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Compton: Difference between revisions

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''This page is about the 5-limit rank-2 temperament. For the 3-limit equal temperament, see [[12edo]].''
{{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.  
'''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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|-
|  
|  
| 5/4
| 7/5
| 382.512
| 382.512
|  
|  
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| 49/48
| 49/48
| 383.924
| 383.924
|
|-
| 73\228
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| 384.211
|  
|  
|-
|-
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| 21/20
| 21/20
| 384.467
| 384.467
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|-
| 50\156
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| 384.615
|
|-
| 77\240
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| 385.000
|  
|  
|-
|-
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