Compton: Difference between revisions

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{{Infobox regtemp

| Title = Compton

| Subgroups = 2.3.5, 2.3.5.7

| Comma basis = [[531441/524288]] (5-limit); <br>[[225/224]], [[250047/250000]] (7-limit)

| Edo join 1 = 12 | Edo join 2 = 72

| Mapping = 12; 0 1 2

| Generators = 5/4

| Generators tuning = 384.1

| Optimization method = CWE

| MOS scales = [[12L 12s]], [[12L 24s]]

| Odd limit 1 = 5 | Mistuning 1 = 1.96 | Complexity 1 = 24

| Odd limit 2 = 9 | Mistuning 2 = 3.91 | Complexity 2 = 36

}}

'''Compton''' is a [[regular temperament|temperament]] that takes [[12edo]]'s [[circle of fifths]] for the [[3-limit]], but the [[5/1|fifth harmonic]] is given its own generator instead of being mapped to one of 12edo's intervals. Essentially, it is the [[5-limit]] temperament which [[tempering out|tempers out]] the Pythagorean comma, [[531441/524288]]. This equates any Pythagorean interval with its [[enharmonic]] counterparts, for example, the diminished fourth [[8192/6561]] with the major third [[81/64]], and the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], are merged 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]], the ptolemaic major third, or 81/80, the syntonic comma itself.

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+{{Infobox regtemp
+| Title = Compton
+| Subgroups = 2.3.5, 2.3.5.7
+| Comma basis = [[531441/524288]] (5-limit); <br>[[225/224]], [[250047/250000]] (7-limit)
+| Edo join 1 = 12 | Edo join 2 = 72
+| Mapping = 12; 0 1 2
+| Generators = 5/4
+| Generators tuning = 384.1
+| Optimization method = CWE
+| MOS scales = [[12L 12s]], [[12L 24s]]
+| Odd limit 1 = 5 | Mistuning 1 = 1.96 | Complexity 1 = 24
+| Odd limit 2 = 9 | Mistuning 2 = 3.91 | Complexity 2 = 36
+}}
 '''Compton''' is a [[regular temperament|temperament]] that takes [[12edo]]'s [[circle of fifths]] for the [[3-limit]], but the [[5/1|fifth harmonic]] is given its own generator instead of being mapped to one of 12edo's intervals. Essentially, it is the [[5-limit]] temperament which [[tempering out|tempers out]] the Pythagorean comma, [[531441/524288]]. This equates any Pythagorean interval with its [[enharmonic]] counterparts, for example, the diminished fourth [[8192/6561]] with the major third [[81/64]], and the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], are merged 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]], the ptolemaic major third, or 81/80, the syntonic comma itself.