364edo: Difference between revisions
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Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
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== Theory == | == Theory == | ||
364edo is consistent through the [[21-odd-limit]] | 364edo is [[consistent]] through the [[21-odd-limit]]. The equal temperament [[tempering out|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo| -65 0 28 }} ([[oquatonic comma]]) in the [[5-limit]]; 65625/65536 ([[horwell comma]]), 390625/388962 ([[dimcomp comma]]), and 420175/419904 (wizma) in the [[7-limit]] (supporting [[fifthplus]] and [[oquatonic]]); 1375/1372, [[6250/6237]], [[19712/19683]], and [[41503/41472]] in the [[11-limit]] (as well as [[9801/9800]]); [[625/624]], [[1716/1715]], [[2080/2079]], [[2200/2197]], and 14641/14625 in the [[13-limit]] (as well as [[4096/4095]], [[4225/4224]], and [[10985/10976]]); [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], and 8624/8619 in the [[17-limit]] (as well as [[2431/2430]], [[4914/4913]], and [[5832/5831]]); [[1216/1215]], 1331/1330, 1540/1539, and [[1729/1728]] in the [[19-limit]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|364|columns=11}} | {{Harmonics in equal|364|columns=11}} | ||
=== Subsets and supersets === | |||
Since 364 factors into {{factorization|364}}, 364edo has subset edos {{EDOs| 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 }}. | |||
=== Miscellaneous properties === | === Miscellaneous properties === | ||
364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of [[11edo]], [[12edo]], [[13edo]] and [[14edo]]. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these | 364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of [[11edo]], [[12edo]], [[13edo]] and [[14edo]]. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these edos are sought after. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" | Subgroup | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning Error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 26: | Line 27: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 577 -364 }} | | {{monzo| 577 -364 }} | ||
| | | {{mapping| 364 577 }} | ||
| -0.0766 | | -0.0766 | ||
| 0.0766 | | 0.0766 | ||
| Line 33: | Line 34: | ||
| 2.3.5 | | 2.3.5 | ||
| 1600000/1594323, {{monzo| -65 0 28 }} | | 1600000/1594323, {{monzo| -65 0 28 }} | ||
| | | {{mapping| 364 577 845 }} | ||
| +0.0350 | | +0.0350 | ||
| 0.1698 | | 0.1698 | ||
| Line 40: | Line 41: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 65625/65536, 390625/388962, 420125/419904 | | 65625/65536, 390625/388962, 420125/419904 | ||
| | | {{mapping| 364 577 845 1022 }} | ||
| -0.0098 | | -0.0098 | ||
| 0.1662 | | 0.1662 | ||
| Line 47: | Line 48: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 1375/1372, 6250/6237, 19712/19683, 41503/41472 | | 1375/1372, 6250/6237, 19712/19683, 41503/41472 | ||
| | | {{mapping| 364 577 845 1022 1259 }} | ||
| +0.0366 | | +0.0366 | ||
| 0.1753 | | 0.1753 | ||
| Line 54: | Line 55: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625 | | 625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625 | ||
| | | {{mapping| 364 577 845 1022 1259 1347 }} | ||
| +0.0245 | | +0.0245 | ||
| 0.1622 | | 0.1622 | ||
| Line 61: | Line 62: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197 | | 625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197 | ||
| | | {{mapping| 364 577 845 1022 1259 1347 1488 }} | ||
| +0.0022 | | +0.0022 | ||
| 0.1599 | | 0.1599 | ||
| Line 68: | Line 69: | ||
| 2.3.5.7.11.13.17.19 | | 2.3.5.7.11.13.17.19 | ||
| 625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728 | | 625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728 | ||
| | | {{mapping| 364 577 845 1022 1259 1347 1488 1546 }} | ||
| +0.0257 | | +0.0257 | ||
| 0.1620 | | 0.1620 | ||
| Line 78: | Line 79: | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br> | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 137: | Line 138: | ||
| [[Oquatonic]] | | [[Oquatonic]] | ||
|- | |- | ||
|91 | | 91 | ||
| 151\364<br>(3\364) | | 151\364<br>(3\364) | ||
| 497.80<br>(3.30) | | 497.80<br>(3.30) | ||
| 4/3<br>(176/175) | | 4/3<br>(176/175) | ||
|[[Protactinium]] | | [[Protactinium]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
[[ | |||
== Scales == | == Scales == | ||
* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30 | |||
* WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30 | |||