one. As mentioned before, a collection
of notes is used to create both melodic and harmonic aspects of a musical work, but as we
will see in the coming pages, this can be done in an infinite way. Before looking at specific
works, let’s see what kind of scales/modes are used in the long history of European Classical
music8.

1. The so-called Church modes were used during the Middle Ages and Renaissance,
roughly from the 8th c. till the 17th c. We call this music modal music since it makes
use of the modes. (See ex. 6a & b)

2. After this, from the 17th c. till the 20th c. during the Baroque, Classic, and Romantic
area, only Major and Minor scales were used. We call this music (functional) tonal
music, which means that there is a clear hierarchy between the notes of the scale,
and a sense of gravity. We will come back to this later. (See ex. 6c)

3. From the 20th c. onwards the Church modes came back in fashion (although
differently used than before), Major and Minor also keep playing a role (also used
differently than before), but also new scales/modes were used. The music from the
20th c. is so diverse, that it is impossible to have one name for it. Some music is neo-
modal, neo-tonal or extra-tonal, but some we could also call chromatic. (See ex. 6d)

Overview of historical periods and type of scales used:

Middle Ages 300 – 1400 modal

Renaissance 1400 – 1600 modal
Baroque 1600 - 1750 tonal
Classicism 1750 - 1830 tonal
Romantic 1800 - 1900 tonal
Impressionism 1880 - 1920 modal, tonal, extra tonal
Expressionism 1909 - 1920 chromatic
Neoclassicism 1920 - 1950 modal, tonal, extra tonal
Serialism 1950 – 1980 chromatic
Minimalism 1960 - modal, tonal, extra tonal
Postmodernism 1980 - modal, tonal, extra tonal

6
If you need, you can check yourself with another instrument f.e. a piano.
7
See footnote 5.
8
Not all possible scales/modes will be mentioned here, but some of the most used scales.

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Intermezzo: Singing/thinking with relative solmization

When we look at a scale, we can name the notes in different ways. There are the absolute
note-names like ‘C’, ‘G#’ or ‘Eb’. But the name can also be related to a position of a note in
a scale, f.e. the note ‘C’ is the 1st note of a C major scale, but the 3rd note of a Ab major
scale, or the 5th note of a F major scale etc.

ex. 5a: The position of the note ‘C’ in three different major scales

Because this ‘C’ has within each context a different ‘function’, f.e. the 1st note of the scale,
or the 5th note of the scale etc., it will have a different feeling, a different colour.
Therefore, each function or colour gets its own relative solmization name:

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ex. 5b: The relative solmization names of the note ‘C’ in three different major scales

Especially in tonal (major/minor) music the function or position of each note is quite clear.
There is a kind of gravity of one note towards another; the feeling that a note has tension
and wants to move (solve) to another note, to release this tension; and in the end the
music wants to end on the 1st note of the scale.

We will see/hear/feel this in later examples that will be discussed.

In modal music this feeling of gravity is less strong, less present, and in chromatic or extra-
tonal music this feeling of gravity can be completely absent.

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ex. 6a: Church modes9 10

9
The way modes are used in the Middle Ages and Renaissance is discussed a lot, see for example a video on
modes in the 16th & 17th century https://youtu.be/lyq48eybjZw . This discussion goes beyond the purpose of
this booklet.
10
Locrian is a theoretical mode and not used in the renaissance, but it is used in the 20th c.

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ex. 6b: Church modes starting from C.

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ex. 6c: Major and Minor starting from C.

Relation between major and minor scales and the church modes.

When comparing the modes to a Major or Minor scale, there is mostly just one note
different. These notes characterize the specific mode and is named as such.

The Lydian scale compared to Major has a raised 4th : the Lydian 4th
The Mixo-lydian scale compared to Major has a lowered 7th : the mixo-lydian 7th

The Dorian scale compared to Minor (aeolian) has a raised 6th : the dorian 6th
The Phrygian scale compared to Minor (aeolian) has a lowered 2nd : the phrygian 2nd

The Locrian scale is the exception having two differences. Compared to (aeolian) it has a
lowered 2nd, and lowered 5th : the Locrian 5th

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ex. 6d: 20th c. scales from C.11

11
Especially from the 20th c. onwards any combination of notes can form a mode or scale. To mention just two
that are not mentioned in this overview: 1. you can start on any note of the acoustic scale to get new scales; 2.
French composer Olivier Messiaen created his own set of seven modes, see
https://en.wikipedia.org/wiki/Mode_of_limited_transposition

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How are scale/modes used in Western music?

