Compton: Difference between revisions
m Text replacement - "Eigenmonzo<br>(unchanged-interval)" to "Unchanged interval<br>(eigenmonzo)" |
→Tunings: + more edo tunings |
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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. | '''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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== Tunings == | == Tunings == | ||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit | |+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings | ||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" | | ||
| Line 163: | Line 176: | ||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit | |+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings | ||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" | | ||
| Line 222: | Line 235: | ||
|- | |- | ||
| | | | ||
| 5 | | 7/5 | ||
| 382.512 | | 382.512 | ||
| | | | ||
| Line 244: | Line 257: | ||
| 49/48 | | 49/48 | ||
| 383.924 | | 383.924 | ||
| | |||
|- | |||
| 73\228 | |||
| | |||
| 384.211 | |||
| | | | ||
|- | |- | ||
| Line 259: | Line 277: | ||
| 21/20 | | 21/20 | ||
| 384.467 | | 384.467 | ||
| | |||
|- | |||
| 50\156 | |||
| | |||
| 384.615 | |||
| | |||
|- | |||
| 77\240 | |||
| | |||
| 385.000 | |||
| | | | ||
|- | |- | ||