User:Unque/19-function System

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

The Six Superfunctions

To avoid diatonic-centrism and indexing ambiguity, the six superfunctions are nicknamed arbitrarily 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 concordant intervals that are used as a basis for chords.
3. Ether: concordant intervals that cluster just below the half-octave.
4. Wind: concordant intervals that cluster just above the half-octave.
5. Wood: large, relatively concordant 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; usually used as a commatic adjustment for chords, and in some cases undesirable entirely.
2. Chroma: The smallest useful unit of melody.
3. Substone: Around the size of the neutral second found in Jins 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 discordant, and usually smaller.
5. Superstone: Vaguely major second-adjacent function. Differs from the Diastone in that it is relatively concordant, and usually larger.
6. Subwave: Around a minor third in size, but often bleeds into semifourth territory. Relatively concordant, but still quite tense.
7. Diawave: Around a minor or neutral third in size. Less concordant than Subwaves; useful as a unit of compact, tense chords.
8. Superwave: Around a major third size. Relatively concordant, but easily distinct as a dyad.
9. Ether: Around a fourth in size. Extremely concordant; its dyad has no distinct color to it.
10. Superether: Around a fourth in size, but less concordant than the Ether. Its dyad is tense, but not always dissonant.
11. Subwind: Around a fifth in size, but less concordant. Its dyad is tense, but not always discordant.
12. Wind: Around a fifth in size. Extremely concordant; its dyad has no distinct color.
13. Subwood: Around a fifth or minor sixth in size. Quite concordant, but with a colorful dyad.
14. Diawood: Around a sixth in size. Its dyad is tense, but not always discordant.
15. Superwood: Around a diminished seventh in size. Less concordant than the Subfire, but quite colorful.
16. Subfire: Around a diminished seventh in size. Quite concordant and colorful.
17. Diafire: Around a major seventh in size. Quite concordant and colorful.
18. Superfire: Slightly narrower than an equave. Its dyad is very tense, but not always discordant.
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.

Example Usage

These categories can be used to compare different tunings of the same scale; as an example, here is a comparison of different types of Diatonic scales using the categories to describe how they differ:

Diatonic Degrees

Degree	26edo (4:3)	19edo (3:2)	12edo (2:1)	17edo (3:1)	22edo (4:1)
m2	Substone	Chroma~Substone	Chroma~Substone	Chroma	Chroma
M2	Diastone	Diastone	Diastone~Superstone	Superstone	Superstone
m3	Diawave	Subwave	Subwave	Subwave	Subwave
M3	Diawave~Superwave	Diawave~Superwave	Superwave	Superwave	Diawave~Superwave
p4	Superether	Ether~Superether	Ether	Ether	Superwave~Ether
A4	Superether	Superether	Superether~Subwind	Subwind	Subwind
d5	Subwind	Subwind	Superether~Subwind	Superether	Superether
P5	Subwind	Subwind~Wind	Wind	Wind	Wind~Subwood
m6	Subwood~Diawood	Subwood~Diawood	Subwood	Subwood	Subwood
M6	Diawood	Superwood	Subfire	Superwood~Subfire	Superwood
m7	Subfire	Subfire~Diafire	Subfire~Diafire	Subfire	Subfire
M7	Diafire	Diafire	Diafire~Superfire	Superfire	Superfire