Breedsmic temperaments: Difference between revisions
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→Tertiaseptal: rework into a no-19 29-limit temp, which is much more natural |
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=== Tertiaseptia === | === Tertiaseptia === | ||
This extension was considered by [[Gene Ward Smith]] as a 41-limit temperament<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_9274.html Yahoo! Tuning Group | ''A 41-limit temperament'']</ref>. It can be extended as such by tempering out 703/702 and 697/696, and mapping 37 and 41 to -81 and +10 steps, respectively. | This extension was considered by [[Gene Ward Smith]] as a 41-limit temperament<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_9274.html Yahoo! Tuning Group | ''A 41-limit temperament'']</ref>. It can be extended as such by tempering out 875/874, 714/713, 703/702 and 697/696, and mapping 19, 31, 37 and 41 to 94, 105, -81 and +10 steps, respectively. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness (Sintel): 0.956 | Badness (Sintel): 0.956 | ||
==== | ==== 2.3.5.7.11.13.17.23 subgroup ==== | ||
Subgroup: 2.3.5.7.11.13.17. | Subgroup: 2.3.5.7.11.13.17.23 | ||
Comma list: 595/594, 625/624, 833/832, 1156/1155 | Comma list: 595/594, 625/624, 833/832, 1105/1104, 1156/1155, 2200/2197 | ||
Mapping: {{mapping| 1 -19 7 0 112 43 49 | Mapping: {{mapping| 1 -19 7 0 112 43 49 114 | 0 22 -5 3 -116 -42 -48 -117 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = 1200. | * WE: ~2 = 1200.0047{{c}}, ~44/23 = 1122.8363{{c}} (~23/22 = 77.1684{{c}}) | ||
* CWE: ~2 = 1200.0000{{c}}, ~ | * CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8319{{c}} (~23/22 = 77.1681{{c}}) | ||
{{Optimal ET sequence|legend=0| 140, 171, 311 }} | {{Optimal ET sequence|legend=0| 31ei, 140, 171, 311 }} | ||
Badness (Sintel): | Badness (Sintel): 0.944 | ||
==== 23 | ==== 2.3.5.7.11.13.17.23.29 subgroup ==== | ||
Subgroup: 2.3.5.7.11.13.17. | Subgroup: 2.3.5.7.11.13.17.23.29 | ||
Comma list: 595/594, 625/624, 833/832, | Comma list: 595/594, 625/624, 784/783, 833/832, 1015/1014, 1105/1104, 1156/1155 | ||
Mapping: {{mapping| 1 -19 7 0 112 43 49 | Mapping: {{mapping| 1 -19 7 0 112 43 49 114 61 | 0 22 -5 3 -116 -42 -48 -117 -60 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1199.9945{{c}}, ~44/23 = 1122.8270{{c}} (~23/22 = 77.1675{{c}}) | ||
* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122. | * CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8322{{c}} (~23/22 = 77.1678{{c}}) | ||
{{Optimal ET sequence|legend=0| 140, 311, 762g }} | {{Optimal ET sequence|legend=0| 31ei, 140, 311, 762g }} | ||
Badness (Sintel): | Badness (Sintel): 0.858 | ||
=== Hemitert === | === Hemitert === | ||