In music, function (also referred to as harmonic function) is a term used to denote the relationship of a
chord["Function", unsigned article, ''Grove Music Online'', .] or a
scale degree to a
tonal centre. Two main theories of tonal functions exist today:
* The German theory created by
Hugo Riemann
Karl Wilhelm Julius Hugo Riemann (18 July 1849 – 10 July 1919) was a German musicologist and composer who was among the founders of modern musicology. The leading European music scholar of his time, he was active and influential as both a musi ...
in his ''Vereinfachte Harmonielehre'' of 1893, which soon became an international success (English and Russian translations in 1896, French translation in 1899), and which is the theory of functions properly speaking.
["It was Riemann who coined the term 'function' in ''Vereinfachte Harmonielehre'' (1893) to describe relations between the dominant and subdominant harmonies and the referential tonic: he borrowed the word from mathematics, where it was used to designate the correlation of two variables, an 'argument' and a 'value'". Brian Hyer, "Tonality", ''Grove Music Online'', .] Riemann described three abstract tonal "functions", tonic, dominant and subdominant, denoted by the letters T, D and S respectively, each of which could take on a more or less modified appearance in any chord of the scale. This theory, in several revised forms, remains much in use for the pedagogy of harmony and analysis in German-speaking countries and in North- and East-European countries.
* The Viennese theory, characterized by the use of Roman numerals to denote the chords of the tonal scale, as developed by
Simon Sechter
Simon Sechter (11 October 1788 – 10 September 1867) was an Austrian music theorist, teacher, organist, conductor and composer. He was one of the most prolific composers who ever lived, although his music is largely forgotten and he is now mainl ...
,
Arnold Schoenberg
Arnold Schoenberg or Schönberg (, ; ; 13 September 187413 July 1951) was an Austrian-American composer, music theorist, teacher, writer, and painter. He is widely considered one of the most influential composers of the 20th century. He was as ...
,
Heinrich Schenker
Heinrich Schenker (19 June 1868 – 14 January 1935) was a Galician-born Austrian music theorist whose writings have had a profound influence on subsequent musical analysis. His approach, now termed Schenkerian analysis, was most fully exp ...
and others,
[Robert E. Wason, ''Viennese Harmonic Theory from Albrecthsberger to Schenker and Schoenberg'' (Ann Arbor, London, 1985) , pp. xi-xiii and passim.] practiced today in Western Europe and the United States. This theory in origin was not explicitly about tonal functions. It considers the relation of the chords to their tonic in the context of harmonic progressions, often following the cycle of fifths. That this actually describes what could be termed the "function" of the chords becomes quite evident in Schoenberg's ''Structural Functions of Harmony'' of 1954, a short treatise dealing mainly with harmonic progressions in the context of a general "monotonality".
Both theories find part of their inspiration in the theories of
Jean-Philippe Rameau
Jean-Philippe Rameau (; – ) was a French composer and music theory, music theorist. Regarded as one of the most important French composers and music theorists of the 18th century, he replaced Jean-Baptiste Lully as the dominant composer of Fr ...
, starting with his ''Traité d'harmonie'' of 1722. Even if the concept of harmonic function was not so named before 1893, it could be shown to exist, explicitly or implicitly, in many theories of harmony before that date. Early usages of the term in music (not necessarily in the sense implied here, or only vaguely so) include those by Fétis (''Traité complet de la théorie et de la pratique de l'harmonie'', 1844), Durutte (''Esthétique musicale'', 1855), Loquin (''Notions élémentaires d'harmonie moderne'', 1862), etc.
The idea of function has been extended further and is sometimes used to translate Antique concepts, such as ''dynamis'' in Ancient Greece, or ''qualitas'' in medieval Latin.
Origins of the concept
The concept of harmonic function originates in theories about
just intonation
In music, just intonation or pure intonation is the tuning of musical intervals
Interval may refer to:
Mathematics and physics
* Interval (mathematics), a range of numbers
** Partially ordered set#Intervals, its generalization from numbers to ...
. It was realized that three perfect major triads, distant from each other by a perfect fifth, produced the seven degrees of the major scale in one of the possible forms of just intonation: for instance, the triads F–A–C, C–E–G and G–B–D (subdominant, tonic, and dominant respectively) produce the seven notes of the major scale. These three triads were soon considered the most important chords of the major tonality, with the tonic in the center, the dominant above and the subdominant under.
This symmetric construction may have been one of the reasons why the fourth degree of the scale, and the chord built on it, were named "subdominant", i.e. the "dominant under
he tonic. It also is one of the origins of the
dualist
Dualism most commonly refers to:
* Mind–body dualism, a philosophical view which holds that mental phenomena are, at least in certain respects, not physical phenomena, or that the mind and the body are distinct and separable from one another
** ...
theories which described not only the scale in just intonation as a symmetric construction, but also the minor tonality as an inversion of the major one. Dualist theories are documented from the 16th century onwards.
