Subgroup temperaments: Difference between revisions
Call it whatever, but the data themselves should remain normalized |
m Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| " |
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[[Subgroup]]: 2.3.11.19 | [[Subgroup]]: 2.3.11.19 | ||
{{Mapping|legend= | {{Mapping|legend=3| 4 5 13 18 | 0 8 5 -6 }} | ||
: sval mapping generators: ~6291456/5285401, ~25289/24576 | : sval mapping generators: ~6291456/5285401, ~25289/24576 | ||
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[[Comma list]]: {{monzo| 28 -2 -19 8 }}, {{monzo| 9 -25 23 6 }} | [[Comma list]]: {{monzo| 28 -2 -19 8 }}, {{monzo| 9 -25 23 6 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 9 6 13 | 0 -298 -188 -521 }} | ||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~531441/524288 = 23.4765 | [[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~531441/524288 = 23.4765 | ||
| Line 110: | Line 110: | ||
[[Comma list]]: 225/224, 3125/3087 | [[Comma list]]: 225/224, 3125/3087 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 3 4 | 0 1 -4 -7 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.170 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.170 | ||
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[[Comma list]]: [[225/224]], [[325/324]], [[640/637]] | [[Comma list]]: [[225/224]], [[325/324]], [[640/637]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 15 25 -28 | 0 1 -4 -7 10 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }} | ||
: [[gencom]]: [2 9/8; 225/224 325/324 640/637] | : [[gencom]]: [2 9/8; 225/224 325/324 640/637] | ||
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Comma list: 100/99, 225/224, 245/242 | Comma list: 100/99, 225/224, 245/242 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 3 4 5 | 0 1 -4 -7 -9 }} | ||
Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.743 | Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.743 | ||
| Line 161: | Line 161: | ||
Comma list: 100/99, 144/143, 225/224, 245/242 | Comma list: 100/99, 144/143, 225/224, 245/242 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 3 4 5 2 | 0 1 -4 -7 -9 10 }} | ||
Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.414 | Optimal tuning (POTE): ~2 = 1\1, ~9/8 = 204.414 | ||
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Comma list: [[2048/2025]] | Comma list: [[2048/2025]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 7| 0 1 -4}} | ||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.136 | Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.136 | ||
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Comma list: 2048/2025, 576/575, 82/81 | Comma list: 2048/2025, 576/575, 82/81 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 1 7 3| 0 1 6 -4 4}} | ||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.264 | Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.264 | ||
| Line 202: | Line 202: | ||
Comma list: 64/63, 225/224, 162/161, 82/81, 177/175 | Comma list: 64/63, 225/224, 162/161, 82/81, 177/175 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 4 1 7 3 10| 0 1 -2 6 -4 4 -7}} | ||
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 706.387 | Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 706.387 | ||
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[[Comma list]]: 45/44, 65/64, 81/80 | [[Comma list]]: 45/44, 65/64, 81/80 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -4 -6 10 | 0 1 2 3 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }} | ||
: [[gencom]]: [2 9/8; 45/44 65/64 81/80] | : [[gencom]]: [2 9/8; 45/44 65/64 81/80] | ||
