User:Unque/19-function System: Difference between revisions

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

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 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:

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:

# '''Stone:''' very small intervals, usually used for sequential progression rather than as an element of chords.

# '''Wave:''' small, relatively ~~consonant~~ intervals that are used as a basis for chords.

# '''Wave:''' small, relatively concordant intervals that are used as a basis for chords.

# '''Ether:''' ~~consonant~~ intervals that cluster just below the half-octave.

# '''Ether:''' concordant intervals that cluster just below the half-octave.

# '''Wind:''' ~~consonant~~ intervals that cluster just above the half-octave.

# '''Wind:''' concordant intervals that cluster just above the half-octave.

# '''Wood:''' large, relatively ~~consonant~~ intervals that can be used as a cap for chords.

# '''Wood:''' large, relatively concordant intervals that can be used as a cap for chords.

# '''Fire:''' very large intervals, often useful in creating tension.

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

# '''Comma:''' The smallest interval; ~~negligible~~ and ~~usually~~ undesirable.

# '''Comma:''' The smallest interval; usually used as a commatic adjustment for chords, and in some cases undesirable entirely.

# '''Chroma:''' The smallest useful unit of melody.

# '''Substone:''' Around the size of the ~~first interval~~ in ~~Maqam~~ Bayati. Ambiguous but distinct in function between the Chroma and Diastone.

# '''Substone:''' Around the size of the neutral second found in Jins Bayati. Ambiguous but distinct in function between the Chroma and Diastone.

# '''Diastone:''' Vaguely whole tone-adjacent function. Differs from the Superstone in that it is relatively ~~dissonant~~, and usually smaller.

# '''Diastone:''' Vaguely whole tone-adjacent function. Differs from the Superstone in that it is relatively discordant, and usually smaller.

# '''Superstone:''' Vaguely major second-adjacent function. Differs from the Diastone in that it is relatively ~~consonant~~, and usually larger.

# '''Superstone:''' Vaguely major second-adjacent function. Differs from the Diastone in that it is relatively concordant, and usually larger.

# '''Subwave:''' Around a minor third in size, but often bleeds into semifourth territory. Relatively ~~consonant~~, but still quite tense.

# '''Subwave:''' Around a minor third in size, but often bleeds into semifourth territory. Relatively concordant, but still quite tense.

# '''Diawave:''' Around a minor or neutral third in size. Less ~~consonant~~ than Subwaves; useful as a unit of compact, tense chords.

# '''Diawave:''' Around a minor or neutral third in size. Less concordant than Subwaves; useful as a unit of compact, tense chords.

# '''Superwave:''' Around a major third size. Relatively ~~consonant~~, but easily distinct as a dyad.

# '''Superwave:''' Around a major third size. Relatively concordant, but easily distinct as a dyad.

# '''Ether:''' Around a fourth in size. Extremely ~~consonant~~; its dyad has no distinct color to it.

# '''Ether:''' Around a fourth in size. Extremely concordant; its dyad has no distinct color to it.

# '''Superether:''' Around a fourth in size, but less ~~consonant~~ than the Ether. Its dyad is tense, but not always dissonant.

# '''Superether:''' Around a fourth in size, but less concordant than the Ether. Its dyad is tense, but not always dissonant.

# '''Subwind:''' Around a fifth in size, but less ~~consonant~~. Its dyad is tense, but not always ~~dissonant~~.

# '''Subwind:''' Around a fifth in size, but less concordant. Its dyad is tense, but not always discordant.

# '''Wind:''' Around a fifth in size. Extremely ~~consonant~~; its dyad has no distinct color.

# '''Wind:''' Around a fifth in size. Extremely concordant; its dyad has no distinct color.

# '''Subwood:''' Around a fifth or minor sixth in size. Quite ~~consonant~~, but with a colorful dyad.

# '''Subwood:''' Around a fifth or minor sixth in size. Quite concordant, but with a colorful dyad.

# '''Diawood:''' Around a sixth in size. Its dyad is tense, but not always ~~dissonant~~.

# '''Diawood:''' Around a sixth in size. Its dyad is tense, but not always discordant.

# '''Superwood:''' Around a diminished seventh in size. Less ~~consonant~~ than the Subfire, but quite colorful.

# '''Superwood:''' Around a diminished seventh in size. Less concordant than the Subfire, but quite colorful.

# '''Subfire:''' Around a diminished seventh in size. Quite ~~consonant~~ and colorful.

# '''Subfire:''' Around a diminished seventh in size. Quite concordant and colorful.

# '''Diafire:''' Around a major seventh in size. Quite ~~consonant~~ and colorful.

# '''Diafire:''' Around a major seventh in size. Quite concordant and colorful.

# '''Superfire:''' Slightly narrower than an ~~octave~~. Its dyad is very tense, but not always ~~dissonant~~.

# '''Superfire:''' Slightly narrower than an equave. Its dyad is very tense, but not always discordant.

# '''Equave:''' The fundamental interval of equivalence; usually a purely-tuned 2/1.

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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:

{| class="wikitable"

|+Diatonic Degrees

!Degree

!26edo (4:3)

!19edo (3:2)

!12edo (2:1)

!17edo (3:1)

