Diatonic functionality Guide, Meaning , Facts, Information and Description

See also: function and functional.

Diatonic functionality, in music, is the assumption used in tonal music theory that pitches may only be used in their recognized roles. This includes the assumption that a pitch or pitch class and its enharmonic equivalents can not be used in the same way. For example a C# cannot be used as a Db, however this is not to say that they are not enharmonic equivalents, for they are in equal temperament, but rather that a Bb minor chord does not have a C# as its third, but a Db, and an F# major scale does not have a Db as its fifth degree, but a C#.

Thus a pitch may or may not fulfill one or more functions. Functional tonality refers to tonality which uses diatonic functions, non-functional tonality being when the diatonic elements are present (for instance the major scale) but do not use or fulfill their possible function as in, for instance, pandiatonicism.

In theory as commonly taught in the US, there are seven different functions, while in Germany, from the theories of Hugo Riemann, there are only three, and functions besides the tonic, subdominant and dominant are named as "parallels" (US: relatives) to those functions. For instance in C major an a minor is the Tonic parallel or Tp. German musicians use only upper case note letter and roman numeral abbreviations, while in the US often upper and lower-case are used to designate major and augmented, and minor and diminised, respectively. (Gjerdingen, 1990)

As d'Indy summarizes: "(1) There is only one chord, a perfect chord; it alone is consonant because it alone generates a feeling of repose and balance; (2) 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; (3) this chord is able to take oon three different tonal functions, tonic, dominant, or subdominant." (1903, p.116)

In the United States, Germany, and other places the diatonic functions are:

Function	Roman Numeral	German	German abbreviation
Tonic	I	Tonic	T
Supertonic	II	Subdominant parallel	Sp
Mediant	III	Dominant parallel	Dp
Sub-Dominant	IV	Subdominant	S
Dominant	V	Dominant	D
Sub-Mediant	VI	Tonic parallel	Tp
Leading/Subtonic	VII	incomplete Dominant seventh	diagonally slashed D7

The degrees listed according to function, in hierarchical order according to importance or centeredness (related to the tonic): I, V, IV, vi, iii, ii, vii°. The first three chords are major, the next minor, and the last diminished.

The tonic, subdominant, and dominant chords, in root position, each followed by its parallel. The parallel is formed by rasing the fifth a whole tone, the root position of the parallel chords is indicated by the small noteheads.

In the US the minor mode or scale is considered a variant of the major, while in German theory it is often considered, per Riemann, the inversion of the major. In the late eighteenth-early nineteenth centuries a large amount of symmetrical chords and relations known as "dualistic" harmony. The root of a major chord is its bass note in first inversion or normal form at the bottom of a third and fifth, but, symmetrically, the root of a major chord is the US fifth of a first inversion minor chord, and the US root is the "fifth". The plus and degree symbols, + and ^o are used to denote that the lower tone of the fifth is the root, as in major, +d, or the higher, as in minor, ^od. Thus, if the major tonic parallel is the tonic, with the fifth raised a whole tone, then the minor tonic is the tonic with the US root/German fifth lowered a whole tone. (Gjerdingen, 1990)

Major			Minor
Parallel	Note letter in C	US name	Parallel	Note letter in C	US name
Tp	A minor	Submediant	tP	Eb major	Mediant
Sp	D minor	Supertonic	sP	Ab major	Submediant
Dp	E minor	Mediant	dP	Bb major	Subtonic

The minor tonic, subdominant, dominant, and their parallels, created by lowering the fifth (German)/root (US) a whole tone.

If chords may be formed by raising (major) or lowering (minor) the fifth a whole step, they may also be formed by lowering (major) or raising (minor) the root a half-step to wechsel, the leading tone or leitton. These chords are Leittonwechselklänge, sometimes called gegenklang or "contrast chord". (Gjerdingen, 1990)

Leittonwechselklänge
Major			Minor
Tl	Sl	Dl	tL	sL	dL
E minor	A minor	B minor	Ab major	Db major	Eb major

Major Leittonwechselklänge, formed by lowering the root a half step.

Minor Leittonwechselklänge, formed by raising the root (US)/fifth (German) a half step.