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[[Comma list]]: 41503/41472, 322102/321489 | [[Comma list]]: 41503/41472, 322102/321489 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 5 3 5 | 0 -19 -2 -16 }} | ||
: mapping generators: ~2, ~77/72 | : mapping generators: ~2, ~77/72 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 5/2 0 3 5 | 0 -19/2 0 -2 -16 }} | ||
: [[gencom]]: [2 77/72; 41503/41472 322102/321489] | : [[gencom]]: [2 77/72; 41503/41472 322102/321489] | ||
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[[Comma list]]: 99/98, 9317/9216 | [[Comma list]]: 99/98, 9317/9216 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 3 | 0 7 4 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 1 3 | 0 7/2 0 4 1 }} | ||
: [[gencom]]: [2 11/8; 99/98 9317/9216] | : [[gencom]]: [2 11/8; 99/98 9317/9216] | ||
| Line 302: | Line 302: | ||
[[Comma list]]: 64/63, 99/98 | [[Comma list]]: 64/63, 99/98 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 6 13 | 0 1 -1 -3 }} | ||
: sval mapping generators: ~2, ~9 | : sval mapping generators: ~2, ~9 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 3/2 0 3 4 | 0 1/2 0 -1 -3 }} | ||
: [[gencom]]: [2 8/7; 64/63 99/98] | : [[gencom]]: [2 8/7; 64/63 99/98] | ||
| Line 325: | Line 325: | ||
[[Comma list]]: 896/891, 26411/26244 | [[Comma list]]: 896/891, 26411/26244 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 6 | 0 5 6 -4 }} | ||
: sval mapping generators: ~2, ~14/9 | : sval mapping generators: ~2, ~14/9 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 5/2 0 5 2 | 0 -5/2 0 -6 4 }} | ||
: [[gencom]]: [2 9/7; 896/891 26411/26244] | : [[gencom]]: [2 9/7; 896/891 26411/26244] | ||
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[[Comma list]]: 729/728, 442/441, 833/832 | [[Comma list]]: 729/728, 442/441, 833/832 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 1 -1 3| 0 6 5 13 3 }} | ||
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~9/7 = 433.836 | [[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~9/7 = 433.836 | ||
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[[Comma list]]: 225/224, 245/243 | [[Comma list]]: 225/224, 245/243 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 2 -1 | 0 5 3 6 }} | ||
: sval mapping generators: ~2, ~14/9 | : sval mapping generators: ~2, ~14/9 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 5/2 5/2 5 | 0 -5/2 -1/2 -6 }} | ||
: [[gencom]]: [2 9/7; 225/224 245/243] | : [[gencom]]: [2 9/7; 225/224 245/243] | ||
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Sval mapping: {{mapping| 1 0 2 -1 6 | 0 5 3 6 -4 }} | Sval mapping: {{mapping| 1 0 2 -1 6 | 0 5 3 6 -4 }} | ||
{{Mapping|legend=4| 1 5/2 5/2 5 2 | 0 -5/2 -1/2 -6 4 }} | |||
: gencom: [2 9/7; 100/99 225/224 245/243] | : gencom: [2 9/7; 100/99 225/224 245/243] | ||
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Sval mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 3 6 -4 9 }} | Sval mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 3 6 -4 9 }} | ||
{{Mapping|legend=4| 1 5/2 5/2 5 2 7 | 0 -5/2 -1/2 -6 4 -9 }} | |||
: gencom: [2 9/7; 100/99 105/104 144/143 196/195] | : gencom: [2 9/7; 100/99 105/104 144/143 196/195] | ||
| Line 450: | Line 450: | ||
[[Comma list]]: 1029/1024 | [[Comma list]]: 1029/1024 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 4 | 0 3 1 }} | ||
: sval mapping generators: ~2, ~21/16 | : sval mapping generators: ~2, ~21/16 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 1 0 3 | 0 3/2 0 -1/2 }} | ||
: [[gencom]]: [2 21/16; 1029/1024] | : [[gencom]]: [2 21/16; 1029/1024] | ||
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Sval mapping: {{mapping| 1 2 0 4 5 | 0 3 6 1 -4 }} | Sval mapping: {{mapping| 1 2 0 4 5 | 0 3 6 1 -4 }} | ||
