Theory of Harmony

As a comparative reading informed by recent work in integration theory and metaphor theory shows, Heinrich Schenker's and Arnold Schoenberg's Harmonielehren adumbrate broader theories of composition based in part on a conception of the tone as a partly unconsciously perceived, living idea, which the artist imitates in a piece of music as a manifestation or development of one particular tone by means of the motive and the key. Schenker and Schoenberg further conceive of a piece as a picture of the tone and a statement about the tone. This analysis reveals that Schenker's and Schoenberg's peculiar clashes, such as in their starkly opposed attitudes toward tonality, are the result of a mere difference in emphasis—attributable to temperament—on the absoluteness of the tone as an idea of nature versus the contingency of the artist's response to the tone in the formation of music, a contradiction inherent in both of their remarkably parallel theories. This deep unity in Schenker's and Schoenberg's musical thought invites a reassessment of the opposed historical categories of tonal and post-tonal music, which have informed our perception of a fundamental conflict between their theories and limited our perception of commonality between their theories.

"Two works (Treber, Denton 2010; Luong, Montreal 2012) have recently reconsidered the collection of papers about opus 90 by Schenker and Elias housed in the Ernst Oster Collection, New York.
Vivian Luong examines the question of Schenker's concepts of performance and analysis, using Agawu's and Smith's definitions of ambiguity and incorporating revisionist Schenkerian theories of multiple analytical and performance interpretation. Her research on Schenker ́s conflicting graphs and annotated scores outlines two critical passages: the exposition ́s transition and the development ́s end. The ambiguity of the placement of the subordinate theme (mm. 45 or 55?) in Schenker's graphs is supported by a consideration of Caplin's formal functions.
On the other hand, Luong's explanation of the transition ignores the Eb (mm. 37-38) in the enharmonic reinterpretation of Bb (mm. 37-44) and underestimates the „few textural changes“ in the recapitulation. Why does the transition begin at the distance of a third (mm. 24/167) and land at the distance of a fifth (mm. 45/188)? I will insert my analysis (Hamburg 2012) here, integrating tools of historical and systematical German-speaking theory, and then compare my results for the first movement with Schenker's ambiguity among “apparent tripartite organization” and “underlying two-part interrupted structure”.
Stefan L. Treber embeds his Schenkerian analysis in a biographical-historical frame: according to Schindler/Krones, a program could explain the two-movement-structure of opus 90. My approach renounces to any non-musical references but the category of Historicism in art applied to Beethoven's harmonics. It extends the definition of enharmonischer Wendepunkt (Besseler 1955, Bahr 2005), reflects on funktionale Mehrdeutigkeit (s. Holtmeier 2011) and opens to a multi-level interpretation of subthematics:
1) Single ton: Distinctiveness principle, autonomous and integrated tone, signum (Hohlfeld) 2) Several tones: Tonfolge (“ton succession”), model(s), paradigm
3) Abstraction: Formel (Dahlhaus/Hohlfeld?), Vehikel (Sprick 2011).
This path conducts to a coherent large-form including both movements of the sonata."

This article follows on the heels of one by Holly Watkins, who argues that music, “a subsystem of the social system of communication,” can evoke the organic (the bodily and the psychic) not by forming a self-contained unity of parts and whole but through the “internal recursiveness” of musical works, their external “recursiveness vis-à-vis other music,” and – crucially – “the knowingness that music displays toward its own operations.” I adopt the premise that music evokes the organic most vividly not through recursive processes in individual systems but through the as-if intentional integration of such processes in multiple systems, of which I concern myself particularly with the harmonic, contrapuntal, and formal domains (or, more precisely, the motivic). I offer correctives to the organicist theories of Arnold Schoenberg and Heinrich Schenker, which similarly concern these domains, and especially to their reception. And I explore this direction through an analysis of Bach’s Prelude No. 7 in E-flat major from book 1 of The Well-Tempered Clavier, BWV 852, a singular piece that billows forth like an unfathomable blossom.

