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Diatonic functionality

From Academic Kids

Diatonic functionality, in tonal music theory, is the interpretation of notes or chords according to specific, recognized roles.

Contents

Diatonic functions of notes

Each degree of a scale, as well as many chromatically-altered notes, has a different diatonic function. A pitch or pitch class and its enharmonic equivalents have different meanings. For example, a C# cannot substitute for a Db, even though in equal temperament they are identical pitches, because the Db can serve as the third of a Bb minor chord while a C# cannot, and the C# can serve as the fifth degree of an F# major scale while a Db cannot. Pandiatonic music is diatonic music without the use of diatonic functions.

Generally speaking, the most important notes are the members of the tonic triad: the tonic, the mediant and the dominant. All other notes are understood to have some relation to those notes. The leading tone, for example, the seventh scale degree, has a significance of being a half-step below the tonic and has a tendency to resolve there. The fourth scale degree, the subdominant, has a tendency to resolve to the third degree, the mediant.

Diatonic functions of chords

Diatonic functionality can also refer to the meaning of a chord in relation to the key.

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 on 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

Missing image
Diatonic_functions_in_hierarchical_order.PNG
Diationic functions in hierarchical order

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.

Missing image
Tonic,_Subdominant,_Dominant,_and_their_parallels.PNG
Major T, S, D, and parallels

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

Functions in the minor mode

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

Missing image
Minor_Tonic,_Subdominant,_Dominant,_and_their_parallels.PNG
Minor T,S,D, and parallel

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

Missing image
Major_Leittonwechselklänge.PNG
Major Leittonwechselklänge

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

Missing image
Minor_Leittonwechselklänge.PNG
Minor Leittonwechselklänge

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

Quotes

  • 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 Riemann's Functionstheorie and the older Stufentheorie, or possibly believing that so-called linear theories have settled all earlier disputes. Yet this ongoing conflict between antithetical theories, with its attendant uncertainties and complexities, has special merits. In particular, 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)

Circle of fifths

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-viio-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)

Tonicization and modulation

Functions during or after modulations and especially 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 inadmissible, may be interpreted as a doubled plagal cadence, IV/V-V-IV-I (IV/V-I/V, IV/I-I/I).

See also

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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