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No-threes subgroup temperaments: Difference between revisions

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moved 2.5.p temperaments from chromatic pairs
ported the last remaining subgroup temps from chromatic pairs
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* 37-11-commatic (rank-1) → [[37th-octave temperaments #37-11-commatic (rank-1)]]
* 37-11-commatic (rank-1) → [[37th-octave temperaments #37-11-commatic (rank-1)]]
* etc.
* etc.
=== Score ===
{{See also| Chromatic pairs #Score }}
[[Subgroup]]: 2.7.11.13
[[Comma list]]: 343/338, 847/832
{{Mapping|legend=2| 1 1 3 1 | 0 4 1 6 }}
{{Mapping|legend=3| 1 0 0 1 3 1| 0 0 0 4 1 6 }}
: [[gencom]]: [2 11/8; 343/338 847/832]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 540.099
{{Optimal ET sequence|legend=1| 5, 7, 9, 11, 20 }}
[[Tp tuning #T2 tuning|RMS error]]: 1.282 cents
=== Bossier ===
{{See also| Chromatic pairs #Bossier }}
Bossier can be described as the 3 & 17 in the 2.7.11.13 subgroup.
[[Subgroup]]: 2.7.11.13
[[Comma list]]: [[1573/1568]], [[15488/15379]]
{{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }}
{{Mapping|legend=3| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}
: [[gencom]]: [2 14/11; 1573/1568 15488/15379]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/11 = 421.309
{{Optimal ET sequence|legend=1| 17, 20, 37, 57, 94, 225, 319cd, 413bcd }}
[[Tp tuning #T2 tuning|RMS error]]: 0.4043 cents
=== Voltage ===
Voltage is the 3 & 7 temperament in the 2.7.13 subgroup.
[[Subgroup]]: 2.7.13
[[Comma list]]: [[28672/28561]]
{{Mapping|legend=2| 1 4 4 | 0 -4 -1 }}
{{Mapping|legend=3| 1 0 0 4 0 4 | 0 0 0 -4 0 -1 }}
: [[gencom]]: [2, 16/13; 28672/28561]
[[Optimal tuning]]:
* [[POTE]]: ~2 = 1\1, ~16/13 = 357.677
* [[TOP tuning|POTT]]: ~2 = 1\1, ~16/13 = 357.794 (1200 - 300 log<sub>2</sub>(7))
{{Optimal ET sequence|legend=1| 3, 7, 10, 27, 37, 47, 57, 104 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.1423 cents


=== Ultrakleismic ===
=== Ultrakleismic ===
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{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 141, 167, 193p, 219p, 245p }}
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 141, 167, 193p, 219p, 245p }}


=== Yer (rank 3) ===
=== Lovecraft ===
[[Subgroup]]: 2.11.13.17.19
{{See also | Chromatic pairs #Lovecraft }}
 
Lovecraft, the 4 & 13 temperament in the 2.11.13 subgroup, is generated by ~13/11. Two generator steps give ~11/8 and three generator steps give ~13/8.
 
[[Subgroup]]: 2.11.13
 
[[Comma list]]: [[1352/1331]]
 
{{Mapping|legend=2| 1 3 3 | 0 2 3 }}
 
{{Mapping|legend=3| 1 0 0 0 3 3 | 0 0 0 0 2 3 }}
 
: [[gencom]]: [2 13/11; 1352/1331]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/11 = 279.318
 
{{Optimal ET sequence|legend=1| 13, 30, 43, 73, 116 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8449 cents
 
=== Blackbirds ===
{{See also | Chromatic pairs #Blackbirds }}
 
Blackbirds is a fairly straightforward temperament. It simply equates ~13/11 to 1/4 of the octave with a generator for prime 11 or 13.
 
[[Subgroup]]: 2.11.13
 
[[Comma list]]: [[29282/28561]]
 
{{Mapping|legend=2| 4 0 1 | 0 1 1 }}
 
{{Mapping|legend=3| 4 0 0 0 12 13 | 0 0 0 0 1 1 }}
 
: [[gencom]]: [13/11 11/8; 29282/28561]
 
[[Optimal tuning]] ([[POTE]]): ~13/11 = 1\4, ~11/8 = 546.660
 
{{Optimal ET sequence|legend=1| 4, 16, 20, 24, 44, 68, 112c, 180bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8685 cents
 
=== Bluebirds ===
{{See also| Chromatic pairs #Bluebirds }}
 
[[Subgroup]]: 2.11.13
 
[[Comma list]]: [[265837/262144]]
 
{{Mapping|legend=2| 1 0 6 | 0 3 -2 }}
 
{{Mapping|legend=3| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }}


[[Comma list]]: 209/208, 2057/2048
: [[gencom]]: [2 143/128; 265837/262144]


[[Sval]] [[mapping]]: {{mapping| 1 0 0 11 4 | 0 1 0 -2 -1 | 0 0 1 0 1 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~143/128 = 182.368


[[Optimal tuning]] ([[TE tuning|TE]]): ~2/1 = 1200.4457, ~11/8 = 548.4934, ~16/13 = 358.638
{{Optimal ET sequence|legend=1| 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc }}


{{Optimal ET sequence|legend=1| 11, 13, 24, 33, 37, 46, 57, 70, 127, 197eh }}
[[Tp tuning #T2 tuning|RMS error]]: 0.4444 cents


=== Yamablu ===
=== Yamablu ===
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{{Optimal ET sequence|legend=1| 7fh, 9, 11, 20 }}
{{Optimal ET sequence|legend=1| 7fh, 9, 11, 20 }}
=== Yer (rank 3) ===
[[Subgroup]]: 2.11.13.17.19
[[Comma list]]: 209/208, 2057/2048
[[Sval]] [[mapping]]: {{mapping| 1 0 0 11 4 | 0 1 0 -2 -1 | 0 0 1 0 1 }}
[[Optimal tuning]] ([[TE tuning|TE]]): ~2/1 = 1200.4457, ~11/8 = 548.4934, ~16/13 = 358.638
{{Optimal ET sequence|legend=1| 11, 13, 24, 33, 37, 46, 57, 70, 127, 197eh }}


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Subgroup temperaments]]
[[Category:Subgroup temperaments]]
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