94th-octave temperaments: Difference between revisions
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== Garistearn == | == Garistearn == | ||
Named by [[Xenllium]] in 2021, the garistearn temperament (94 & 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]]. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Comma list: 540/539, 4000/3993, 33554432/33480783 | Comma list: 540/539, 4000/3993, 33554432/33480783 | ||
{{Mapping|legend=0| 94 149 0 264 107 | 0 0 1 0 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 540/539, 729/728, 1575/1573, 28672/28561 | Comma list: 540/539, 729/728, 1575/1573, 28672/28561 | ||
{{Mapping|legend=0| 94 149 0 264 107 348 | 0 0 1 0 1 0 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873 | Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873 | ||
{{Mapping|legend=0| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
Latest revision as of 12:33, 24 September 2026
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
94edo is a "wheel" for some fractional-octave temperaments because of its excellent perfect fifth.
Garistearn
Named by Xenllium in 2021, the garistearn temperament (94 & 282) tempers out the same commas as 94edo in the 2.3.7 subgroup while adding an independent generator for prime 5.
Subgroup: 2.3.5.7
Comma list: 118098/117649, 33554432/33480783
Mapping: [⟨94 149 0 264], ⟨0 0 1 0]]
- mapping generators: ~1029/1024, ~5
- WE: ~1029/1024 = 12.7638 ¢, ~5/4 = 386.7156 ¢ (~5120/5103 = 3.8011 ¢)
- error map: ⟨-0.201 -0.146 -0.000 +0.822]
- CWE: ~1029/1024 = 12.7660 ¢, ~5/4 = 386.6637 ¢ (~5120/5103 = 3.6850 ¢)
- error map: ⟨0.000 +0.173 +0.350 +1.387]
Optimal ET sequence: 94, 188, 282, 658d, 940dd
Badness (Sintel): 7.77
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 33554432/33480783
Mapping: [⟨94 149 0 264 107], ⟨0 0 1 0 1]]
Optimal tunings:
- WE: ~1029/1024 = 12.7637 ¢, ~5/4 = 386.5270 ¢ (~5120/5103 = 3.6174 ¢)
- CWE: ~1029/1024 = 12.7660 ¢, ~5/4 = 386.4545 ¢ (~5120/5103 = 3.4758 ¢)
Optimal ET sequence: 94, 188e, 282, 376, 658de
Badness (Sintel): 2.72
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573, 28672/28561
Mapping: [⟨94 149 0 264 107 348], ⟨0 0 1 0 1 0]]
Optimal tunings:
- WE: ~169/168 = 12.7628 ¢, ~5/4 = 386.7181 ¢ (~352/351 = 3.8344 ¢)
- CWE: ~169/168 = 12.7660 ¢, ~5/4 = 386.6570 ¢ (~352/351 = 3.6783 ¢)
Optimal ET sequence: 94, 188e, 282, 658deff, 940ddeefff
Badness (Sintel): 1.90
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873
Mapping: [⟨94 149 0 264 107 348 166], ⟨0 0 1 0 1 0 1]]
Optimal tunings:
- WE: ~169/168 = 12.7628 ¢, ~5/4 = 386.7471 ¢ (~352/351 = 3.8623 ¢)
- CWE: ~169/168 = 12.7660 ¢, ~5/4 = 386.6751 ¢ (~352/351 = 3.6963 ¢)
Optimal ET sequence: 94, 188eg, 282, 658deff, 940ddeefffg
Badness (Sintel): 1.41