Porcupine/Chords: Difference between revisions

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Though we are used to thinking of 4:5:6 as the definitive "major chord", with all inversions coming from that, there is nothing definitive about calling these lists below "chord" or "inversion". That is just the way the generators came out.

The '''bolded''' inversions are named using [[ups and downs]] as described on the [[Pergen]] page. The pergen is (P8, P4/3) third-of-a-4th, #7 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. One up is -7 generators, octave-reduced, which is a third-sharp. Thus ^3C = C# and the enharmonic ~~interval~~ is v3A1. The generator is vM2 = 167¢ - ''c''/3, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. ^1 = 33¢ + 2.33''c''. In 22edo, ^1 = 1\22 = 54.5¢.

The '''bolded''' inversions are named using [[ups and downs]] as described on the [[Pergen]] page. The pergen is (P8, P4/3) third-of-a-4th, #7 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. One up is -7 generators, octave-reduced, which is a third-sharp. Thus ^3C = C# and the [[enharmonic unison]] is v3A1. The generator is vM2 = 167¢ - ''c''/3, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. ^1 = 33¢ + 2.33''c''. In 22edo, ^1 = 1\22 = 54.5¢.

In porcupine, 5/4 = vM3, 7/4 = m7 and 11/8 = ^4. Thus ^1 equals ~81/80 and ~33/32. This may not be true for other (P8, P4/3) temperaments. So the ratios in the table below are specific to Porcupine, but the chord names apply to any (P8, P4/3) temperament.

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 Though we are used to thinking of 4:5:6 as the definitive "major chord", with all inversions coming from that, there is nothing definitive about calling these lists below "chord" or "inversion". That is just the way the generators came out.
-The '''bolded''' inversions are named using [[ups and downs]] as described on the [[Pergen]] page. The pergen is (P8, P4/3) third-of-a-4th, #7 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. One up is -7 generators, octave-reduced, which is a third-sharp. Thus ^<sup>3</sup>C = C# and the enharmonic interval is v<sup>3</sup>A1. The generator is vM2 = 167¢ - ''c''/3, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. ^1 = 33¢ + 2.33''c''. In 22edo, ^1 = 1\22 = 54.5¢.
+The '''bolded''' inversions are named using [[ups and downs]] as described on the [[Pergen]] page. The pergen is (P8, P4/3) third-of-a-4th, #7 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. One up is -7 generators, octave-reduced, which is a third-sharp. Thus ^<sup>3</sup>C = C# and the [[enharmonic unison]] is v<sup>3</sup>A1. The generator is vM2 = 167¢ - ''c''/3, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. ^1 = 33¢ + 2.33''c''. In 22edo, ^1 = 1\22 = 54.5¢.
 In porcupine, 5/4 = vM3, 7/4 = m7 and 11/8 = ^4. Thus ^1 equals ~81/80 and ~33/32. This may not be true for other (P8, P4/3) temperaments. So the ratios in the table below are specific to Porcupine, but the chord names apply to any (P8, P4/3) temperament.