{{Mapping|legend=4| 1 1 0 3 5 | 0 3/2 6 -1/2 -4 }} | |||
: gencom: [2 21/16; 81/80 99/98 385/384] | : gencom: [2 21/16; 81/80 99/98 385/384] | ||
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[[Comma list]]: [[24576/24565]] ({{monzo| 13 1 -3 }}) | [[Comma list]]: [[24576/24565]] ({{monzo| 13 1 -3 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 5 | 0 3 1 }} | ||
: mapping generators: ~2, ~85/32 | : mapping generators: ~2, ~85/32 | ||
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Comma list: 2025/2023 ({{monzo| 2 -2 1 0 }}), 24576/24565 ({{monzo| 13 1 0 -3 }}) | Comma list: 2025/2023 ({{monzo| 2 -2 1 0 }}), 24576/24565 ({{monzo| 13 1 0 -3 }}) | ||
{{Mapping|legend=2| 1 2 6 5 | 0 3 -4 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 551: | Line 551: | ||
[[Comma list]]: 15625/15552 | [[Comma list]]: 15625/15552 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 3 | 0 -6 -5 }} | ||
: Mapping generators: ~4, ~5/3 | : Mapping generators: ~4, ~5/3 | ||
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[[Comma list]]: 81/80 | [[Comma list]]: 81/80 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 2 | 0 -1 -4 }} | ||
: Mapping generators: ~4, ~4/3 | : Mapping generators: ~4, ~4/3 | ||
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[[Comma list]]: 3125/3072 | [[Comma list]]: 3125/3072 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 | 0 5 1 }} | ||
: Mapping generators: ~4, ~5/4 | : Mapping generators: ~4, ~5/4 | ||
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[[Comma list]]: 256/243 | [[Comma list]]: 256/243 | ||
{{Mapping|legend= | {{Mapping|legend=3| 5 4 6 | 0 0 -1 }} | ||
: Mapping generators: ~4, ~16/15 | : Mapping generators: ~4, ~16/15 | ||
| Line 610: | Line 610: | ||
[[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }} | [[Comma list]]: [[81/80]] = {{monzo| -4 4 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -4| 0 1 4 }} | ||
: mapping generators: ~4, ~6 | : mapping generators: ~4, ~6 | ||
| Line 625: | Line 625: | ||
[[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }} | [[Comma list]]: [[36/35]] = {{monzo| 0 2 -1 -1 }}, [[64/63]] = {{monzo| 4 -2 0 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -4 4 | 0 1 4 -2 }} | ||
[[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622 | [[Optimal tuning]] (subgroup [[CTE]]): ~4 = 2\1, ~3/2 = 699.622 | ||
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[[Comma list]]: [[6561/6400]] | [[Comma list]]: [[6561/6400]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 4 | 0 1 4 }} | ||
Mapping generators: ~4, ~9/64 | Mapping generators: ~4, ~9/64 | ||
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[[Comma list]]: 4096/3969 | [[Comma list]]: 4096/3969 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 0 | 0 1 -2 }} | ||
Mapping generators: ~4, ~9/64 | Mapping generators: ~4, ~9/64 | ||
| Line 922: | Line 922: | ||
[[Comma list]]: 64/63 | [[Comma list]]: 64/63 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 2 | 0 1 -1 }} | ||
: sval mapping generators: ~8, ~9 | : sval mapping generators: ~8, ~9 | ||
| Line 945: | Line 945: | ||
[[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }}) | [[Comma list]]: 100/99 ({{monzo| 2 2 0 -1 }}), 385/384 ({{monzo| -7 1 1 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 5 2 | 0 1 -3 2 }} | ||
: mapping generators: ~2, ~5/3 | : mapping generators: ~2, ~5/3 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }} | ||
: [[gencom]]: [2 6/5; 100/99 385/384] | : [[gencom]]: [2 6/5; 100/99 385/384] | ||
| Line 969: | Line 969: | ||
