Breedsmic temperaments: Difference between revisions
→Tertiaseptal: sorting |
→Tertiaseptal: move no-11 13- and 17-limit extensions here |
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[[171edo]] makes for an excellent tuning, although [[140edo]] ({{nowrap| {{=}} 171 - 31 }}) also makes sense, and in very high limits [[311edo]] ({{nowrap| {{=}} 140 + 171 }}) is especially notable. The 15- or 16-note [[mos]] can be used to explore no-threes harmony, and the 31-note mos gives plenty of room for those as well. | [[171edo]] makes for an excellent tuning, although [[140edo]] ({{nowrap| {{=}} 171 - 31 }}) also makes sense, and in very high limits [[311edo]] ({{nowrap| {{=}} 140 + 171 }}) is especially notable. The 15- or 16-note [[mos]] can be used to explore no-threes harmony, and the 31-note mos gives plenty of room for those as well. | ||
=== 7-limit === | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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[[Badness]] (Sintel): 0.329 | [[Badness]] (Sintel): 0.329 | ||
==== 2.3.5.7.13 subgroup ==== | |||
Subgroup: 2.3.5.7.13 | |||
Comma list: 625/624, 2401/2400, 4096/4095 | |||
{{Mapping|legend=2| 1 -19 7 0 43 | 0 22 -5 3 -42 }} | |||
{{Mapping|legend=4| 1 -19 7 0 0 43 | 0 22 -5 3 0 -42 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.9931{{c}}, ~224/117 = 1122.8203{{c}} (~117/112 = 77.1729{{c}}) | |||
* CWE: ~2 = 1200.0000{{c}}, ~224/117 = 1122.8267{{c}} (~117/112 = 77.1733{{c}}) | |||
{{Optimal ET sequence|legend=0| 31, 109, 140, 171, 311, 793f }} | |||
Badness (Sintel): 0.682 | |||
==== 2.3.5.7.13.17 subgroup ==== | |||
Subgroup: 2.3.5.7.13.17 | |||
Comma list: 625/624, 833/832, 1225/1224, 4096/4095 | |||
{{Mapping|legend=2| 1 -19 7 0 43 49 | 0 22 -5 3 -42 -48 }} | |||
{{Mapping|legend=4| 1 -19 7 0 0 43 49 | 0 22 -5 3 0 -42 -48 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1200.0139{{c}}, ~65/34 = 1122.8361{{c}} (~68/65 = 77.1779{{c}}) | |||
* CWE: ~2 = 1200.0000{{c}}, ~65/34 = 1122.8230{{c}} (~68/65 = 77.1770{{c}}) | |||
{{Optimal ET sequence|legend=1| 31, 109g, 140, 171, 311, 482 }} | |||
Badness (Sintel): 0.574 | |||
=== Tertia === | === Tertia === | ||
Subgroup:2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Comma list: 385/384, 1331/1323, 1375/1372 | Comma list: 385/384, 1331/1323, 1375/1372 | ||