Before answering this question, it is important to mention that in a mature composition

hardly ever only the notes of one scale are used. A composition is mostly built from a
combination of scales as we can see in the previous example 4b of Rebikov: from bar 17
onwards the melody is using a full chromatic scale.

In the next example 7a Bach is using in the first four bars, two different scales: in bar 1-2 and
4 he uses the notes of a G major scale, while in bar 3 he uses the notes of a C major scale
because in that bar he altered (= changed) the F# into an F12.

Ex. 7a: Sarabande BWV 1007 (1717-1723) of J.S. Bach https://youtu.be/ve0UA1t0xkM

In the next example Debussy uses first the D aeolian scale (bar 1 – 4), and then by changing
the Bb into a B in bar 5, moves to a D dorian scale (bar 5 – 7).

Ex. 7b: Des pas sur la neige (1909-1910) of Debussy https://youtu.be/5ZpysYzdIrk

12
You could also say that the altered note ‘F’ is ‘borrowed’ from the C major scale.

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Ex. 7c: Stockhausen – Tierkreis (1974-1975) https://youtu.be/BbV7D4es0Zs

The melody of Stockhausen’s Aquarius uses all the notes of the chromatic scale. Since there
is only one chromatic scale, there is no room to switch to another scale.

Especially with late 19th- and 20th c. melodies, there are more ways of analysing tone-
collections. In the case of Stockhausen’s Aquarius, another valid perspective would be to say
that the melody (upper staff only) starts in Eb minor, after which bar 3 goes to Eb major.
From bar 6 onwards we see a clear chromatic descend from a D to A, jumps to F and
continues chromatically down to Eb. (In the next chapter we will talk about the chords)

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Exercises
1. a. Write 5 short melodies using the following rhythm:

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 b. Play and record the melodies on your instrument, with attention to
intonation, tempo, articulation, and dynamics.

2. a. Write five short melodies choosing the scale, rhythm, tempo, articulation, and
dynamics yourself
b. Play and record the melodies on your instrument, with attention to intonation,
tempo, articulation, and dynamics.

For two players:

3. Improvise using a single scale upon a drone. The drone is the root-note of the
scale. The players alternate.
Example: chose a scale starting from G, f.e. G phrygian. One player plays a G
drone, the other player improvises using the G phrygian scale. After some
moments the players change role.

Improvise using multiple scales on multiple drones. Start with two which are a
minor third apart. The drone is the root-note of the scale. The players alternate.
Example: chose two scales a minor third apart, f.e. D and F major. One player
plays the two drones in a regular way -two bars D two bars F, the other player
improvises using the corresponding scale to the played drone. After some
moments the players change role.

While playing a drone, you can rhythmically embellish the note you play; or
alternate with the fifth of the scale.
You can also experiment with other ideas to enhance the improvisation.

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1.2. Analysis: Recognizing scales in context

To recognize scales in the context of a composition is not always easy. Firstly, as mentioned
before, composers rarely tend to use just one scale, one set of notes, in their mature
compositions. Secondly, when they use a scale, they tend to use notes outside the scale to
color or enrich the music13. These ‘outside the scale’-notes can be added as described in the
previous examples: to temporarily change the scale, but they can also be used as ornament
or extra colour in the harmony.

The two basic questions we will deal with in this chapter are:
How do we determine the scale used?
How do we decide when a scale moves to another scale?

We will see that the approach will be different for different historical periods. Sometimes,
more than one answer is possible, depending on the perspective you take.
Apart that we can use our brain to determine the scale, it would be advisable you to use
your (musical) ear, by singing or playing the examples, since that helps a lot in deciding.

a. J.S. Bach (1717-1723) - Sarabande BWV 1007 https://youtu.be/ve0UA1t0xkM

For our first example 8a we revisit the Sarabande BWV 1007 of J.S. Bach (1685 – 1750)

The first step to take is to determine the historical period of the composition.