German functional theory
The term 'functional harmony' derives from
Hugo Riemann
Karl Wilhelm Julius Hugo Riemann (18 July 1849 – 10 July 1919) was a German musicologist and composer who was among the founders of modern musicology. The leading European music scholar of his time, he was active and influential as both a musi ...
and, more particularly, from his ''Harmony Simplified''. Riemann's direct inspiration was Moritz Hauptmann's dialectic description of tonality. Riemann described three abstract functions: the tonic, the dominant (its upper fifth), and the subdominant (its lower fifth).
[Dahlhaus, Carl (1990). "A Guide to the Terminology of German Harmony", ''Studies in the Origin of Harmonic Tonality'', trans. Gjerdingen, Robert O. (1990). Princeton University Press. .] He also considered the minor scale to be the inversion of the major scale, so that the dominant was the fifth above the tonic in major, but below the tonic in minor; the subdominant, similarly, was the fifth below the tonic (or the fourth above) in major, and the reverse in minor.
Despite the complexity of his theory, Riemann's ideas had huge impact, especially where German influence was strong. A good example in this regard are the textbooks by Hermann Grabner. More recent German theorists have abandoned the most complex aspect of Riemann's theory, the dualist conception of major and minor, and consider that the dominant is the fifth degree above the tonic, the subdominant the fourth degree, both in minor and in major.
![Tonic parallel in C major](https://upload.wikimedia.org/wikipedia/commons/f/fc/Tonic_parallel_in_C_major.png)
In
Diether de la Motte
Diether de la Motte (30 March 1928 – 15 May 2010) was a German musician, composer, music theorist, music critic and academic teacher.
Life
Born in Bonn, de la Motte studied at the Hochschule für Musik Detmold from 1947 to 1950, composition ...
's version of the theory, the three tonal functions are denoted by the letters T, D and S, for Tonic, Dominant and Subdominant respectively; the letters are uppercase for functions in major (T, D, S), lowercase for functions in minor (t, d, s). Each of these functions can in principle be fulfilled by three chords: not only the main chord corresponding to the function, but also the chords a third lower or a third higher, as indicated by additional letters. An additional letter P or p indicates that the function is fulfilled by the relative (German ''Parallel'') of its main triad: for instance Tp for the minor relative of the major tonic (e.g., A minor for C major), tP for the major relative of the minor tonic (e.g. E major for c minor), etc. The other triad a third apart from the main one may be denoted by an additional G or g for ''Gegenparallelklang'' or ''Gegenklang'' ("counterrelative"), for instance tG for the major counterrelative of the minor tonic (e.g. A major for C minor).
The relation between triads a third apart resides in the fact that they differ from each other by one note only, the two other notes being common notes. In addition, within the diatonic scale, triads a third apart necessarily are of opposite mode. In the simplified theory where the functions in major and minor are on the same degrees of the scale, the possible functions of triads on degrees I to VII of the scale could be summarized as in the table below (degrees II in minor and VII in major, diminished fifths in the diatonic scale, are considered as chords without fundamental). Chords on III and VI may exert the same function as those a third above or a third below, but one of these two is less frequent than the other, as indicated by parentheses in the table.
In each case, the mode of the chord is denoted by the final letter: for instance, Sp for II in major indicates that II is the minor relative (p) of the major subdominant (S). The major VIth degree in minor is the only one where both functions, sP (major relative of the minor subdominant) and tG (major counterparallel of the minor tonic), are equally plausible. Other signs (not discussed here) are used to denote altered chords, chords without fundamental, applied dominants, etc. Degree VII in harmonic sequence (e.g. I–IV–VII–III–VI–II–V–I) may at times be denoted by its roman numeral; in major, the sequence would then be denoted by T–S–VII–Dp–Tp–Sp–D–T.
As summarized by Vincent d'Indy (1903), who shared the conception of Riemann:
#There is only ''one chord'', a ''perfect'' chord; it alone is consonant because it alone generates a feeling of repose and balance;
#this chord has two ''different forms'', ''major and minor'', depending whether the chord is composed of a minor third over a major third, or a major third over a minor;
#this chord is able to take on ''three different tonal functions, tonic, dominant, or subdominant''.
Viennese theory of the degrees
The Viennese theory on the other hand, the "Theory of the degrees" (''Stufentheorie''), represented by
Simon Sechter
Simon Sechter (11 October 1788 – 10 September 1867) was an Austrian music theorist, teacher, organist, conductor and composer. He was one of the most prolific composers who ever lived, although his music is largely forgotten and he is now mainl ...