[[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }}) | [[Comma list]]: [[126/125]] ({{monzo| 1 -3 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 | 0 1 3 }} | ||
: mapping generators: ~2, ~5/3 | : mapping generators: ~2, ~5/3 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1 0 1 | 0 4/3 1/3 -5/3 }} | ||
: [[gencom]]: [2 6/5; 126/125] | : [[gencom]]: [2 6/5; 126/125] | ||
| Line 993: | Line 993: | ||
[[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }}) | [[Comma list]]: 121/120 ({{monzo| -3 -1 0 2 }}), 126/125 ({{monzo| 1 -3 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 2 2 | 0 -2 -6 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }} | ||
: [[gencom]]: [2 11/10; 121/120 126/125] | : [[gencom]]: [2 11/10; 121/120 126/125] | ||
| Line 1,016: | Line 1,016: | ||
[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }}) | [[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 91/90 ({{monzo| -1 -1 1 0 1 }}), 100/99 ({{monzo| 2 2 0 -1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 2 2 | 0 1 3 2 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }} | ||
: [[gencom]]: [2 6/5; 56/55 91/90 100/99] | : [[gencom]]: [2 6/5; 56/55 91/90 100/99] | ||
| Line 1,041: | Line 1,041: | ||
[[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }}) | [[Comma list]]: [[275/273]] ({{monzo| 0 2 -1 -1 }}), [[847/845]] ({{monzo| 0 -1 1 -2 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 0 0 | 0 3 5 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }} | ||
: [[gencom]]: [2 13/11; 275/273 847/845] | : [[gencom]]: [2 13/11; 275/273 847/845] | ||
| Line 1,063: | Line 1,063: | ||
[[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }}) | [[Comma list]]: [[3025/3024]] ({{monzo| -4 2 -1 2 }}), [[3125/3087]] ({{monzo| 0 5 -3 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 0 2 | 0 6 10 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }} | ||
: [[gencom]]: [2 12/11; 3025/3024 3125/3087] | : [[gencom]]: [2 12/11; 3025/3024 3125/3087] | ||
| Line 1,087: | Line 1,087: | ||
[[Comma list]]: [[121/120]] ({{monzo| -3 -1 0 2 }}), [[169/168]] ({{monzo| -3 0 -1 0 2 }}), [[275/273]] ({{monzo| 0 2 -1 1 -1 }}) | [[Comma list]]: [[121/120]] ({{monzo| -3 -1 0 2 }}), [[169/168]] ({{monzo| -3 0 -1 0 2 }}), [[275/273]] ({{monzo| 0 2 -1 1 -1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 5 3 4 | 0 -6 -10 -3 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }} | ||
: [[gencom]]: [2 13/10; 121/120 169/168 275/273] | : [[gencom]]: [2 13/10; 121/120 169/168 275/273] | ||
| Line 1,109: | Line 1,109: | ||
[[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }}) | [[Comma list]]: [[245/243]] ({{monzo| 0 1 -2 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 0 | 0 2 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 | 0 0 2 -1 }} | ||
: [[gencom]]: [2 9/7; 245/243] | : [[gencom]]: [2 9/7; 245/243] | ||
| Line 1,132: | Line 1,132: | ||
[[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }}) | [[Comma list]]: [[325/324]] ({{monzo| -2 2 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 2 | 0 1 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }} | ||
: [[gencom]]: [2 6/5; 325/324] | : [[gencom]]: [2 6/5; 325/324] | ||
| Line 1,155: | Line 1,155: | ||
[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -1 }}) | [[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[540/539]] ({{monzo| 2 1 -2 -1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 3 | 0 -3 1 -5 }} | ||
: mapping generators: ~2, ~7/6 | : mapping generators: ~2, ~7/6 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }} | ||
: [[gencom]]: [2 7/6; 176/175 540/539] | : [[gencom]]: [2 7/6; 176/175 540/539] | ||
| Line 1,177: | Line 1,177: | ||