The article describes an approach to the classification of chords in order to develop auditory probabilistic prediction of harmony. The proposed approach is intended for teaching children, starting from primary school age, but also students of various levels of training.
Keywords: harmony, solfeggio, auditory prediction, classification of chords

In routine everyday discussions of the term ‘tonality’, it is generally and very readily taken to signify the musical language that had reigned supreme in the works of all Western-oriented composers from the late 17th to the first half of the 20th century. There are, however, several serious problems with this a posteriori statement. The theoretical handbooks, treatises and studies published in Europe in the 18th and 19th centuries offer no uniform definition or a widely accepted understanding of what this system represents. Furthermore, in many texts which have become accepted as ‘formative’ (such as Rameau’s Traité de l’harmonie), tonality is almost axiomatically being taken for granted. If theoretical writings give rise to confusion, creative production only adds fuel to the flame, because its treatment is hardly consistent in either the historical (chronological) or geographical sense, and seems to be remarkably nation- and culture-specific.
For instance, tonality in the sense used by early theorists and composers comes very close to a modal system; Russian and Soviet handbooks tend to combine it with folk music scales; and the tonality of musicians of a Wagnerian-Lisztonian orientation go as far as to eliminate the need for that which is considered the main postulate of the tonal system: tension and resolution.
This paper will attempt to analyze key theoretical postulates and musical practice in order to answer the following question: is there such as thing as a common denominator that allows the existence of a single tonality? Or is this in fact a multitude of different systems which display some complementary rules?

Çeşitli müzik okullarında müzik eğitimi alan öğrenciler için Armoni derslerinde kullanabilecekleri "Hazır Armoni Defteri Şablonu" hazırladım.
Bu Armoni Şablonu'nun Komposizyon öğrencileri için olan 4 anahtarlı versiyonunu daha sonra hazırlayacak ve buraya yükleyeceğim.
İyi çalışmalar

An approach towards outlining a practical understanding of ancient music. Particularly dealing with aspects of ancient Greek music, as recounted by the translated fragments of Aristoxenus, Ptolemy and others. In brief, a summary guide defining a method for practically realising harmonic relations, rhythmic poetics, the varieties of the tonal genera, and tetrachord theory using standard techniques of rational string division.
(Please note: This is an incomplete review copy and as such does not contain the full text of this manuscript. If you would like the full picture, please do get in touch with me.)

How does rock harmony differ from that of the common practice? As several recent writings have shown, motions between individual chords-that is, functional behaviors-are often vastly different from that of the common practice. 1 Precisely how these and other harmonic differences coalesce to form surface-level progressions that depart from common-practice conventions, however, is a question that has been approached only peripherally. 2 With an emphasis on the classic-rock canon of the late 1960s through the 1980s, this article therefore investigates rock harmony from the larger perspective of the progression in an attempt to paint a more detailed picture of rock's idiosyncratic harmonic syntax. In particular, classifying triads as Tonic, Dominant, or Subdominant based largely on the similarity of their scale-degree content, or functional "kinship," reveals three central aspects of rock progressions. 3 First, they do not constrain the functional motion of their chords. In other words, unlike the TSDT paradigm of the common practice, the kinship functions of Subdominant and Dominant both move regularly to each other and to Tonic-functioned harmonies. Thus, there is no single kinship-functional paradigm that encompasses most rock progressions; rather, two paradigms appear more than any other: the authentic and plagal (described in more detail further below). Second, rock progressions that diverge from the common practice, which feature in the vast majority of songs, do so in two ways: by the ordering of the kinship functions into a form of the plagal paradigm, and/or by secondary triads that are unusual by common-practice norms, namely subtonic and mediant triads. Third, even when there appear secondary triads that are more typical by common-practice norms, namely submediant and supertonic triads, their behavior is often in opposition to those norms. This article will examine these elements of rock harmony in two parts. The first and larger part will establish a number of definitions necessary to parse progressions by their functional kinship. These include harmonic function, tonic perception, scale-degree assemblies, progressions, and types of progressions. The second part of the article will apply these definitions to a wide range of specific examples and generalizations in order to demonstrate how progressions in rock differ from those of the common practice. 1 See Nobile 2016, Quinn and White 2015, Doll 2007, and Stephenson 2002 (ch. 5). 2 Moore 2012 (71-79) views rock progressions as strongly modal, offering a flexible system for their analysis. Moore 1992 has also catalogued an extensive list of rock progressions by prominent root motions. Everett 2009 (214-301) offers a similarly-organized, comprehensive examination of rock progressions but, to categories based on root motions, he adds others based on contrapuntal motions, minor keys, modes, and chromaticism rather than by their distance from common-practice norms. De Clercq and Temperley 2011 provide a glimpse into some of rock's common "trigrams," which are three-chord successions that may occur across any perceptual boundaries rather than progressions that have a discernible beginning and end. And Biamonte 2010 is devoted to three rock-specific categories of harmonic progression: the double-plagal progression, the Aeolian progression, and modal scales thickened by harmonization in parallel triads. See also Biamonte 2012 for an extension of some of these ideas. 3 Following Harrison 1994, I capitalize the names of kinship functions (Tonic, Dominant, Subdominant) in order to distinguish them from specific triads with the same names, which remain uncapitalized.