,
Heinrich Schenker
Heinrich Schenker (19 June 1868 – 14 January 1935) was a Galician-born Austrian music theorist whose writings have had a profound influence on subsequent musical analysis. His approach, now termed Schenkerian analysis, was most fully exp ...
and
Arnold Schoenberg
Arnold Schoenberg or Schönberg (, ; ; 13 September 187413 July 1951) was an Austrian-American composer, music theorist, teacher, writer, and painter. He is widely considered one of the most influential composers of the 20th century. He was as ...
among others, considers that each degree has its own function and refers to the tonal center through the cycle of fifths; it stresses harmonic progressions above chord quality. In music theory as it is commonly taught in the US, there are six or seven different functions, depending on whether degree VII is considered to possess an independent function.
Comparison of the terminologies
The table below compares the English and German terminologies for the major scale. In English, the names of the scale degrees are also the names of their function, and they remain the same in major and in minor.
Note that ii, iii, and vi are lowercase: this indicates that they are minor chords; vii° indicates that this chord is a diminished triad.
Reviewing usage of harmonic theory in American publications, William Caplin writes:
[William Caplin, ''Analyzing Classical Form. An Approach for the Class Room''. Oxford and New York: Oxford University Press, 2013. . pp. 1–2.]
Caplin further explains that there are two main types of pre-dominant harmonies, "those built above the fourth degree of the scale () in the bass voice and those derived from the dominant of the dominant (V/V)" (p. 10). The first type includes IV, II
6 or II
6, but also other positions of these, such as IV
6 or II. The second type groups harmonies which feature the raised-fourth scale degree () functioning as the leading tone of the dominant: VII
7/V, V
6V, or the three varieties of
augmented sixth chord
In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, was further developed in the Baroque, and became a distinctive part of the musi ...
s.
See also
*
Common practice period
In European art music, the common-practice period is the era of the tonal system. Most of its features persisted from the mid- Baroque period through the Classical and Romantic periods, roughly from 1650 to 1900. There was much stylistic evoluti ...
*
Constant structure
In jazz, a constant structure is a chord progression consisting of three or more chords of the same type or quality.Rawlins, Robert (2005). ''Jazzology: The Encyclopedia of Jazz Theory for All Musicians'', p.131. . Popularized by pianists Bill Eva ...
*
Diatonic and chromatic
Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, ...
*
Nondominant seventh chord
In music theory, a nondominant seventh chord is both a diatonic chord and a seventh chord, but it does not possess dominant function, and thus it is ''not'' a dominant seventh chord.
Since the V and vii chords are the dominant function chord ...
*
Secondary dominant
A secondary chord is an analytical label for a specific harmonic device that is prevalent in the tonal idiom of Western music beginning in the common practice period: the use of diatonic functions for tonicization.
Secondary chords are a typ ...
*
Subsidiary chord
In music and musical analysis, a subsidiary chord is an elaboration of a principal harmonic chord in a chord progression.
If the principal chord (''X'') is partially replaced by the subsidiary (''Y''), there are three possible positions - begin ...
*
Roman numeral analysis
In music theory, Roman numeral analysis is a type of musical analysis in which chords are represented by Roman numerals (I, II, III, IV, …). In some cases, Roman numerals denote scale degrees themselves. More commonly, however, they represent t ...
References
Further reading
*Imig, Renate (1970). ''System der Funktionsbezeichnung in den Harmonielehren seit Hugo Riemann''. Düsseldorf: Gesellschaft zur Förderung der systematischen Musikwissenschaft. ''
erman Erman Rašiti may refer to:
Given name
* Erman Bulucu (born 1989), Turkish footballer
* Erman Eltemur (born 1993), Turkish karateka
* Erman Güraçar (born 1974), Turkish footballer
* Erman Kılıç (born 1983), Turkish footballer
* Erman Kunter (b ...
'
*Rehding, Alexander: ''Hugo Riemann and the Birth of Modern Musical Thought'' (New Perspectives in Music History and Criticism). Cambridge University Press (2003). .
*Riemann, Hugo: ''Vereinfachte Harmonielehre, oder die Lehre von den tonalen Funktionen der Akkorde'' (1893). ASIN: B0017UOATO.
*Schoenberg, Arnold: ''Structural Functions of Harmony''. W.W.Norton & Co. (1954, 1969) , .
External links
Unlocking the Mysteries of Diatonic Harmonywww.artofcomposing.com
* Example of Music theory course description from
Juilliard
The Juilliard School ( ) is a private performing arts conservatory in New York City. Established in 1905, the school trains about 850 undergraduate and graduate students in dance, drama, and music. It is widely regarded as one of the most elit ...
"Principles of harmony"(Archive from 24 November 2010, accessed 28 May 2013).
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