13
Often, but not always, composers start by stating the tonal environment clearly, but then derive from this.

18
The Sarabande was written in the 18th c during the so-called Baroque period. Bach wrote six
cello suites, probably between 1717 – 1723. A Baroque suite consists of a prelude after
which a series of dances follow. A Sarabande is a dance with a slow tempo, in ¾ time with an
accent on the second beat.

As we can see in the overview on p. 5, in the Baroque period, music was tonal. The tonal
period is the easiest period to determine which basic scale or basic key is used for the
composition because the number of accidentals tells us the possible major- or minor key.
To decide between major or minor we listen/look how the composition begins and ends.

This Sarabande has one sharp so we can choose between G major or E minor.
If we then take the beginning and ending in account, we hear/see that it is in G major.

As we have seen already in Ex. 7a, there are notes used that do not belong to the G major
scale. These notes are called alterations, i.e. notes that are changed from the original scale,
in this case the G major scale. There are two types of alterations:
1. Incidental alterations: these are there for just a short moment
2. Structural alterations: these are there for a longer period

If we look at bar 3 we see an 'F natural'. This alteration appears just once, after this, in bar 4,
the 'F#' returns. This is an example of an incidental alteration. Just for one bar, bar 3, Bach
used the scale of 'C'14, to return in bar 4 to the scale of 'G'.

In bar 6 a new alteration appears: the 'C#', but as we can see it stays there until bar 8. This is
an example of a structural alteration. We change, or modulate, to the new scale of 'D'15,
which is confirmed in bar 8 by arriving at D as a new 'do' or tonic. This confirmation of
arriving to a tonic is called a cadence16.
These important moments of arrival or cadences, which end a section, can also be find in bar
12 and 16.

Exercises:

1. What alterations do you see from bar 9 – 16?

2. Is the alteration incidental or structural?
3. What scale(s) is (are) used?

14
G major = 1#, if we take that sharp away we have 0# = C major
15
G major = 1#, if we add the second sharp c#, we get 2# = D major
16
We come back to the concept of the cadence in the next chapter.

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Alterations are used to spice up the music, they bring a specific kind of colour or tension. In
this style there is a clear relationship between the alteration, which creates tension, and the
note that should follow: it's resolution. See ex. 7b below:

Exercises:

1. Analyse the Menuet in a similar way. Indicate Scales, incidental -, and

structural alterations, how these alterations solve, and the important
moments of arrival (cadence).
2. Analyse the Sarabande from the B minor violin partita (BWV 1002) in a
similar way

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 For two players:
3. Improvise using a single major or minor scale with alterations upon a
drone. The drone is the root-note of the scale. The players alternate.
4. Improvise using multiple major or minor scales with alterations on
multiple drones. Start with two which are a minor third apart. The drone
is the root-note of the scale. The players alternate.

Extra Exercises: Analyse one of the following Bach compositions in a similar way:

Flute, Bassoon: BWV 1035, 1st movement

Harp, Keyboard, Guitar, Marimba: BWV 998, 2nd movement

Clarinet: BWV 1005: 3rd movement (from the 15 etudes no. 13)

Hobo: BWV 1055: 1st movement (just the hobo-part)

Hoorn: BWV 1007: Last movement Gigue

Violin: BWV 1001: Last movement Presto

Cello, Viola, Double bass: BWV 1008: Last movement Gigue

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 b. C. Debussy - Des Pas sur la Neige

For our second example 9a we revisit …Des Pas sur la Neige of C. Debussy (1862 – 1918):

Debussy wrote between 1909 and 1913 24 preludes for piano solo. Each of the preludes has
a poetic title that is placed between brackets at the end of the prelude. Des Pas sur la Neige
is the sixth prelude. As we can see in the overview on p. 5, Debussy had a lot of scale
possibilities to chose from: modal, tonal or extra-tonal, which makes it more difficult to
determine the scales used. One method, that we will use here, is to listen/read carefully, and
hear/look where the set of notes17 change, see example 9b:

17
Set of notes, or tone-set is a collection of notes used during a certain fragment. From a tone-set one can
derive a scale.