[[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 0 }}), [[540/539]] ({{monzo| 2 1 -2 -1 0 }}), [[1573/1568]] ({{monzo| -5 0 -2 2 1 }}) | [[Comma list]]: [[176/175]] ({{monzo| 4 -2 -1 1 0 }}), [[540/539]] ({{monzo| 2 1 -2 -1 0 }}), [[1573/1568]] ({{monzo| -5 0 -2 2 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 3 1 | 0 -3 1 -5 12 }} | ||
: mapping generators: ~2, ~12/7 | : mapping generators: ~2, ~12/7 | ||
| Line 1,198: | Line 1,198: | ||
[[Comma list]]: [[144/143]] ({{monzo| 4 0 0 -1 -1 }}), [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[196/195]] ({{monzo| 2 -1 2 0 -1 }} | [[Comma list]]: [[144/143]] ({{monzo| 4 0 0 -1 -1 }}), [[176/175]] ({{monzo| 4 -2 -1 1 }}), [[196/195]] ({{monzo| 2 -1 2 0 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 2 -2 6 | 0 3 -1 5 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }} | ||
: [[gencom]]: [2 7/6; 144/143 176/175 196/195] | : [[gencom]]: [2 7/6; 144/143 176/175 196/195] | ||
| Line 1,222: | Line 1,222: | ||
[[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 78/77 ({{monzo| 1 0 -1 -1 1 }}), 91/90 ({{monzo| -1 -2 1 0 1 }}) | [[Comma list]]: 56/55 ({{monzo| 3 -1 1 -1 }}), 78/77 ({{monzo| 1 0 -1 -1 1 }}), 91/90 ({{monzo| -1 -2 1 0 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 1 2 2 | 0 3 2 -1 1 }} | ||
: mapping generators: ~2, ~13/12 | : mapping generators: ~2, ~13/12 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }} | ||
: [[gencom]]: [2 13/12; 56/55 78/77 91/90] | : [[gencom]]: [2 13/12; 56/55 78/77 91/90] | ||
| Line 1,245: | Line 1,245: | ||
[[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }}) | [[Comma list]]: 100/99 ({{monzo| 2 -2 0 -1 }}), 245/242 ({{monzo| -1 -1 2 -2 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 1 0 | 0 -2 3 4 }} | ||
: mapping generators: ~2, ~21/20 | : mapping generators: ~2, ~21/20 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }} | ||
: [[gencom]]: [2 21/20; 100/99 245/242] | : [[gencom]]: [2 21/20; 100/99 245/242] | ||
| Line 1,268: | Line 1,268: | ||
[[Comma list]]: [[99/98]] ({{monzo| -1 -2 1 }}) | [[Comma list]]: [[99/98]] ({{monzo| -1 -2 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 | 0 1 2 }} | ||
: mapping generators: ~2, ~7/3 | : mapping generators: ~2, ~7/3 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }} | ||
: [[gencom]]: [2 7/6; 99/98] | : [[gencom]]: [2 7/6; 99/98] | ||
| Line 1,292: | Line 1,292: | ||
[[Comma list]]: 225/224 ({{monzo| -5 2 1 }}) | [[Comma list]]: 225/224 ({{monzo| -5 2 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 5 | 0 1 -2 }} | ||
: mapping generators: ~2, ~5 | : mapping generators: ~2, ~5 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 2 0 -1 | 0 -4/5 1 2/5 }} | ||
: [[gencom]]: [2 5; 225/224] | : [[gencom]]: [2 5; 225/224] | ||
| Line 1,314: | Line 1,314: | ||
[[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }}) | [[Comma list]]: 99/98 ({{monzo| -1 0 2 1 }}), 176/175 ({{monzo| 4 -2 1 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 5 -9 | 0 1 -2 4 }}] | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
| Line 1,332: | Line 1,332: | ||
[[Comma list]]: [[50/49]] | [[Comma list]]: [[50/49]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 2 3 1 | 0 1 0 }} | ||
[[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962 | [[Optimal tuning]] (inharmonic [[TE]]): ~1\2 = 590.998, ~[[10/7]]-1\2 = 128.962 | ||
| Line 1,345: | Line 1,345: | ||
[[Comma list]]: [[5120/5103]] = {{monzo| 10 -6 -1 }} | [[Comma list]]: [[5120/5103]] = {{monzo| 10 -6 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 10 | 0 1 -6 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
