Breedsmic temperaments: Difference between revisions

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Osiris: - unexplained see also
Tertiaseptal: - extensions beyond 31
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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.
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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Badness (Sintel): 1.18
Badness (Sintel): 1.18
==== 37-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 595/594, 625/624, 703/702, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 }}
Optimal tunings:
* WE: ~2 = 1199.9824{{c}}, ~44/23 = 1122.8139{{c}} (~23/22 = 77.1685{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8304{{c}} (~23/22 = 77.1696{{c}})
{{Optimal ET sequence|legend=0| 140, 171, 311 }}
Badness (Sintel): 1.19
==== 41-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
Comma list: 595/594, 625/624, 697/696, 703/702, 714/713, 784/783, 820/819, 833/832, 875/874, 900/899, 931/930
Mapping: {{mapping| 1 -19 7 0 112 43 49 -94 114 61 -83 81 -4 | 0 22 -5 3 -116 -42 -48 105 -117 -60 94 -81 10 }}
Optimal tunings:
* WE: ~2 = 1199.9957{{c}}, ~44/23 = 1122.8266{{c}} (~23/22 = 77.1691{{c}})
* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8306{{c}} (~23/22 = 77.1694{{c}})
{{Optimal ET sequence|legend=0| 140, 171, 311 }}
Badness (Sintel): 1.20


=== Hemitert ===
=== Hemitert ===