In the history of music, compositions now seen as masterpieces were often given a harsh reception by both professional critics and the general public upon their first performance. This was also the case with the Symphony in D minor by César Franck (1822-1890). The premiere was very poorly received, and was criticized by Franck’s contemporaries and critics for (among other things) being too ‘German.’ The attacks were primarily aimed at the question of orchestration and instrumentation, as well as claims that the piece supposedly had a ‘hidden program’ – another possible element of the German tradition of the 19th century, although Franck strongly denied this accusation.
Anti-German feelings were on the rise in France after the country’s defeat in the Franco-Prussian War of 1870, and this antagonism soon found its way into the cultural scene. As a result, in 1871 Société Nationale de Musique was founded in Paris with the aim of preserving the French music tradition. However, merely fifteen years later, the Société was split into two factions. The first faction, led by Camille Saint-Saëns (1835-1921), continued to insist on the 'purity' of French music. The other faction, led by Franck and his students, championed foreign (primarily German) influence. Although it was Franck's faction that eventually emerged victorious from this duel (with the group of Saint-Saëns leaving the Société), the circles of French music academia remained deeply divided and mostly continued to harbor chauvinistic inclinations. It was in this climate that Franck decided to compose his symphony in the late 1880s. Upon its completion in late 1888, the symphony could not be performed by any relevant institutions due to opposition in leading musical circles, and the composer had no choice but to have its premiere performed by the orchestra of Conservatoire de Paris, the college where he taught.
Of course, 130 years later, Franck’s Symphony in D-minor is seen as one of the most important works of this genre in both France and the Romantic era. However, in view of the historical information presented above, this analysis will attempt to explain if the accusations against its composer had been justified – in other words, if a work with marked German characteristics had really been written in France in the era of national purism.

As mais diversas tendências da harmonia moderna são explicadas neste método inédito no mercado nacional, de autoria do pianista e professor Bebeto von Buettner. O livro é direcionado aos instrumentistas, arranjadores e estudantes que desejam se aprofundar no estudo das técnicas de harmonia. Entre outros, o método aborda os temas - blocos abertos, substituição das dominantes e interpolação dos acordes.

This article attempts to establish a systematic categorization of tonal sequences since 1600 based on historical practice and theoretical sources. Canonic sequences and variants of "gemelli" (sequential phrases based on parallel "imperfect consonances") from the renaissance era are being related to the bass line in the baroque era around 1600. This presupposes a basic outer-voice-setting which is conceived intervallically and provides a framework for diminutions and chromaticized versions. The models emerging from this practice can be systematically categorized according to the movements of the bass, the intervals between the outer voices and the numbers of the thorough-bass. Important sources for such systems can be found in treatises by Spiridionis a Monte Carmelo (1670), Georg Muffat (1699), Fedele Fenaroli (1775) und Luigi Cherubini (1847). The centralist systems of 19th-century "Harmonielehre", in contrast, are generally ill-suited to explain sequential structures. Whereas combinatorial thinking plays an important role in the development of sequences in the 17th century, the musical language after 1700 tends to become more idiomatic, which implies a reduction of sequence types. Handel, in his didactic writings, presents only the most commonly used sequence types. In the 19th century, tendencies towards the building of multiple-part-sequences and increasingly chromaticized variants can be observed that, however, usually still elaborate on baroque outer-voice-settings. Since sequences are omnipresent in tonal music, they acquire semantic meaning and therefore function as "topoi" only in concurrence with their historical and stylistic contexts.