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[[Comma list]]: [[196/195]] = {{monzo| 2 -1 2 0 -1 }}, [[352/351]] = {{monzo| 5 -3 0 1 -1 }}, [[364/363]] = {{monzo| 2 -1 1 -2 1 }} | [[Comma list]]: [[196/195]] = {{monzo| 2 -1 2 0 -1 }}, [[352/351]] = {{monzo| 5 -3 0 1 -1 }}, [[364/363]] = {{monzo| 2 -1 1 -2 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 10 17 22 | 0 1 -6 -10 -13 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }} | ||
: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363] | : [[gencom]]: [2 3/2; 196/195, 352/351, 364/363] | ||
| Line 1,389: | Line 1,389: | ||
[[Comma list]]: [[352/351]], [[676/675]], [[847/845]] | [[Comma list]]: [[352/351]], [[676/675]], [[847/845]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 10 -6 -1 | 0 2 -12 9 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }} | ||
: [[gencom]]: [2 15/13; 352/351 676/675 847/845] | : [[gencom]]: [2 15/13; 352/351 676/675 847/845] | ||
| Line 1,410: | Line 1,410: | ||
[[Comma list]]: 364/363, 441/440, 1001/1000 | [[Comma list]]: 364/363, 441/440, 1001/1000 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 0 1 2 | 0 -6 7 2 -9 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~21/20 = 83.016 | ||
| Line 1,428: | Line 1,428: | ||
[[Comma list]]: [[250047/250000]] | [[Comma list]]: [[250047/250000]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 1 3 | 0 1 -1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }} | ||
: [[gencom]]: [63/50 10/9; 250047/250000] | : [[gencom]]: [63/50 10/9; 250047/250000] | ||
| Line 1,449: | Line 1,449: | ||
[[Comma list]]: [[847/845]], [[1001/1000]] | [[Comma list]]: [[847/845]], [[1001/1000]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 0 1 | 0 -4 3 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }} | ||
: [[gencom]]: [2 13/10; 847/845 1001/1000] | : [[gencom]]: [2 13/10; 847/845 1001/1000] | ||
| Line 1,465: | Line 1,465: | ||
[[Comma list]]: [[170/169]], [[221/220]], [[847/845]] | [[Comma list]]: [[170/169]], [[221/220]], [[847/845]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 0 1 1 | 0 -4 3 1 2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 -3/4 5/4 -3/4 1/4 1/4 | 0 0 0 -4 3 1 2 }} | ||
: [[gencom]]: [2 13/10; 170/169 221/220 847/845] | : [[gencom]]: [2 13/10; 170/169 221/220 847/845] | ||
| Line 1,488: | Line 1,488: | ||
[[Comma list]]: [[2200/2197]] | [[Comma list]]: [[2200/2197]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1| 0 3 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }} | ||
: [[gencom]]: [2 13/10; 2200/2197] | : [[gencom]]: [2 13/10; 2200/2197] | ||
| Line 1,508: | Line 1,508: | ||
[[Comma list]]: [[352/351]], [[676/675]] | [[Comma list]]: [[352/351]], [[676/675]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -6 -1 | 0 2 9 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }} | ||
: [[gencom]]: [2 15/13; 352/351 676/675] | : [[gencom]]: [2 15/13; 352/351 676/675] | ||
| Line 1,526: | Line 1,526: | ||
[[Comma list]]: 169/168, 540/539, 729/728 | [[Comma list]]: 169/168, 540/539, 729/728 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -3 8 0 | 0 3 11 -13 7 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~13/9 = 633.518 | ||
| Line 1,543: | Line 1,543: | ||
[[Comma list]]: 1029/1024, 4000/3993 | [[Comma list]]: 1029/1024, 4000/3993 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 0 10 5 | 0 3 -1 -1 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.742 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.742 | ||
| Line 1,556: | Line 1,556: | ||
