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A diatonic function, in tonal music theory, is the specific, recognized roles of notes or chords in relation to the key.
Three general and inseparable essential features of harmonic function in tonal music are:
A fourth feature is the ambiguity that arises from the use of the same terms to describe functions across all temporal spans of a hierarchical structure from the surface to the deepest level, and that the longer term or deeper functions act as a center for shorter higher level ones and that the functions of each tend to counteract each other (ibid).
Pandiatonic music is diatonic music without the use of diatonic functions.
Each degree of a scale, as well as many chromatically-altered notes, has a different diatonic function as does each chord built upon those notes. A pitch or pitch class and its enharmonic equivalents have different meanings. For example, a C♯ cannot substitute for a D♭, even though in equal temperament they are identical pitches, because the D♭ can serve as the third of a B♭ minor chord while a C♯ cannot, and the C♯ can serve as the fifth degree of an F♯ major scale while a D♭ cannot.
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 diminished, 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:
Note that the ii, iii, vi, and vii are lowercase; this is because in relation to the key, they are minor chords. Without accidentals, the vii is a diminished vii°.
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 raising 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 were 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 <sup>o</sup> are used to denote that the lower tone of the fifth is the root, as in major, +d, or the higher, as in minor, <sup>o</sup>d. 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)
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)
Major Leittonwechselklänge, formed by lowering the root a half step.
Minor Leittonwechselklänge, formed by raising the root (US)/fifth (German) a half step.
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<sup>o</sup>-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 precedes V. It may also be quite logically construed as an incomplete ii<sup>7</sup> 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)
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).
From the viewpoint of musical behaviour or structure there are three essential functions:
Other functions serve to support the Tonic and Dominant functions listed above:
The dominant, dominant preparation and the tonic substitution all involve more than one scale degree with only the tonic and subdominant containing only one scale degree. Several scale degrees exercise more than one function. (Wilson 1992, p.35)
The tonic includes four separate activities or roles as the: