Compton: Difference between revisions

Line 1:

[[Category:Temperaments]]

[[Category:Compton family]]

'''Compton''' is a 5-limit regular temperament similar to [[12edo]], except that instead of being mapped to one of 12edo's intervals, the [[5/1|fifth harmonic]] is given its own generator. Equivalently, it is the rank-2 temperament which tempers out the Pythagorean comma [[531441/524288]]. This equates Pythagorean comma-flat or -sharp intervals with their simpler counterparts (for example, the comma-flat major third [[8192/6561]] with the standard major third [[81/64]]), and if the comma-flat third is seen as a diminished fourth, it can be seen as tempering together the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], into a single interval of 1/12 octave, which serves as the period. The generator can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a syntonic comma), but is most usefully 5/4 or 81/80.

'''Compton''' is a 5-limit regular temperament similar to [[12edo]], except that instead of being mapped to one of 12edo's intervals, the [[5/1|fifth harmonic]] is given its own generator. Equivalently, it is the rank-2 temperament which tempers out the Pythagorean comma [[531441/524288]]. This equates Pythagorean comma-flat or -sharp intervals with their simpler counterparts (for example, the comma-flat major third [[8192/6561]] with the standard major third [[81/64]]), and if the comma-flat third is seen as a diminished fourth, it can be seen as tempering together the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], into a single interval of 1/12 octave, which serves as the period. The generator can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a syntonic comma), but is most usefully 5/4 or 81/80. The generator does not have any explicit constraints, unlike in many other temperaments.

As such, in terms of equal temperaments, compton is only supported by equal temperaments that are a multiple of 12, with 60edo, 72edo, 84edo, 96edo, 108edo, and [[240edo]] perhaps being best.

@@ Line 1: / Line 1: @@
 [[Category:Temperaments]]
 [[Category:Compton family]]
-'''Compton''' is a 5-limit regular temperament similar to [[12edo]], except that instead of being mapped to one of 12edo's intervals, the [[5/1|fifth harmonic]] is given its own generator. Equivalently, it is the rank-2 temperament which tempers out the Pythagorean comma [[531441/524288]]. This equates Pythagorean comma-flat or -sharp intervals with their simpler counterparts (for example, the comma-flat major third [[8192/6561]] with the standard major third [[81/64]]), and if the comma-flat third is seen as a diminished fourth, it can be seen as tempering together the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], into a single interval of 1/12 octave, which serves as the period. The generator can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a syntonic comma), but is most usefully 5/4 or 81/80.
+'''Compton''' is a 5-limit regular temperament similar to [[12edo]], except that instead of being mapped to one of 12edo's intervals, the [[5/1|fifth harmonic]] is given its own generator. Equivalently, it is the rank-2 temperament which tempers out the Pythagorean comma [[531441/524288]]. This equates Pythagorean comma-flat or -sharp intervals with their simpler counterparts (for example, the comma-flat major third [[8192/6561]] with the standard major third [[81/64]]), and if the comma-flat third is seen as a diminished fourth, it can be seen as tempering together the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], into a single interval of 1/12 octave, which serves as the period. The generator can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a syntonic comma), but is most usefully 5/4 or 81/80. The generator does not have any explicit constraints, unlike in many other temperaments.
 As such, in terms of equal temperaments, compton is only supported by equal temperaments that are a multiple of 12, with 60edo, 72edo, 84edo, 96edo, 108edo, and [[240edo]] perhaps being best.