[[Comma list]]: 1029/1024, 1575/1573, 2080/2079 | [[Comma list]]: 1029/1024, 1575/1573, 2080/2079 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 0 10 5 0 | 0 3 -1 -1 7 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.918 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 1\3, ~13/9 = 633.918 | ||
| Line 1,569: | Line 1,569: | ||
[[Comma list]]: 273/272, 833/832, 1575/1573, 2080/2079 | [[Comma list]]: 273/272, 833/832, 1575/1573, 2080/2079 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 0 10 5 0 -2 | 0 3 -1 -1 7 9 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.820 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.820 | ||
| Line 1,582: | Line 1,582: | ||
[[Comma list]]: 210/209, 273/272, 286/285, 595/594, 2080/2079 | [[Comma list]]: 210/209, 273/272, 286/285, 595/594, 2080/2079 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 0 10 5 0 -2 8 | 0 3 -1 -1 7 9 3 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.894 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 633.894 | ||
| Line 1,595: | Line 1,595: | ||
[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 595/594, 2080/2079 | [[Comma list]]: 210/209, 231/230, 273/272, 286/285, 595/594, 2080/2079 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 0 10 5 0 -2 8 12 | 0 3 -1 -1 7 9 3 1 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 634.038 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 1\3, ~13/9 = 634.038 | ||
| Line 1,608: | Line 1,608: | ||
[[Comma list]]: 210/209, 231/230, 273/272, 286/285, 320/319, 595/594, 2080/2079 | [[Comma list]]: 210/209, 231/230, 273/272, 286/285, 320/319, 595/594, 2080/2079 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 0 10 5 0 -2 8 12 13 | 0 3 -1 -1 7 9 3 1 1 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~29/23 = 1\3, ~13/9 = 634.102 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~29/23 = 1\3, ~13/9 = 634.102 | ||
| Line 1,624: | Line 1,624: | ||
[[Comma list]]: {{monzo| 8 -5 }} (256/243) | [[Comma list]]: {{monzo| 8 -5 }} (256/243) | ||
{{Mapping|legend= | {{Mapping|legend=3| 5 8 0 | 0 0 1 }} | ||
: mapping generators: ~9/8, ~11/7 | : mapping generators: ~9/8, ~11/7 | ||
| Line 1,645: | Line 1,645: | ||
[[Comma list]]: 352/351, 364/363 | [[Comma list]]: 352/351, 364/363 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 7 12 | 0 1 -4 -7 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }} | ||
: [[gencom]]: [2 3/2; 352/351 364/363] | : [[gencom]]: [2 3/2; 352/351 364/363] | ||
| Line 1,686: | Line 1,686: | ||
[[Comma list]]: [[243/242]], [[676/675]] | [[Comma list]]: [[243/242]], [[676/675]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 2 0 -1 -2 | 0 2 5 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }} | ||
: [[gencom]]: [55/39 15/13; 243/242 676/675] | : [[gencom]]: [55/39 15/13; 243/242 676/675] | ||
| Line 1,702: | Line 1,702: | ||
[[Comma list]]: 221/220, 243/242, 289/288 | [[Comma list]]: 221/220, 243/242, 289/288 | ||
{{Mapping|legend= | {{Mapping|legend=3| 2 0 -1 -2 5 | 0 2 5 3 2 }} | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
| Line 1,718: | Line 1,718: | ||
[[Comma list]]: 64/63, 91/90 | [[Comma list]]: 64/63, 91/90 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 6 -5 | 0 1 -2 4 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~3/2 = 713.910 | ||
| Line 1,738: | Line 1,738: | ||
edo join: 29 & 146 | edo join: 29 & 146 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 1 | 0 17 11 }} | ||
: mapping generators: ~2, ~2250/2197 | : mapping generators: ~2, ~2250/2197 | ||
| Line 1,757: | Line 1,757: | ||
edo join: 29 & 146 | edo join: 29 & 146 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 1 1 | 0 17 4 11 }} | ||
: mapping generators: ~2, ~169/165 | : mapping generators: ~2, ~169/165 | ||
