Diaschismic/Chords: Difference between revisions

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Diaschsmic has [[mos scale]]s of size 10, 12, 22, 34, 46 and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.

Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period. ^1 = 6c, where c = the amount in cents the tempered fifth exceeds 700¢. For 46edo, c = 4.3¢ and ^1 = 1\46 = 26.1¢.

Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. This is literally a semi-tone, but it's better to call it a "halftone", since the term "semitone" is used much more broadly and has so many other connotations. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period, which is half a pythagorean comma. ^1 = 6c, where c = the amount in cents the tempered fifth exceeds 700¢. For 46edo, c = 4.3¢ and ^1 = 1\46 = 26.1¢.

In Diaschismic, 5/4 = vM3, 7/4 = vm7 and 11/8 = vd5 or vvvA4. Thus ^1 equals ~81/80 and ~64/63 and ~[[8192/8019]] = [13 -6 0 0 -1⟩. This won't be true for most (P8, P5/2) temperaments. So although the ratios are specific to diaschismic, the chord names apply to any (P8, P5/2) temperament with A4 > d5. If A4 < d5, the arrows flip direction.

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 Diaschsmic has [[mos scale]]s of size 10, 12, 22, 34, 46 and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.
-Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period. ^1 = 6c, where c = the amount in cents the tempered fifth exceeds 700¢. For 46edo, c = 4.3¢ and ^1 = 1\46 = 26.1¢.
+Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. This is literally a semi-tone, but it's better to call it a "halftone", since the term "semitone" is used much more broadly and has so many other connotations. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period, which is half a pythagorean comma. ^1 = 6c, where c = the amount in cents the tempered fifth exceeds 700¢. For 46edo, c = 4.3¢ and ^1 = 1\46 = 26.1¢.
 In Diaschismic, 5/4 = vM3, 7/4 = vm7 and 11/8 = vd5 or vvvA4. Thus ^1 equals ~81/80 and ~64/63 and ~[[8192/8019]] = [13 -6 0 0 -1⟩. This won't be true for most (P8, P5/2) temperaments. So although the ratios are specific to diaschismic, the chord names apply to any (P8, P5/2) temperament with A4 > d5. If A4 < d5, the arrows flip direction.