Kite's color notation: Difference between revisions

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In adaptive JI, chords are just, but roots move by tempered intervals. Comma pumps are indicated with brackets roughly halfway through the pump: Cy - yAg - [y=w]Dg - Gy - Cy. The pattern is [''old''=''new'']: the previous chord implies yDg and the following chord implies wDg. See [[Comma pump examples]].

Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key of A minor is A gu and the scale is the gu scale. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb ~~yozo~~. Like chords, scales can be classified as bicolored (A gu), tricolored (Bb yo zo), etc.

Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key of A minor is A gu and the scale is the gu scale. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb yo-zo. The [[centaur]] scale is yo-zo-zogu. Like chords, scales can be classified as bicolored (A gu), tricolored (Bb yo-zo), quadricolored (centaur), etc.

Scales can be named more precisely analogous to how chords are named. The tonic, 2nd, 4th and 5th default to wa. Thus a yo scale is w1 w2 y3 w4 w5 y6 y7 w8. If the 2nd were instead yo, it would be a yo yo-2 scale, written y(y2). If the 2nd is sometimes yo, sometimes wa, the scale is yo plus yo-2, written y+y2. (A hexatonic scale might use "minus".) The 5-limit harmonic minor scale is gu yo-7. The Bbh7 - Ebh7 - Bbh7 - Fh9 scale is Bb yo plus zo-3-4-7, written Bb y+z347.

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Just as there is a har7 chord, there is a har15 scale: w1 w2 y3 1o4 w5 3o6 z7 y7 w8. A har-N scale (where N is odd) is harmonics (N+1)/2 to N+1. The tonic of the scale is always a power of 2. Thus the har9 scale is not 5:6:7:8:9:10 but 8:9:10:12:14:16 = w1 w2 y3 w5 z7 w8. The 5:6:7:8:9:10 scale is the over-5 mode of this scale, written "har9 /5". Since there are no gaps in the harmonic series fragment, 5:6:7:8:9:10 can be abbreviated as 5::10. Likewise there are subharmonic scales and modes. The sub15 scale is 16:15:14:13:12:11:10:9:8 or 16::8. The notes are w1 g2 r2 3u3 w4 1u5 g5 w7 w8.

A pentatonic scale is assumed to be a major or minor pentatonic scale with an altered 3rd, 6th or 7th. Yo and ru imply a major pentatonic scale, and zo and gu imply minor. Thus zo pentatonic = w1 z3 w4 w5 z7 w8. Wa, ila or tha pentatonic scales need to specify major or minor, e.g. ilo major pentatonic = w1 w2 1o3 w5 1o6 w8 and ilo minor pentatonic = w1 1o3 w4 w5 1o7 w8. Hemitonic scales can be named e.g. yo minor pentatonic = w1 y3 w4 w5 y7 w8 or zo major pentatonic = w1 w2 z3 w5 z6 w8.

Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu means using gu chords on <u>wa</u> roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate '''fourthward''' or '''fifthward''', abbreviated '''4thwd''' or '''5thwd'''. Modulating in either direction is modulating '''waward'''. Modulating from a yo key to the relative gu, and perhaps from there to the parallel yo is modulating '''yoward'''. A root movement by a yo interval (e.g. Iy - yVIg) is a yoward move. Likewise, there's '''guward''', and '''y<u>a</u>ward''' includes both. Likewise, there's '''zoward''', '''ruward''', '''zaward''', '''iloward''', etc.

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 In adaptive JI, chords are just, but roots move by tempered intervals. Comma pumps are indicated with brackets roughly halfway through the pump: Cy - yAg - [y=w]Dg - Gy - Cy. The pattern is [''old''=''new'']: the previous chord implies yDg and the following chord implies wDg. See [[Comma pump examples]].
-Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key of A minor is A gu and the scale is the gu scale. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb yozo. Like chords, scales can be classified as bicolored (A gu), tricolored (Bb yo zo), etc.
+Keys and scales are loosely named after the colors used. Wa is assumed present. In 5-limit JI, the key of A minor is A gu and the scale is the gu scale. The Bbh7 - Ebh7 - Bbh7 - Fh9 example in the staff notation section is in Bb yo-zo. The [[centaur]] scale is yo-zo-zogu. Like chords, scales can be classified as bicolored (A gu), tricolored (Bb yo-zo), quadricolored (centaur), etc.
 Scales can be named more precisely analogous to how chords are named. The tonic, 2nd, 4th and 5th default to wa. Thus a yo scale is w1 w2 y3 w4 w5 y6 y7 w8. If the 2nd were instead yo, it would be a yo yo-2 scale, written y(y2). If the 2nd is sometimes yo, sometimes wa, the scale is yo plus yo-2, written y+y2. (A hexatonic scale might use "minus".) The 5-limit harmonic minor scale is gu yo-7. The Bbh7 - Ebh7 - Bbh7 - Fh9 scale is Bb yo plus zo-3-4-7, written Bb y+z347.
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 Just as there is a har7 chord, there is a har15 scale: w1 w2 y3 1o4 w5 3o6 z7 y7 w8. A har-N scale (where N is odd) is harmonics (N+1)/2 to N+1. The tonic of the scale is always a power of 2. Thus the har9 scale is not 5:6:7:8:9:10 but 8:9:10:12:14:16 = w1 w2 y3 w5 z7 w8. The 5:6:7:8:9:10 scale is the over-5 mode of this scale, written "har9 /5". Since there are no gaps in the harmonic series fragment, 5:6:7:8:9:10 can be abbreviated as 5::10. Likewise there are subharmonic scales and modes. The sub15 scale is 16:15:14:13:12:11:10:9:8 or 16::8. The notes are w1 g2 r2 3u3 w4 1u5 g5 w7 w8.
+A pentatonic scale is assumed to be a major or minor pentatonic scale with an altered 3rd, 6th or 7th. Yo and ru imply a major pentatonic scale, and zo and gu imply minor. Thus zo pentatonic = w1 z3 w4 w5 z7 w8. Wa, ila or tha pentatonic scales need to specify major or minor, e.g. ilo major pentatonic = w1 w2 1o3 w5 1o6 w8 and ilo minor pentatonic = w1 1o3 w4 w5 1o7 w8. Hemitonic scales can be named e.g. yo minor pentatonic = w1 y3 w4 w5 y7 w8 or zo major pentatonic = w1 w2 z3 w5 z6 w8.
 Analogous to the relative and parallel major or minor, one can modulate to relative gu, parallel ru, etc. Modulating from a yo key to the relative gu means using gu chords on yo roots. Modulating from yo to the parallel gu means using gu chords on <u>wa</u> roots. Going from yo zo to the relative gu means using chords with gu and/or ru in them on yo roots. Going to the relative ru means using the same chords on zo roots. Going from yo zo to the parallel gu ru means using the same chords on wa roots. One can also modulate '''fourthward''' or '''fifthward''', abbreviated '''4thwd''' or '''5thwd'''. Modulating in either direction is modulating '''waward'''. Modulating from a yo key to the relative gu, and perhaps from there to the parallel yo is modulating '''yoward'''. A root movement by a yo interval (e.g. Iy - yVIg) is a yoward move. Likewise, there's '''guward''', and '''y<u>a</u>ward''' includes both. Likewise, there's '''zoward''', '''ruward''', '''zaward''', '''iloward''', etc.