The harmonic progression of aFCG (Am–F–C–G) and its transpositions constitute one rotation of what I call Axis progressions, namely progressions that begin with one of these four chords and cycle through the others in order, hence the Axis-a, -F, -C, and -G, respectively. Of these four progressions, the a-form and C-form, and to a lesser extent, the F-form, have become staples of mainstream popular songs from the last decades of the twentieth century and the first decades of the twenty-first. The a-form is especially noteworthy for being both extremely widespread and tonally ambiguous, in that the perception of its tonality may waver between the major and Aeolian modes. Not only does the progression conflate aspects of the two modes, but it may also vary the degree to which those modes are expressed and their proportion within the progression, resulting in a vast array of possible tonal settings. This article posits that tonality in these settings depends primarily on the melodic content of the progression. A methodology for melodic analysis is then presented and applied to a number of examples of Axis-a (as well as some Axis-F) progressions, to demonstrate how diverse its settings can be.

A partir de: FREITAS, Sérgio Paulo Ribeiro de. Que acorde ponho aqui?  Harmonia, práticas teóricas e o estudo de planos tonais em música popular. Tese (Doutorado em Música). Instituto de Artes, Universidade Estadual de Campinas, 2010. p. 434-449.

Igor Sposobin (Игорь Владимирович Способин, 1900-1954) was one of the most influential music theorists of the Soviet Russia. His scientific and pedagogical works primarily focus on musical harmony and forms. His textbooks have been translated into many languages and are used with certain adjustments as primary teaching tools in Eastern Europe and, above all, in China even today. This article will attempt to explain why Sposobin's harmony methodology has had so much success. Apart from the relations between politics and culture, which are apparent, we set out to explore whether there are other underlying reasons for the success of Sposobin's theories. The purpose of simplifying some of the previous theories, as well as the reasons for introducing the new ones shall be investigated.

In 1937–38, Igor V. Sposobin and three co-authors at the Moscow Conservatory published Uchebnik garmonii [Harmony Textbook]. This was the first officially approved harmony textbook in the USSR, which came to be adopted as “the basic textbook for courses on harmony in the music
schools of the Soviet Union” (Vladimir Protopopov, 1960). Characterized by its promulgation of the “scientifically based” theory of harmonic functions, this book was destined to be read by many more musicians in a foreign land. In 1955–56, Boris A. Arapov decreed at meetings held at the Central Conservatory of Music in China that the problem posed by the ethnicization of harmony should be solved by combining musical elements that are considered ethnically distinct with functional harmony. Wu Zuqiang, who had studied at the Moscow Conservatory in the 1950s before he headed the Central Conservatory in the 1980s, published a chapter from Uchebnik
garmonii already in 1955. The first Chinese translation of the whole book by Zhu Shimin was then published in 1957–58. The book soon attained canonic status in China and has been used in virtually all Chinese music institutions up to the present day. It is listed in the entrance examination
syllabi of selected conservatories and reputable music theorists have published model answers to the exercises it contains. This article investigates how the Chinese reception of Uchebnik garmonii
diverges from the sources that had inspired Sposobin and his colleagues to compose it in the first place, and throws light on the far-reaching impacts and ramifications of Uchebnik garmonii in China.

Western music is characterized by the use of harmony that enriches the melody, which was written for orchestra, some instruments, or choir through different styles of harmonic accompaniments and chord functions. While Arabic music is characterized by the rich melody, which depends on a great number of Oriental Modes without relying on Harmony, which was written in a monophonic style. Many of the Arab composers managed the integrate of their melodic ideas that based on Oriental Modes with harmony through their experience and their serious attempts. Moreover, they relied heavily on the taste without relying on scientific literature of Arabic harmony, because of its unavailability. Through this research, the researcher tries to contribute and develop those experiences through detailed analysis of all the Arabs Modes, which are free of three-quarters intervals, and to build a harmonic structure on all degrees, in order to get out a scientific study of harmony. This will open the gate for the development of the Arabic harmonic theories that provide the structure of harmonic voices, which will serve the character of Arabic music away from tradition. The researcher also considers this research as a step in the direction of creating the practical harmony just as the study of western music harmony, which relies on correct chord progressions.
تتميز الموسيقى الغربية باستخدام علوم الهارموني التي تثري اللحن الذي يتم توزيعه للأوركسترا أو لمجموعة من الآلات أو الكورال من خلال اساليب المصاحبات الهارمونية المختلفة Homophonic بينما تتميز الموسيقى العربية بثراء اللحن الذي يعتمد على كم كبير من المقامات العربية دون الإعتماد على علوم الهارموني ، حيث تعتمد على الصوت الواحد Monophonic ، استطاع العديد من المؤلفين العرب دمج أفكارهم اللحنية المبنية على المقامات العربية مع علوم الهارموني من خلال خبرتهم بتلك العلوم ومحاولاتهم الجادة ، ولكنها اعتمدت بدرجة كبيرة على الذوق والتذوق دون الإعتماد على المراجع العلمية لعلوم الهارموني العربي لعدم توفرها ، يحاول الباحث في هذا البحث المساهمة في بلورة تلك التجارب من خلال التحليل التفصيلي لجميع المقامات العربية الخالية من ثلاث أرباع البعد ، والبناء الهارموني على جميع تلك الدرجات بهدف الخروج بدراسة علمية تفتح المجال لوضع نظريات للهارموني العربي الذي من شأنه تقديم أصوات هارمونية تخدم الهوية العربية بعيداً عن التقليد .

