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| * [[Barton11]] – 11-tone chromatic scale | | * [[Barton11]] – 11-tone chromatic scale |
| * [[Barton13]] – 13-tone mega-chromatic scale | | * [[Barton13]] – 13-tone mega-chromatic scale |
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| == Voltage ==
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| Voltage is the 3 & 7 temperament in the 2.7.13 subgroup.
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| [[Subgroup]]: 2.7.13
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| [[Comma list]]: [[28672/28561]]
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| {{Mapping|legend=2| 1 4 4 | 0 -4 -1 }}
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| {{Mapping|legend=3| 1 0 0 4 0 4 | 0 0 0 -4 0 -1 }}
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| : [[gencom]]: [2, 16/13; 28672/28561]
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| [[Optimal tuning]]:
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| * [[POTE]]: ~2 = 1\1, ~16/13 = 357.677
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| * [[TOP tuning|POTT]]: ~2 = 1\1, ~16/13 = 357.794 (1200 - 300 log<sub>2</sub>(7))
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| {{Optimal ET sequence|legend=1| 3, 7, 10, 27, 37, 47, 57, 104 }}
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| [[Tp tuning #T2 tuning|RMS error]]: 0.1423
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| == Tridec == | | == Tridec == |
| Line 195: |
Line 174: |
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| == Bossier == | | == Bossier == |
| Bossier can be described as the 3 & 17 in the 2.7.11.13 subgroup.
| | {{See also| No-threes subgroup temperaments #Bossier }} |
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| [[Subgroup]]: 2.7.11.13
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| [[Comma list]]: [[1573/1568]], [[15488/15379]]
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| {{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }} | |
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| {{Mapping|legend=3| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}
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| : [[gencom]]: [2 14/11; 1573/1568 15488/15379]
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/11 = 421.309
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| {{Optimal ET sequence|legend=1| 17, 20, 37, 57, 94, 225, 319cd, 413bcd }}
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| [[Tp tuning #T2 tuning|RMS error]]: 0.4043 cents
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| [[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]] | | [[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]] |
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| == Bluebirds == | | == Bluebirds == |
| [[Subgroup]]: 2.11.13
| | {{See also| No-threes subgroup temperaments #Bluebirds }} |
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| [[Comma list]]: [[265837/262144]]
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| {{Mapping|legend=2| 1 0 6 | 0 3 -2 }} | |
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| {{Mapping|legend=3| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }}
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| : [[gencom]]: [2 143/128; 265837/262144]
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~143/128 = 182.368
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| {{Optimal ET sequence|legend=1| 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc }}
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| [[Tp tuning #T2 tuning|RMS error]]: 0.4444 cents
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| Scales: | | Scales: |
| Line 412: |
Line 361: |
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| == Lovecraft == | | == 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.
| | {{See also | No-threes subgroup temperaments #Lovecraft }} |
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| [[Subgroup]]: 2.11.13
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| [[Comma list]]: [[1352/1331]]
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| {{Mapping|legend=2| 1 3 3 | 0 2 3 }} | |
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| {{Mapping|legend=3| 1 0 0 0 3 3 | 0 0 0 0 2 3 }}
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| : [[gencom]]: [2 13/11; 1352/1331]
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/11 = 279.318
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| {{Optimal ET sequence|legend=1| 13, 30, 43, 73, 116b }}
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| [[Tp tuning #T2 tuning|RMS error]]: 0.8449 cents
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| [[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]] | | [[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]] |
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Line 371: |
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| == Blackbirds == | | == 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.
| | {{See also | No-threes subgroup temperaments #Blackbirds }} |
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| [[Subgroup]]: 2.11.13
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| [[Comma list]]: [[29282/28561]]
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| {{Mapping|legend=2| 4 0 1 | 0 1 1 }} | |
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| {{Mapping|legend=3| 4 0 0 0 12 13 | 0 0 0 0 1 1 }}
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| : [[gencom]]: [13/11 11/8; 29282/28561]
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| [[Optimal tuning]] ([[POTE]]): ~13/11 = 1\4, ~11/8 = 546.660
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| {{Optimal ET sequence|legend=1| 4, 16, 20, 24, 44, 68, 112c, 180bc }}
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| [[Tp tuning #T2 tuning|RMS error]]: 0.8685 cents
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| Scales: | | Scales: |
| Line 567: |
Line 484: |
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| == Score == | | == Score == |
| [[Subgroup]]: 2.7.11.13
| | {{See also|No-threes subgroup temperaments #Score }} |
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| [[Comma list]]: 343/338, 847/832
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| {{Mapping|legend=2| 1 1 3 1 | 0 4 1 6 }} | |
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| {{Mapping|legend=3| 1 0 0 1 3 1| 0 0 0 4 1 6 }}
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| : [[gencom]]: [2 11/8; 343/338 847/832]
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 540.099
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| {{Optimal ET sequence|legend=1| 5, 7, 9, 11, 20 }}
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| [[Tp tuning #T2 tuning|RMS error]]: 1.282 cents
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| [[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]] | | [[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]] |