22
example 9b : The red lines indicate a change of tone-set.

Once we established where a change of tone-set takes place, we can write down the used
notes in a scalar way, from low to high. See example 9c:

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As we have already seen, the first 4 bars make use of a D aeolian (or D natural minor) scale.
In bar 5 -7, a B is used instead of a Bb which changes the scale to a D dorian scale.

Exercises:
1. What scales/modes do you see in bar 8 – 18?
(In bar 8 -11 the two crossed notes between brackets are the missing notes to make
this scale complete, in bar 14 - 15, the (blue) B can be considered an ornamental
alteration not belonging to the scale, bar 16 – 18 you might recognize the scale if you
start from the F).
2. Write down the scales of bar 19 – 36 in the same manner as ex. 8c.
3. How would you analyze these scales?

If we compare the use of scales in this example with the Sarabande of Bach, we see that
Debussy had more scales to choose from.
Another important difference is that the use of alterations in Bach’s music have a direct
consequence for the note following the alteration, see ex. 8b.
In Debussy’s music, and in a lot of music from the 20th c. onwards, this relation between an
alteration, causing tension, and the resolution of this tension is weakened or even absent.
The alterations are still used to spice up the music, to bring a specific kind of colour or
tension or variation in the sound-pallet of a composition, but it stands more on its own and
doesn’t have a direct consequence for what follows. See for example the ‘B’ in bar 5 in the
left hand moving down to ‘A’, while in the right hand it moves up to the ‘C’.
A consequence of this is that not only the tension is weakened or even absent, but also
cadences and a feeling for a root-note is weakened or even absent.
In that sense the scale representation in ex. 9c is sometimes arbitrary18.

18
From bar 8 – 11, It would be logic from ‘C#’.

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Exercises:

1. Analyse the first page of Bartok’s Village Joke (1926-1939), in a

similar way. The moments the tone-set is changing is already
given. https://youtu.be/0tob_Jf3G6A?t=482

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 For two players:
2. Improvise using a single 20th c. scale with alterations upon a drone.
The drone is the root-note of the scale. The players alternate.
3. Improvise using multiple 20th c. scales with alterations on multiple
drones. Start with two which are a minor third apart. The drone is
the root-note of the scale. The players alternate.

Extra Exercises: Find 20th, 21st c. solo compositions for your own instrument and analyse the
scale content.

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 c. O. di Lassus – Beatus Vir (1577) https://youtu.be/yn9Mjzy4LYg ex. 9a:

The last example is a bicinium, a composition in two parts of the Flemish Renaissance
composer Orlando di Lasso (1532 – 1594). Bicinia were composed for educational use, either
for singing or composition. Looking at the historical period, the 16th c., composers used the
church modes. To define in which church mode this Beata vir is written, we look at the

27
sharps or flats at the beginning, and the ending note. In this case: no sharps/flats, and
ending on D. This means that it is written in D – dorian.
Also here we see some alterations in the score, see ex. 9a:

In bar 2 a C# and bar 3 a Bb, which make the tone-set similar to the later D minor (harmonic)
scale. In the next bars 4 and 5 these alterations disappear (blue circle). In bar 9 – 10 (green

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circle) the first sentence ends on an ‘A’. This important moment of arrival, or cadence
confirms the temporary use of the A aeolian mode19.
In bar 21 and 27 we see some incidental alterations that color the mode for a short moment.

Exercises:
1. In bar 17-18 and 31-32 we see cadential moments (moments of
arrival). Which modes do they confirm?

2. Analyse Bicinium V in a similar way

19
The sharp above the G in bar 9 was added by the publisher for the ‘modern’ musician. Singers in the 16th c.
would know that they had to sing a leading-tone G# at the end of a sentence. See also the very ending of this
Bicinium.

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 For two players:
3. Improvise using a single church mode with alterations upon a
drone. The drone is the root-note of the scale. The players
alternate.
4. Improvise using multiple church modes with alterations on
multiple drones. Start with two which are a minor third apart.
The drone is the root-note of the scale. The players alternate.

Extra Exercises: Analyse, sing and play Bicinium 1 of J. dez Prez

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31
 Chapter 2: Chords

2.1 Introduction:

What are chords?