This document is intended to provide an explanation of the evolution of the harmonic practice in the Romantic period. Although there are many other techniques that help to understand the harmonic thinking of the composers of that period, we tried to focus on the basic ones in order to give the student a first approach.

A substantial analytical literature has been devoted to Syrinx. The piece’s importance for the flute repertoire as well as its unconventional harmonic language has inspired a wide variety of approaches. Through the lens of Schenkerian theory, this paper provides an alternative reading of the piece. It demonstrates how tonal infiltration affects Syrinx’s harmonic discourse, generating a unique process of directional tonality, in which 1^  in Bb minor eventually becomes 3^  in Gb major. The conclusion shows that the procedure not only defines the harmonic structure of the piece, but also reflects the programmatic content originally intended for it.

The harmonic-functional system is based on a conception of harmony and the chords of the tonality derived from the notion of differential hierarchy, fifth relationships and functional affinity, whose consequence is the recognition of three basic functions – tonic, dominant and subdominant – and of three other secondary or derivative functions, each with two variants, which complete the rest of useful chords as secondary tonic within a given tonality.

A revision of the harmonic-functional system must begin with the very introduction of the concept of ‘function’ in musical theory and, more specifically, in musical analysis. Secondly, it is necessary to recall and discuss succinctly the same foundation of harmony, according to several authors (Rameau, Riemann, Schönberg), although focusing only on those aspects of its theoretical tradition that concern the origin of the chord, its position within the system, its typology and relationships between chords.

Finally, the paper develops a complete view of the harmonic-functional system which provides an overview of all types of chords that are studied in any academic harmony treatise, but grouped according to their function in harmonic discourse, that is, summarized under the cover of the three basic functions and their derived functions, in an organic unit that immediately gives each chord its role in speech and thus its harmonic function. In this section we will review the definition of basic functions and secondary functions, the numbering of chord sounds, movement of voices, cadential functions (dominant, dominant of the dominant and subdominant), tonicization and modulation, to end with extensions of the system that allow to use it even in the limits of the tonal system.

El navarro Hilarión Eslava fue extraordinariamente influyente como pedagogo musical. Su célebre tratado de armonía (iniciación a la composición) fue el texto de referencia en la materia durante la segunda mitad del siglo XIX en España. En este artículo describiremos y analizaremos este tratado estudiando sus aportaciones, para luego centrarnos en su recepción histórica y la influencia que alcanzó sobre teóricos posteriores.

L'acquisizione delle competenze necessarie per armonizzare un basso rappresenta da sempre, nella tradizione italiana, un passaggio obbligato per poter intraprendere lo studio dell'armonia e della composizione. Questa Introduzione allo studio dell'armonia, che costituisce una rivisitazione del precedente Elementi di armonia e analisi musicale (2014) dello stesso autore, rappresenta fondamentalmente un agile prontuario di regole utili per poter armonizzare correttamente un basso di media difficoltà. L'impostazione didattica che contraddistingue il manuale si basa su un tentativo di sintesi fra le principali tecniche di analisi e cifratura del basso: partendo dalla teoria del basso numerato (i suoni del basso, inteso come una linea melodica, vengono identificati con i corrispondenti numeri romani), e passando per la teoria dei gradi fondamentali (che nel testo vengono indicati, dove necessario, fra parentesi sotto i primi), si giunge infine all'introduzione di alcuni principi e simboli peculiari della teoria funzionale dell'armonia.

