User:Unque/19-function System

The Nineteen Function System is a categorization of intervals into nineteen major groups based on their size, consonance, and melodic function.

The Six Superfunctions

To avoid diatonic-centrism and indexing ambiguity, the six superfunctions are nicknamed after the five elements of classical Chinese philosophy, with the addition of Ether from medieval European tradition. These six superfunctions can be defined first and foremost by their size:

1. Stone: very small intervals, usually used for sequential progression rather than as an element of chords.
2. Wave: small, relatively consonant intervals that are used as a basis for chords.
3. Ether: consonant intervals that cluster just below the half-octave.
4. Wind: consonant intervals that cluster just above the half-octave.
5. Wood: large, relatively consonant intervals that can be used as a cap for chords.
6. Fire: very large intervals, often useful in creating tension.

Nineteen Functions

The six superfunctions can be broken down into subcategories based on variations in size and consonance, as well as ambiguities in melodic function:

1. Comma: The smallest interval; negligible and usually undesirable.
2. Chroma: The smallest useful unit of melody.
3. Substone: Around the size of the first interval in Maqam Bayati. Ambiguous but distinct in function between the Chroma and Diastone.
4. Diastone: Vaguely whole tone-adjacent function. Differs from the Superstone in that it is relatively dissonant, and usually smaller.
5. Superstone: Vaguely major second-adjacent function. Differs from the Diastone in that it is relatively consonant, and usually larger.
6. Subwave: Around a minor third in size, but often bleeds into semifourth territory. Relatively consonant, but still quite tense.
7. Diawave: Around a minor or neutral third in size. Less consonant than Subwaves; useful as a unit of compact, tense chords.
8. Superwave: Around a major third size. Relatively consonant, but easily distinct as a dyad.
9. Ether: Around a fourth in size. Extremely consonant; its dyad has no distinct color to it.
10. Superether: Around a fourth in size, but less consonant than the Ether. Its dyad is tense, but not always dissonant.
11. Subwind: Around a fifth in size, but less consonant. Its dyad is tense, but not always dissonant.
12. Wind: Around a fifth in size. Extremely consonant; its dyad has no distinct color.
13. Subwood: Around a fifth or minor sixth in size. Quite consonant, but with a colorful dyad.
14. Diawood: Around a sixth in size. Its dyad is tense, but not always dissonant.
15. Superwood: Around a diminished seventh in size. Less consonant than the Subfire, but quite colorful.
16. Subfire: Around a diminished seventh in size. Quite consonant and colorful.
17. Diafire: Around a major seventh in size. Quite consonant and colorful.
18. Superfire: Slightly narrower than an octave. Its dyad is very tense, but not always dissonant.
19. Equave: The fundamental interval of equivalence; usually a purely-tuned 2/1.

Ambiguity

These nineteen functions are not perfectly-distinct boxes, and some intervals may ambiguously fall between two categories due to a lack of melodic resolution; for instance, one step of 6-EDO has an ambiguous function in between the Diastone and Superstone due to its ambiguous level of consonance.

Similarly, some tuning systems have high melodic resolution, leading to intervals that are similarly ambiguous; for instance, 23\41 lies somewhere in between the functions of the Subwind and Wind functions, with 22\41 and 24\41 being used as the cardinal forms of each function.

In some cases, it is useful to have intervals with ambiguous function, as this ambiguity can allow for intervals to be interpreted as either or both of the functions that it falls into. As the nineteen functions are intended to describe the functions of intervals (rather than to prescribe how they can be used), it is very common for an interval not to fit squarely and unambiguously into one category.