A diatonic function, in tonal music theory, is the specific, recognized roles of notes or chords in relation to the key. Tonality is a system of writing music according to certain hierarchical pitch relationships around a center or tonic. ... Music theory is a field of study that describes the elements of music and includes the development and application of methods for analyzing and composing music, and the interrelationship between the notation of music and performance practice. ... A function is part of an answer to a question about why some object or process occurred in a system that evolved or was designed with some goal. ... The examples and perspective in this article or section may not represent a worldwide view. ... In music theory, the key identifies the tonic triad, the chord, major or minor, which represents the final point of rest for a piece, or the focal point of a section. ...

Three general and inseparable essential features of harmonic function in tonal music are that:

1. Position within a gamut (the available collection) of notes determines a note's function
2. Each note within the gamut is a generator and collector of other notes in the gamut, in other words both the root and its chord exercise function, and
3. Exercise and identification of function depends on musical behaviour or structure. (Wilson 1992, p.33)

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). The root (basse fondamentale) of a chord is the note upon which that chord is perceived or labelled as built or centered, the root of a chord in root position or normal form. ... The term musical form is used in two related ways: a generic type of composition such as the symphony or concerto the structure of a particular piece, how its parts are put together to make the whole; this too can be generic, such as binary form or sonata form Musical...

Pandiatonic music is diatonic music without the use of diatonic functions. In music pandiatonic chords and successions are those formed freely from all degrees of a diatonic scale without regard for their diatonic function, sometimes to the extent of no single pitch being felt as a tonic. ... In Music theory, the diatonic major scale (also known as the Guido scale), from the Greek diatonikos or to stretch out, is a fundamental building block of the European-influenced musical tradition. ...

Diatonic functions of notes and chords

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 music theory, a scale degree is the name of a particular note of a scale in relation to the tonic (the first note in the scale). ... In music, a scale is a set of musical notes that provides material for part or all of a musical work. ... The examples and perspective in this article or section may not represent a worldwide view. ... In music, pitch is the perception of the frequency of a note. ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). ... In music, see the following intervals: Major third Minor third The mediant, and the chord built on the mediant, is often called simply the third, as it is the third degree of the diatonic scale. ... Generally speaking, a minor chord is any chord which has a minor third above its root, as opposed to a major chord which has a major third. ... Fifth means one part out of five (1/5, 0. ... In music theory, a scale degree is the name of a particular note of a scale in relation to the tonic (the first note in the scale). ... In music theory, the major scale (or major mode) is one of the diatonic scales. ...

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) Dr. Hugo Riemann (full name: Karl Wilhelm Julius Hugo Riemann) (July 18, 1849 - July 10, 1919) was a German musicologist. ...

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, ii, vi, and vii are lowercase; this is because in relation to the key, they are minor scales. Without accidentals, the vii is a diminished vii°. In music or music theory, the supertonic is the second degree of the scale, it is the second note of a diatonic scale. ... In music theory, the subdominant parallel is terminology used in German theory derived mainly from Hugo Riemann, Sp, in major, and sP, in minor, is the (US) relative to the subdominant and is thus considered to have or fulfill the function of the subdominant. ... For mediant in mathematics, see Mediant (mathematics) In music, the mediant is the third degree of the diatonic scale. ... In music theory, the dominant parallel is terminology used in German theory derived mainly from Hugo Riemann, Dp, in major, and dP, in minor, is the (US) relative to the dominant and is thus considered to have or fulfill the function of the dominant. ... In music, the subdominant is the technical name for the fourth degree of the scale. ... In music, the subdominant is the technical name for the fourth tonal degree of the diatonic scale. ... In music, the dominant is the fifth degree of the scale. ... In music, the submediant is the sixth degree of the scale. ... In music theory, the tonic parallel is terminology used in German theory derived mainly from Hugo Riemann, Tp, in major, and tP, in minor, is the (US) relative to the tonic and is thus considered to have or fulfill the function of the tonic. ... In music theory, a leading-tone (called the leading-note outside the US) is a note or pitch which resolves or leads to a note one semitone higher or lower, being a lower and upper leading-tone, respectively. ... In music, the subtonic is the lowered seventh degree of the scale, as opposed to the leading tone. ...

Image File history File links Download high resolution version (868x101, 3 KB)Diatonic functions in hierarchical order Created by Hyacinth using Sibelius and Paint. ...

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.

Image File history File links Download high resolution version (892x128, 3 KB)Tonic, Subdominant, Dominant, and their parallels Created by Hyacinth using Sibelius. ...

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 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 ^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) The term normal form is used in a variety of contexts. ...

Image File history File links Download high resolution version (870x100, 3 KB)Minor Tonic, Subdominant, Dominant, and their parallels Created by Hyacinth using Sibelius. ...

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)

Image File history File links Download high resolution version (868x105, 3 KB)Major Leittonwechselklänge Created by Hyacinth using Sibelius. ...

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

Image File history File links Download high resolution version (863x105, 3 KB)Minor Leittonwechselklänge Created by Hyacinth using Sibelius and Paint. ...

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 Leittonwechselklang (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 Funktionstheorie 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)

In music theory, a Neapolitan chord is a major chord built on the lowered second (supertonic) scale degree. ...

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-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 precedes 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) In music theory, the circle of fifths is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ... Jean-Jacques Nattiez is a musical semiologist or semiotician and professor of Musicology at the University of Montreal. ...

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). In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. ... In music, tonicization is the treatment of a pitch other than the overall tonic as a tonic for a part of a composition. ... Twelve bar blues is a chord progression, typical of blues and later, blues-influenced, music. ... Jargon used in the chemical manufacturing and petroleum refining industries. ... In Western musical theory a cadence (Latin cadentia, a falling) is a particular series of intervals (a caesura) or chords that ends a phrase, section, or piece of music. ...

Functional behaviours

From the viewpoint of musical behaviour or structure there are five functions:

1. Tonic: I
2. Dominant: V and vii
3. Subdominant: IV
4. Dominant preparation
5. Tonic substitution or extension

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:

1. Principal goal tone or event
2. Initiating event
3. Generator of other tones, and the
4. Stable center neutralizing the tension between dominant and subdominant,

while the dominant has only the role of creating instability that requires the tonic or goal-tone for release. The subdominant also acts as a dominant preparation. A tonic extension is an elaboration of an initiating event while substitution is an alteration of a cadential point or goal tone. Many of these functions may still be found in post-tonal music. (ibid, p.37-39)

See also

• chord progression

A chord progression (also chord sequence and harmonic progression or sequence), as its name implies, is a series of chords played in an order. ...

Further reading

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

Sources

• 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.
• Wilson, Paul (1992). The Music of Béla Bartók. ISBN 0300051115.