This essay presents evidence that James Joyce was knowledgeable about — and appreciated — modernist classical music. It provides an exposition of his musical life in Zurich and Paris, from 1915 onwards, with connection to his acquaintances with the composers Phillipe Jarnach, Otto Luening, and Georges Antheil; the modern musicological theory he learned in both cities; the concerts he attended; and how this lengthy collective experience realized itself artistically during the writing of episode 11 of Ulysses (titled “Sirens”) and throughout Finnegans Wake. This research into 20th century classical music in the works of Joyce stems largely from my dissatisfaction with contemporary critical summaries of his personal taste in music. I have concerns in regard to the general critical consensus that Joyce was traditional, non-eclectic and disliked the contemporary musical avant-garde despite being an experimental modernist himself. I feel that the current evidence supporting his apparent aversion to modernist classical music is inconclusive. The writing of this essay was also instigated by the considerable shortage of biographical and critical information available on the subject. ISBN 978-608-234-073-9

This is the book I have prepared and used for 20 years in the class of Musical Analysis I, as Professor of Musical Analysis and Composition in the Real Conservatorio Superior de Música de Madrid. This is a subject intended for students (players, conductors, composers, musicologists and pedagogues) in college or university level. It contains my own reflections in theory and analysis, as well as quotations from well-known scholars in the field of Theory of Music. It encompass a first theme devoted to the definition, place and types of analysis, followed by another theme with varied concepts as function, Fibonacci series, golden section and psychology of music. The third theme goes back to Gregorian modes and rhythmic modes, as well as the world of tones. The fourth is devoted to Rethoric of music and the Theory of topics, and this is a good place to propose an analysis of a fugue of Bach. The fifth theme explains the functional harmony, a field from which I have written several papers before in Academia. And the sixth theme updates the theory of sonata with the last publications and contrubutions of scholars as William Caplin and Hepokosky & Darcy. It ends with the analysis of a binary sonata of Scarlatti and a classical sonata by Mozart.
The book contains a list of works to analyse from Gregorian Chant to 19th century, an extended bibliography and many pages devoted to theory including several charts, figures, examples and analysis.

INVESTIGACIÓN REALIZADA ENTRE 1972-74 CON EL ING. JORGE GIL MENDIETA (IIMAS-UNAM), SOBRE LA RELACIÓN ENTRE LA ESCALA DIATÓNICA Y LA ESTRUCTURA DE GRUPO DEL CUBO (IIES-UNAM 1984). COMPRENDE UNA INTRODUCCIÓN A LA TEORÍA DE GRUPOS, A LAS RELACIONES ENTRE GRUPO Y ESCALA, AL ESTUDIO DE RELACIONES MELÓDICAS, ARMÓNICAS Y CONTRAPUNTÍSTICAS, ASÍ COMO APLICACIONES AL ANÁLISIS MUSICAL (BACH Y BEETHOVEN).

The present database UUPart, also called The Uppsala Partimento Database, represents the work of cataloguing and linking the repertoire of the Italian partimento for the time span roughly between 1700 and 1850. Initially, it was developed as a research tool at a doctoral dissertation project called "Counterpoint and Partimento: Methods of Teaching Composition in Late Eighteenth-Century Naples," recently published as nr. 25 in the series Studia Musicologica Upsaliensia of the Swedish publisher Acta Universitatis Upsaliensis.

Through an identification string of the first ten pitches, UUPart facilitates the searching and identification of concordant sources within the repertoire of the Italian partimento. For a list of sources of this database, click here.

You can search for a partimento by using the "Partimento Note String" scroll bar on top of the search menu, or you can enter a number of pitches manually in the fields "begins with" or "contains." Click search to find the matching partimenti. The content of a source can be investigated by scrolling the "RISM Siglum / call number" list.

Citations of The Uppsala Partimento Database UUPart should be made in the same style as for printed books in a series. It should include the URL, followed by the date of access. We provide the following as a model:

Peter van Tour. UUPart, The Uppsala Partimento Database. Compiled and edited by Peter van Tour. Launched 2015, Uppsala. http://www2.musik.uu.se/UUPart/UUPart.php; accessed 9 May 2015.