A Chord is any combination of at least three notes that sound simultaneous20.

If you recognize chords easily, if you can play chords easily on your instrument you will read
scores more easily and you have a better understanding of how the musical language of a
composition works. If you can sing chords easily you will develop your inner hearing which
helps you interpreting a musical work.
Each musical style, or character of a work is partly defined by the type of chords that is used.

For example in Bartok’s Melody in the mist (1926-1939), the mist is portrayed here by so-
called secundal-chords, i.e. chords made of seconds Ex. 2.1a:
https://youtu.be/JWBPCv7TWsw?t=682

20
Two notes sounding simultaneously would be an interval.

32
If we would write down the notes of the chords of the right- and left hand, we see that it
forms an almost full chromatic secundal chord between G and Eb; only the B is missing.

See Ex. 2.1b: stems down are the notes of the left hand, stems up of the right hand

The melody, as contrast, has a more pentatonic-like character21.

In the next example, Lassus 4-part chanson Bonjour mon coeur (1564), the chords are all
tertian, i.e. made from thirds. See Ex. 2.2a: : https://youtu.be/zFVvCFGz36g

21
The following 5 notes are used in the melody: G A C D F#, which is a different 5-notre collection that the
previous discussed pentatonic scales. At the end the F# is changed to an F, giving it a more modal character
because of the mixo-lydian 7th.

33
To see tertian-chords clearly, we write the different notes within one octave, and only using
thirds to stack the notes22 See Ex. 2.2b:

In the two examples above, the chords are played/sung simultaneously. But they can also be
performed in a broken, or arpeggiated manner, like in the beginning of Mozart’s Fantasia in
D minor (± 1782). See: Ex. 2.3a: https://youtu.be/1BkZ8ci8_k4

If we write the different notes of this Fantasia within one octave, we can see clearly the
third-build-structure See: Ex. 2.3b, here we see 3-, and 4-note chords23:

22
In bar 4 in the Bassus, and bar 5 in the Superius we can see some melodic ornamentation, we will talk about
this in a later stage.
23
Also in this example we see some ornamental notes in bar 7-8 and 10 that are omitted in the harmonic
reduction.

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Ex. 2.3b

Exercises

1. Play the chords discussed in this chapter on your instrument from the low note to the
high note and/or simultaneously on a chord-instrument. Pay attention to
intonation24, tempo25, articulation, and dynamics.

2. Sing the chords26 discussed in this chapter from the low note to the high note. Pay
attention to intonation, tempo, articulation, and dynamics.

How are chords used?

As with scales, this question is more difficult to answer because this can be done in a
countless way. Before looking at specific works, let’s see what kind of chords are used in the
long history of European Classical music27.
Like scales, chords can be grouped in different categories. The categories of different chords
are based on the intervallic structure:
1. Secundal chords based on seconds (the triad has a root – second – third)
2. Tertian chords based on thirds (the triad has a root – third – fifth)
3. Quartal chords based on fourths (the triad has a root – fourth – seventh)
4. Quintal chords based on fifths (the triad has a root – fifth – ninth)
5. Mixed intervals (many different possibilities, here root – fourth – fifth)

See: Ex. 2.4a

24
If you need, you can check yourself with another instrument f.e. a piano.
25
Important is a steady tempo, not necessarily the exact tempo of the composition.
26
If you need, you can check yourself with another instrument f.e. a piano.
27
Not all possible chords will be mentioned here, but some of the most used.

35
Chords can be played simultaneously (2.4a), but they can also be played as an arpeggio:

Ex. 2.4b

In different historical periods, different types of chords were used, and they align quite well
with the historical division of the scales:

1. During the Middle Ages and Renaissance, roughly from the 8th c. till the 17th c.,
Church modes were used, and from the Renaissance onwards tertian 3-note chords
were used.
2. After this, during the Baroque, Classicism, and the Romantic area, only Major and
Minor scales were used. The chords were still tertian chords, but expanded to 3-, and
4-note tertian chords. In time this was from the 17th c. till the 20th c.
3. From the 20th c. onwards the Church modes came back in fashion, Major and Minor
also played a role, but also new scales/modes were used. In this period we find
secundal-, tertian-, quartal-, quintal, and mixed chords.

Overview of historical periods and type of chords used:

Middle Ages 300 – 1400

Renaissance 1400 – 1600 tertian
Baroque 1600 - 1750 tertian
Classicism 1750 - 1830 tertian
Romantic 1800 - 1900 tertian
Impressionism 1880 - 1920 secundal. tertian, quartal,
quintal, mixed interval
Expressionism 1909 - 1920 secundal and quartal, mixed
interval
Neoclassicism 1920 - 1950 secundal. tertian, quartal,
quintal, mixed interval
Serialism 1950 – 1980 secundal and quartal, mixed
interval
Minimalism 1960 - secundal. tertian, quartal,
quintal, mixed interval
Postmodernism 1980 - secundal. tertian, quartal,
quintal, mixed interval

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Ex. 2.5a: different chord categories (3- and 4 note chords)

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Pronunciation

Ex. 2.5b: Some examples of how to pronounce the chords

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Sub-categories

One can make also other categories of chords that can be seen as sub-categories of the
previous categories:

a. Added note chords: 3-note chords in which a note is added different than the
interval used for chord itself.

ex. 2.6a is a secundal chord with an added 6

ex. 2.6b is a tertian chord with an added 2

ex. 2.6c is a quintal chord with an added 6

b. Whole tone chords: all the chord members come from the same whole tone scale

ex. 2.7a is a whole tone secundal chord

ex. 2.7b is a whole tone tertian chord

ex. 2.7c is a whole tone tertian chord with an added 4#

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 c. Polychords: combination of two or more tertian chords

ex. 2.8 is a polychord consisting of an F# chord over a C chord

Chords and inversions

When in the category of tertian chords, the chord has another bass note than the root, it is
inverted. Look at the 2nd chord of the Mozart in Ex. 2.3a and Ex. 2.3b

Tertian chords have the following inversions:

ex. 2.9 Of each position/inversion, two versions are given: a so called ‘closed voicing’ and
an ‘open voicing’. For the type of inversion this doesn’t matter, only which chord-member is
in the lowest voice matters.

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The numbers underneath the chords are the intervals counted from the lowest note.
Composers would use this during the baroque period to indicate which chords needs to be
played (see below: figured bass).

If there is a number next to this, then this is a shorter version of the same chord. Sometimes
these numbers are also used to name a specific chord, f.e. a C chord in 6th position is the
same as a C chord in first inversion or a C/E. This last notation, C/E, is called a chord symbol
(see below: chord symbol)

In the other categories inverted chords do not exist28.

28
There are 20th c. harmony books that discuss inversions of secundal- and quartal chords, f.e. Periscetti’s
Twentieth Century Harmony; p. 95, but also indicate that this is not without problems.

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Chord Notation

There are three ways of notating chords:

1. Figured bass
2. Roman Numeral
3. Chord symbols

1. Figured bass is a musical notation that came into fashion during the Baroque period and is
a kind of shorthand notation for the notes the accompaniment -mostly a keyboard
instrument, but also a lute or guitar is possible- should play upon a given bass-part. During
the Classical period this way of notating disappeared.
The principle is rather simple: there is a bass-note, and the numbers tell you which diatonic29
intervals you must play on the bass. If there is no number it means you play the 3rd and 5th,
or root-position chord. We will use Figured bass for reading only.

ex. 2.10

2. Roman Numerals is a notation to indicate the scale degree upon which a chord is build.
This also originates in the Baroque period and became a way of analyzing chords at most
conservatoires during the 20th century.

ex. 2.11a

29
Diatonic means within the scale.

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For inversions, the same numbers as in figured bass notation is used:

ex. 2.11b

We will use Roman Numerals for analysis, mainly for tonal repertoire and a bit in modal
repertoire.

3. Chord symbols are originally used by jazz- and pop musicians to have a quick reference to
what chord needs to be played. In jazz music often only the melody is notated with the
chords added to this. An example of this can be seen in Ex. 1.2b: Gershwin’s song
Summertime. Inversions are notated with the chord/bass-note; see also ex. 2.9.
Chord symbols are also useful for notating non-tertian chords like described in Ex. 2.5 and
Ex. 2.6. We can use Chord symbols in any repertoire.