"Three categories can appear in any one of three chordal guises in either of two modes, eighteen positions in all: T, Tp, Tl, t, tP, tL, S, Sp, Sl, s, sP, sL, D, Dp, Dl, d, dP, dL. Why all this complexity? Perhaps the central reason is that this ingenious, occasionally convoluted system enabled Riemann to achieve a grand and masterful synthesis of both the old and the new in late 19-century music. Ostensibly remote triads could be interpreted through the traditional terms of the I-IV-V-I, or now T-S-D-T, cadential schema. A sequence of Ab-major, Bb-major, and C-major chords, for example, could be neatly interpreted as a subdominant (sP) to dominant (dP) to tonic (T) progression in C-major, a reading of these chords not without support in certain late-Romantic cadences. And a chord that often perplexes harmony students, the Neapolitan chord Db major in a C-major context, could be shown to be nothing more than a minor-mode subdominant Liettonwechselklang (sL)." - (Gjerdingen, 1990, p.xiii-xiv)

"Some may at first be put off by the overt theorizing apparent in German harmony, wishing perhaps that a choice be made once and for all between Reichmann's Functionstheorie and the older Stufentheorie, or possibly believing that so-called linear theories have settled all earlier disputes. Yet this ongoing conflict between antdithetical theories, with its attendent uncertainties and complexities, has special merits. In particuler, whereas an English-speaking student may falsely believe that he or she is learning harmony "as it really is," the German student encounters what are obviously theoretical constructs and must deal with them accordingly." (Gjerdingen, 1990, p.xv)

Another theory regarding harmonic functionality is that "functional succession is explained by the circle of fifths (in which, therefore, scale degree II is closer to the dominant than scale degree IV)." According to Goldman's Harmony in Western Music, "the IV chord is actually, in the simplest mechanisms of diatonic relationships, at the greatest distance from I. In terms of the circle of fifths, it leads away from I, rather than toward it." (1965, p.68) Thus the progression I-ii-V-I would comply more with tonal logic. However, Goldman (ibid., chapter 3), as well as Jean-Jacques Nattiez, points out that "the chord on the fourth degree appears long before the chord on II, and the subsequent final I, in the progression I-IV-vii^o-iii-vi-ii-V-I." (Nattiez 1990, p. 226) Goldman also points out that, "historically the use of the IV chord in harmonic design, and especially in cadences, exhibits some curious features. By and large, one can say that the use of IV in final cadences becomes more common in the nineteenth century than it was in the eighteenth, but that it may also be understood as a substitute for the ii chord when it proceeds V. It may also be quite logically construed as an incomplete ii⁷ chord (lacking root)." (1968, p.68) However, Nattiez calls this, "a narrow escape: only the theory of a ii chord without a root allows Goldman to maintain that the circle of fifths is completely valid from Bach to Wagner." (1990, p.226)

Table of contents

1 Tonicization and modulation 2 Further reading 3 Source

Tonicization and modulation

Functions during or after modulations and especiallyl tonicizations are often notated in relation to the function, in the original key, which the tonicization was to. Sometimes called "function of function", for example, in C major, a D major chord root, is notated as II, but during a tonicization on G major, it would be notated, as in G major, V, as it is the dominant of (in C major) the dominant, it is notated V/V (five of five). For example, the twelve bar blues turnaround, I-V-IV-I, considered tonally inadmissable, may be interpreted as a doubled plagal cadence, IV/V-V-IV-I (IV/V-I/V, IV/I-I/I).

See: Function, chord progression.

Further reading

• Innig, Renate (1970). System der Funktionsbezeichnung in den Harmonielehren seit Hugo Riemann. Dusseldorf: Gesellschaft zur Förderung der systematichen Musik wissenschaft.

Source

• Gjerdingen, Robert O. (1990). "A Guide to the Terminology of German Harmony", Studies in the Origin of Harmonic Tonality by Dahlhaus, Carl, trans. Gjerdingen (1990). Princeton University Press. ISBN 0691091358.
• Nattiez, Jean-Jacques (1990). Music and Discourse: Toward a Semiology of Music (Musicologie générale et sémiologue, 1987). Translated by Carolyn Abbate (1990). ISBN 0691027145.
  • D'Indy (1903).
  • Goldman (1965). Harmony in Western Music.

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