Catalog of rank-4 temperaments: Difference between revisions
m →Nexus (1771561/1769472): fix generator preimage |
→Vishdelismic (5632/5625): + intro |
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Comma list: 273/272, 441/440, 561/560 | Comma list: 273/272, 441/440, 561/560 | ||
{{Mapping|legend=0| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 633: | Line 633: | ||
== Vishdelismic (5632/5625) == | == Vishdelismic (5632/5625) == | ||
Vishdelismic tempers out 5632/5625, the [[vishdelisma]], and adds to [[vishdelic]] an independent generator for prime 7. From 5632/5625 = ([[176/175]])/([[225/224]]), vishdelismic has the feature of making [[14/9]], [[25/16]], and [[11/7]] equidistant. | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
| Line 911: | Line 913: | ||
Comma list: 1216/1215, 1540/1539, 2080/2079 | Comma list: 1216/1215, 1540/1539, 2080/2079 | ||
{{Mapping|legend=0| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,022: | Line 1,024: | ||
Comma list: 2080/2079, 3510/3509, 4096/4095 | Comma list: 2080/2079, 3510/3509, 4096/4095 | ||
{{Mapping|legend=0| 1 0 0 0 17 12 -21 | 0 1 0 0 -5 -2 11 | 0 0 1 0 0 -1 0 | 0 0 0 1 -2 -1 3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,041: | Line 1,043: | ||
Comma list: 2080/2079, 3250/3249, 4096/4095 | Comma list: 2080/2079, 3250/3249, 4096/4095 | ||
{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,058: | Line 1,060: | ||
Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095 | Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095 | ||
{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,077: | Line 1,079: | ||
Comma list: 2080/2079, 4096/4095, 35000/34969 | Comma list: 2080/2079, 4096/4095, 35000/34969 | ||
{{Mapping|legend=0| 1 0 0 1 15 11 -13 | 0 1 0 0 -5 -2 5 | 0 0 1 0 0 -1 2 | 0 0 0 2 -4 -2 5 }} | |||
: mapping generators: ~2, ~3, ~5, ~187/100 | : mapping generators: ~2, ~3, ~5, ~187/100 | ||
| Line 1,095: | Line 1,097: | ||
Comma list: 2080/2079, 3250/3249, 4096/4095, 4200/4199 | Comma list: 2080/2079, 3250/3249, 4096/4095, 4200/4199 | ||
{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,112: | Line 1,114: | ||
Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095, 4200/4199 | Comma list: 2080/2079, 3250/3249, 3510/3509, 4096/4095, 4200/4199 | ||
{{Mapping|legend=0| 1 0 0 1 15 11 -13 6 -18 | 0 1 0 0 -5 -2 5 -2 -11 | 0 0 1 0 0 -1 2 1 0 | 0 0 0 2 -4 -2 5 -1 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,202: | Line 1,204: | ||
Comma list: 352/351, 715/714, 155771/155520 | Comma list: 352/351, 715/714, 155771/155520 | ||
{{Mapping|legend=0| 1 0 -6 0 1 6 0 | 0 1 3 0 2 -1 3 | 0 0 5 0 -1 -1 3 | 0 0 0 1 0 0 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,217: | Line 1,219: | ||
Comma list: 352/351, 715/714, 1463/1458, 2057/2052 | Comma list: 352/351, 715/714, 1463/1458, 2057/2052 | ||
{{Mapping|legend=0| 1 0 -6 0 1 6 0 0 | 0 1 3 0 2 -1 3 4 | 0 0 5 0 -1 -1 3 1 | 0 0 0 1 0 0 -1 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,250: | Line 1,252: | ||
Comma list: 676/675, 6656/6655 | Comma list: 676/675, 6656/6655 | ||
{{Mapping|legend=0| 3 0 0 0 8 -3 | 0 2 0 0 1 3 | 0 0 1 0 0 1 | 0 0 0 1 0 0 }} | |||
Optimal tunings: | Optimal tunings: | ||