If we would use all three notation systems in ex. 2.12, it would look like this:

Exercises

1. Take the melodies you composed in the previous chapter and add harmony to each
melody. Experiment with using the different chord-categories. Write the harmonies as
chord-symbols to the melody.
2. Record the harmonized melodies.

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What is the relation between Chords and Scales? 30

Just as a scale is the basis for making melodies, it is also the basis for making chords. As we
have seen, on every note of a scale a chord can be made. In different scales, this gives a
different succession of chords.

At the end of the first movement of Bartok’s Piano concerto no. 2 (between 295-305), the
trumpets play a theme in D-dorian, while the solo-piano plays an ascending scale, starting
from the 3rd note of the same Dorian scale, each note harmonized with a tertian triad:
https://youtu.be/Qku2K6vbQtM?t=53

ex. 2.13

30
As mentioned in the chapter about scales: ‘it is important to mention that in a mature composition hardly
ever only the notes of one scale are used’. This also affects the chords. See the Mozart example Ex. 2.3a and Ex.
2.3b

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The harmonic landscape changes when another type of chord is used. In the second
movement of Bartok’s 2nd piano concerto, from 121-123, the left-hand piano plays an
ascending B-Locrian scale, but now harmonized with secundal chords.
See how the orchestra (strings pizzicato) is continuing the scale from 124 onwards, while the
left-hand piano plays the secundal chords arpeggiated (till 140, not shown in the example).
https://youtu.be/Qku2K6vbQtM?t=1003

ex. 2.14

The right-hand plays an ascending A# pentatonic scale, harmonized with chords belonging to
that scale. Together they form complete chromatic chords, similar to Ex. 2.1a: Bartok’s
Melody in the mist

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To summarize: on every scale-degree a chord can be made. The chosen type of chord
(partly) defines the style of the composition (see: Overview of historical periods and type of
chords used).

ex. 2.15: C major scale harmonized with secundal, tertian, quartal and quintal chords

In the previous examples we have seen that chords are used as accompaniment (ex. 2.10), as
a dialogue with a melody (Ex. 2.1a), or as the main musical idea (Ex. 2.3a).

2.2 Analysis: Recognising chords in context

Like scales, to recognize chords in the context of a composition is not always easy.

The question we will deal with in this chapter are:

How do we determine the chord used?

We will see that the approach will be different for different historical periods. Sometimes,
more than one answer is possible, depending on the perspective you take.
Apart that we can use our brain to determine the chord, it would be advisable you to use
your (musical) ear, by singing or playing the examples, since that helps a lot in deciding.

Let’s revisit some pieces we have already seen:

a. Mozart - Fantasia in D minor (± 1782). https://youtu.be/1BkZ8ci8_k4

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ex. 2.16a Mozart - Fantasia in D minor bar 1 - 19

47
First we establish the historical period and style, to know what scale and chord options we
have. The Fantasia is written around 1782 during the classical period, which is part of the
tonal period. This means that it can only be written in a major- or minor key. In this case it is
in D minor as is already revealed in the title.
For the chords we will only look for tertian-chords.

The D minor scale provides the following chords:

ex. 2.16b

If we compare these chords to the Fantasia, we see that most chords match, but as we
know, a composer can also use altered notes that are coming from other scales, and these
chords don’t match.

As with altered notes in a melody, altered notes in chords relate to what is coming next. F.e.
the D7/C chord in bar 5/6 has an ‘F#’, and as we learned: a note that is raised will solve
upwards to the next note from the scale, in this case to a ‘G’ as part of a Gm chord in bar 7.
The same with the ‘G#’ -as part of the G#o7- that moves up to A.

The Eb chord is a special case that we will discuss later.

We also see some notes in bar 7,8 and 10 that do not fit the tertian-chords. These notes
embellish the chords but will always move to a chord-note:
in bar 7: the ‘A’ goes to the ‘G’, or in bar 10: the ‘D#’ goes to an ‘E’.

Exercises:

1. Analyse the chords from bar 12 – 19. Write the chord-symbols and the roman
numerals
2. Indicate the alterations
3. Which chords do not belong to D minor. Explain their relationship with the next
chord.

