Kite's thoughts on pergens: Difference between revisions

Line 1,003:

P4/3: C - vD - ^Eb - F

A4:/3 C - D - E - F# (the lack of ups and downs indicates that this interval was already split)

A4:/3 C - D - E - F# (the lack of ups and downs indicates that this interval was already split into 3 parts)

m7/3: C - ^Eb - vG - Bb (also m7/6: C - vD - ^Eb - F - vG - ^Ab - Bb)

m7/3: C - ^Eb - vG - Bb (because m7 is already split into halves, we also have m7/6: C - vD - ^Eb - F - vG - ^Ab - Bb)

M7/3: C - vE - ^G - B

m10/3: C - F - Bb - Eb (~~also~~ already split~~) (~~m10/9 also occurs)

m10/3: C - F - Bb - Eb (m10 is already split into 3 parts, thus m10/9 also occurs)

M10/3: C - ^F - vB - E

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vM7/2: C - ^F - vB (vM7 = 15/8, probably more harmonious than M7 = 243/128)

More remote intervals include A1, d4, d7 and d10. These require a very long genchain. The most interesting melodically is A1: C - ^C - vC# - C#. From C to C# is 7 5ths, which equals 21 generators, so the genchain would contain 22 notes if it had no gaps.

More remote intervals include A1, d4, d7 and d10. These unfortunately require a very long genchain. The most interesting melodically is A1: C - ^C - vC# - C#. From C to C# is seven 5ths, which equals 21 generators, so the genchain would have to contain 22 notes if it had no gaps. Note that A1 is the bare enharmonic of third-4th. The bare enharmonic is always a secondary split.

For a pergen (P8, (a,b)/n), any interval generated by n octaves and the multigen splits into at least n parts. For a pergen (P8/m, P5), any interval generated by the octave and m 5ths splits into at least m parts. Thus any naturally occurring split of m parts occurs in all voicings of that interval. For example, M9 naturally splits into two 5ths, therefore (P8/2, P5) splits all voicings of M9, including M2.

@@ Line 1,003: / Line 1,003: @@
 P4/3: C - vD - ^Eb - F
-A4:/3 C - D - E - F# (the lack of ups and downs indicates that this interval was already split)
+A4:/3 C - D - E - F# (the lack of ups and downs indicates that this interval was already split into 3 parts)
-m7/3: C - ^Eb - vG - Bb (also m7/6: C - vD - ^Eb - F - vG - ^Ab - Bb)
+m7/3: C - ^Eb - vG - Bb (because m7 is already split into halves, we also have m7/6: C - vD - ^Eb - F - vG - ^Ab - Bb)
 M7/3: C - vE - ^G - B
-m10/3: C - F - Bb - Eb (also already split) (m10/9 also occurs)
+m10/3: C - F - Bb - Eb (m10 is already split into 3 parts, thus m10/9 also occurs)
 M10/3: C - ^F - vB - E
@@ Line 1,023: / Line 1,023: @@
 vM7/2: C - ^F - vB (vM7 = 15/8, probably more harmonious than M7 = 243/128)
-More remote intervals include A1, d4, d7 and d10. These require a very long genchain. The most interesting melodically is A1: C - ^C - vC# - C#. From C to C# is 7 5ths, which equals 21 generators, so the genchain would contain 22 notes if it had no gaps.
+More remote intervals include A1, d4, d7 and d10. These unfortunately require a very long genchain. The most interesting melodically is A1: C - ^C - vC# - C#. From C to C# is seven 5ths, which equals 21 generators, so the genchain would have to contain 22 notes if it had no gaps. Note that A1 is the bare enharmonic of third-4th. The bare enharmonic is always a secondary split.
 For a pergen (P8, (a,b)/n), any interval generated by n octaves and the multigen splits into at least n parts. For a pergen (P8/m, P5), any interval generated by the octave and m 5ths splits into at least m parts. Thus any naturally occurring split of m parts occurs in all voicings of that interval. For example, M9 naturally splits into two 5ths, therefore (P8/2, P5) splits all voicings of M9, including M2.