12edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 342: | Line 334: | ||
| 81/80, 128/125 | | 81/80, 128/125 | ||
| {{mapping| 12 19 28 }} | | {{mapping| 12 19 28 }} | ||
| | | −1.56 | ||
| 3.11 | | 3.11 | ||
| 3.11 | | 3.11 | ||
| Line 349: | Line 341: | ||
| 36/35, 50/49, 64/63 | | 36/35, 50/49, 64/63 | ||
| {{mapping| 12 19 28 34 }} | | {{mapping| 12 19 28 34 }} | ||
| | | −3.95 | ||
| 4.92 | | 4.92 | ||
| 4.94 | | 4.94 | ||
| Line 356: | Line 348: | ||
| 36/35, 50/49, 51/49, 64/63 | | 36/35, 50/49, 51/49, 64/63 | ||
| {{mapping| 12 19 28 34 49 }} | | {{mapping| 12 19 28 34 49 }} | ||
| | | −2.92 | ||
| 4.86 | | 4.86 | ||
| 4.87 | | 4.87 | ||
| Line 363: | Line 355: | ||
| 36/35, 50/49, 51/49, 57/56, 64/63 | | 36/35, 50/49, 51/49, 57/56, 64/63 | ||
| {{mapping| 12 19 28 34 49 51 }} | | {{mapping| 12 19 28 34 49 51 }} | ||
| | | −2.53 | ||
| 4.52 | | 4.52 | ||
| 4.53 | | 4.53 | ||
| Line 370: | Line 362: | ||
| 51/50, 81/80, 128/125 | | 51/50, 81/80, 128/125 | ||
| {{mapping| 12 19 28 49 }} | | {{mapping| 12 19 28 49 }} | ||
| | | −0.87 | ||
| 2.95 | | 2.95 | ||
| 2.95 | | 2.95 | ||
| Line 377: | Line 369: | ||
| 51/50, 76/75, 81/80, 128/125 | | 51/50, 76/75, 81/80, 128/125 | ||
| {{mapping| 12 19 28 49 51 }} | | {{mapping| 12 19 28 49 51 }} | ||
| | | −0.81 | ||
| 2.64 | | 2.64 | ||
| 2.64 | | 2.64 | ||
{{comma basis end}} | |||
* 12et (12f val) is lower in relative error than any previous equal temperaments in the 3-, 5-, 7-, 11-, 13-, and 19-limit. The next equal temperaments doing better in those subgroups are 41, 19, 19, 22, 19/19e, and 19egh, respectively. 12et is even more prominent in the 2.3.5.7.17.19 subgroup, and the next equal temperament that does this better is 72. | * 12et (12f val) is lower in relative error than any previous equal temperaments in the 3-, 5-, 7-, 11-, 13-, and 19-limit. The next equal temperaments doing better in those subgroups are 41, 19, 19, 22, 19/19e, and 19egh, respectively. 12et is even more prominent in the 2.3.5.7.17.19 subgroup, and the next equal temperament that does this better is 72. | ||
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{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! Periods <br> per 8ve | ! Periods<br />per 8ve | ||
! Generator | ! Generator* | ||
! Pergen | ! Pergen | ||
! Temperaments | ! Temperaments | ||
| Line 806: | Line 798: | ||
| [[Hexe]] | | [[Hexe]] | ||
|} | |} | ||
{{orf}} | |||
== Scales == | == Scales == | ||