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ex. 2.16c

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 b. Lassus - Bonjour mon coeur (1564) Bar 1 - 16 https://youtu.be/zFVvCFGz36g

ex. 2.17a

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This 4-part Chanson was written around 1564, so at the end of the Renaissance. The scales
that are used in this period are modal, and the chords will be tertian.

The Chanson starts (and ends – see https://youtu.be/zFVvCFGz36g) in D. With one sharp at
the staff this means D mixolydian. You hear the typical mixolydian seventh immediately in
the 2nd chord!

Let’s look at the chords in a D mixolydian scale:

ex. 2.17b

We see that most chords fit this scale, but again -like the Mozart example- some don’t fit. If
we examine these chords in relation to what follows, we see that in bar 5 the ‘G#’, as part of
an E chord solves to an A chord. The ‘C#’ in the A chord solves to a D chord.
A different case of solution is the E chord in bar 13: the melody has a ‘G#’ solving to an ‘A’,
but the chord is not A but D. This would be a typical ‘modal’ chord progression (because the
chord does not really solve.

Exercises:
1. Analyse the chords from bar 11 – 16
2. All chords but two are triads in root-position. Which two chords are not, and in which
inversion?
3. From a modal perspective, how would you analyse the cadential arrival at the last
chord of this fragment?

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 c. Debussy - …Des pas sur la neige (1909-1910) bar 1 – 15 https://youtu.be/5ZpysYzdIrk

In the next example of the Impressionistic composer Debussy, we already know that there
are several scale-options and that the scale often changes (see the red lines). The same
counts for the chords-options. All kinds of chords, not only tertian chords, are possible. This
makes the analysis a bit more complex.
Another complicating factor is that in this style, it is not very clear which notes belong to a
chord and which one not, for this we can chose between analytical perspectives.

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Before we discuss two perspectives, first observe the following: it seems as if there are
several independent elements operating:
element 1: the ostinato31 motive in bar 1 – 11
element 2: bar 2 – 7 a melody above the ostinato, bar 8 – 11 a melody below the ostinato,
bar 12 – 15 a melody without the ostinato
element 3: bar 5 – 7 chords below the ostinato and melody, bar 2 – 4 and bar 8 – 15 chords
formed by all the layers

We take bar 5 -7 to discuss two analytical perspectives on the chords:

Perspective 1.
We see the separate elements (ostinato, melody, and chords) operating individually, and we
don’t consider them all as part of a whole. We separate the chords from the other elements.
Then the chords are quite easy to analyse:

The scale at that moment is a D dorian scale, and all the (tertian) chords match with this
scale.

The advantage of this perspective is clear: it leads to a nice ‘clean’ chord-result. The
disadvantage is that we cannot use this strategy in other parts …Des pas sur la neige

Perspective 2.
We incorporate the separate elements in the chord structure.
For the ostinato, we take the second note as a chord-note. This adds a 6th to the G chord, the
melody adds a 9th. This makes the first chord more complicated: it becomes a G chord with
added 6th and 9th.

The advantage of this perspective is that we can use this strategy in other parts.

31
Ostinato means a repeating musical figure

53
Exercises:
1. What notes are added to the other 3 chords in bar 5 – 6?
2. Analyse the 12 boxed chords (see below) with the strategy of perspective 2. Be aware
that there are other chords than tertian chords. In chord no. 8: consider the ‘F’ as an ‘E#’,
what tertian-chord can you make?
3. What is the relation between chord 8 and 9?
4. There are two chords from the sub-category ‘Whole tone chords’. Which two?

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 d. Stockhausen – Tierkreis (1974-1975) https://youtu.be/BbV7D4es0Zs

In this last example we face a similar situation as in the Debussy example, except that the
set-up is much simpler: a melody with chords.
We still need to choose if we follow perspective 1: seeing the chords separate from the
melody; or perspective 2: incorporate the melody into the chords.

For this piece we follow perspective 1.

Exercises:

1. In the first 13 bars we see 2 chords alternating. Name these chords.

2. In bar 14 – 16 we only see 2 notes. Why?
3. Name the last chord.

Extra exercise: you can try perspective 2.

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