!22edo (4:1)

|-

|m2

|Substone

|Chroma~Substone

|Chroma

|-

|M2

|Diastone

|Diastone~Superstone

|Superstone

|-

|m3

|Diawave

|Subwave

|-

|M3

|Diawave~Superwave

|Superwave

|Diawave~Superwave

|-

|p4

|Superether

|Ether~Superether

|Ether

|Superwave~Ether

|-

|A4

|Superether

|Superether~Subwind

|Subwind

|-

|d5

|Subwind

|Superether~Subwind

|Superether

|-

|P5

|Subwind

|Subwind~Wind

|Wind

|Wind~Subwood

|-

|m6

|Subwood~Diawood

|Subwood

|-

|M6

|Diawood

|Superwood

|Subfire

|Superwood~Subfire

|Superwood

|-

|m7

|Subfire

|Subfire~Diafire

|Subfire

|-

|M7

|Diafire

|Diafire~Superfire

|Superfire

|}

@@ Line 1: / Line 1: @@
-The Nineteen Function System is a categorization of intervals into nineteen major groups based on their size, consonance, and melodic function.
+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 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:
+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:
 # '''Stone:''' very small intervals, usually used for sequential progression rather than as an element of chords.
-# '''Wave:''' small, relatively consonant intervals that are used as a basis for chords.
+# '''Wave:''' small, relatively concordant intervals that are used as a basis for chords.
-# '''Ether:''' consonant intervals that cluster just below the half-octave.
+# '''Ether:''' concordant intervals that cluster just below the half-octave.
-# '''Wind:''' consonant intervals that cluster just above the half-octave.
+# '''Wind:''' concordant intervals that cluster just above the half-octave.
-# '''Wood:''' large, relatively consonant intervals that can be used as a cap for chords.
+# '''Wood:''' large, relatively concordant intervals that can be used as a cap for chords.
 # '''Fire:''' very large intervals, often useful in creating tension.
@@ Line 14: / Line 14: @@
 The six superfunctions can be broken down into subcategories based on variations in size and consonance, as well as ambiguities in melodic function:
-# '''Comma:''' The smallest interval; negligible and usually undesirable.
+# '''Comma:''' The smallest interval; usually used as a commatic adjustment for chords, and in some cases undesirable entirely.
 # '''Chroma:''' The smallest useful unit of melody.
-# '''Substone:''' Around the size of the first interval in Maqam Bayati. Ambiguous but distinct in function between the Chroma and Diastone.
+# '''Substone:''' Around the size of the neutral second found in Jins Bayati. Ambiguous but distinct in function between the Chroma and Diastone.
-# '''Diastone:''' Vaguely whole tone-adjacent function. Differs from the Superstone in that it is relatively dissonant, and usually smaller.
+# '''Diastone:''' Vaguely whole tone-adjacent function. Differs from the Superstone in that it is relatively discordant, and usually smaller.
-# '''Superstone:''' Vaguely major second-adjacent function. Differs from the Diastone in that it is relatively consonant, and usually larger.
+# '''Superstone:''' Vaguely major second-adjacent function. Differs from the Diastone in that it is relatively concordant, and usually larger.
-# '''Subwave:''' Around a minor third in size, but often bleeds into semifourth territory. Relatively consonant, but still quite tense.
+# '''Subwave:''' Around a minor third in size, but often bleeds into semifourth territory. Relatively concordant, but still quite tense.
-# '''Diawave:''' Around a minor or neutral third in size. Less consonant than Subwaves; useful as a unit of compact, tense chords.
+# '''Diawave:''' Around a minor or neutral third in size. Less concordant than Subwaves; useful as a unit of compact, tense chords.
-# '''Superwave:''' Around a major third size. Relatively consonant, but easily distinct as a dyad.
+# '''Superwave:''' Around a major third size. Relatively concordant, but easily distinct as a dyad.
-# '''Ether:''' Around a fourth in size. Extremely consonant; its dyad has no distinct color to it.
+# '''Ether:''' Around a fourth in size. Extremely concordant; its dyad has no distinct color to it.
-# '''Superether:''' Around a fourth in size, but less consonant than the Ether. Its dyad is tense, but not always dissonant.
+# '''Superether:''' Around a fourth in size, but less concordant than the Ether. Its dyad is tense, but not always dissonant.
-# '''Subwind:''' Around a fifth in size, but less consonant. Its dyad is tense, but not always dissonant.
+# '''Subwind:''' Around a fifth in size, but less concordant. Its dyad is tense, but not always discordant.
-# '''Wind:''' Around a fifth in size.  Extremely consonant; its dyad has no distinct color.
+# '''Wind:''' Around a fifth in size.  Extremely concordant; its dyad has no distinct color.
-# '''Subwood:''' Around a fifth or minor sixth in size. Quite consonant, but with a colorful dyad.
+# '''Subwood:''' Around a fifth or minor sixth in size. Quite concordant, but with a colorful dyad.
-# '''Diawood:''' Around a sixth in size.  Its dyad is tense, but not always dissonant.
+# '''Diawood:''' Around a sixth in size.  Its dyad is tense, but not always discordant.
-# '''Superwood:''' Around a diminished seventh in size. Less consonant than the Subfire, but quite colorful.
+# '''Superwood:''' Around a diminished seventh in size. Less concordant than the Subfire, but quite colorful.
-# '''Subfire:''' Around a diminished seventh in size. Quite consonant and colorful.
+# '''Subfire:''' Around a diminished seventh in size. Quite concordant and colorful.
-# '''Diafire:''' Around a major seventh in size. Quite consonant and colorful.
+# '''Diafire:''' Around a major seventh in size. Quite concordant and colorful.
-# '''Superfire:''' Slightly narrower than an octave. Its dyad is very tense, but not always dissonant.
+# '''Superfire:''' Slightly narrower than an equave. Its dyad is very tense, but not always discordant.
 # '''Equave:''' The fundamental interval of equivalence; usually a purely-tuned 2/1.
@@ Line 40: / Line 40: @@
 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:
+{| class="wikitable"
+|+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
+|}