| Line 1,778: | Line 1,778: | ||
[[Comma list]]: 2401/2400 | [[Comma list]]: 2401/2400 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 3 | 0 2 1 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~49/40 = 350.966 | ||
| Line 1,794: | Line 1,794: | ||
[[Comma list]]: 136/135 ({{monzo| 3 -3 1 }}) | [[Comma list]]: 136/135 ({{monzo| 3 -3 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -3 | 0 1 3 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
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[[Comma list]]: [[57/56]] ({{Monzo| -3 1 1 }}) | [[Comma list]]: [[57/56]] ({{Monzo| -3 1 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 3 | 0 1 -1 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
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[[Comma list]]: [[5491/5488]] ({{Monzo| -4 2 1 }}) | [[Comma list]]: [[5491/5488]] ({{Monzo| -4 2 1 }}) | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 4 | 0 1 -2 }} | ||
: mapping generators: ~2, ~17/7 | : mapping generators: ~2, ~17/7 | ||
| Line 1,883: | Line 1,883: | ||
[[Comma list]]: [[10976/10935]] | [[Comma list]]: [[10976/10935]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 3 | 0 3 1 }} | ||
[[Optimal tuning]] (subgroup [[CTE]]): ~[[3/2]] = 1\[[1edf]], ~[[28/27]] = 60.909 | [[Optimal tuning]] (subgroup [[CTE]]): ~[[3/2]] = 1\[[1edf]], ~[[28/27]] = 60.909 | ||
| Line 1,896: | Line 1,896: | ||
[[Comma list]]: 9604/9375 | [[Comma list]]: 9604/9375 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 4 | 0 -4 -5 }} | ||
: sval mapping generators: ~3/2, ~15/14 | : sval mapping generators: ~3/2, ~15/14 | ||
| Line 1,909: | Line 1,909: | ||
[[Comma list]]: 1232/1215, 27783/27500 | [[Comma list]]: 1232/1215, 27783/27500 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 4 4 | 0 -4 -5 1 }} | ||
: sval mapping generators: ~3/2, ~15/14 | : sval mapping generators: ~3/2, ~15/14 | ||
| Line 1,922: | Line 1,922: | ||
[[Comma list]]: 275/273, 1232/1215, 1323/1300 | [[Comma list]]: 275/273, 1232/1215, 1323/1300 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 4 4 5 | 0 -4 -5 1 -2 }} | ||
[[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 129.381 | [[Optimal tuning]] (subgroup [[CTE]]): ~3/2 = 1\1edf, ~15/14 = 129.381 | ||
| Line 1,934: | Line 1,934: | ||
[[Comma list]]: 245/243 | [[Comma list]]: 245/243 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 2 | 0 2 -1 }} | ||
: sval mapping generators: ~3/2, ~9/7 | : sval mapping generators: ~3/2, ~9/7 | ||
| Line 1,947: | Line 1,947: | ||
[[Comma list]]: 100/99, 245/243 | [[Comma list]]: 100/99, 245/243 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 2 0 | 0 2 -1 4 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 264.3771 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 264.3771 | ||
| Line 1,958: | Line 1,958: | ||
[[Comma list]]: 245/243, 441/440 | [[Comma list]]: 245/243, 441/440 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 2 5 | 0 2 -1 -4 }} | ||
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 261.5939 | [[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~7/6 = 261.5939 | ||
| Line 1,972: | Line 1,972: | ||
[[Comma list]]: 121/120 | [[Comma list]]: 121/120 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 1 | 0 2 -1 }}] | ||
: [[gencom]]: [3/2 12/11; 121/120] | : [[gencom]]: [3/2 12/11; 121/120] | ||
| Line 1,986: | Line 1,986: | ||
[[Comma list]]: 87808/85293 | [[Comma list]]: 87808/85293 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -8 | 0 1 3 }} | ||
: sval mapping generators: ~3/2, ~7 | : sval mapping generators: ~3/2, ~7 | ||
| Line 2,000: | Line 2,000: | ||
[[Comma list]]: 1352/1323 | [[Comma list]]: 1352/1323 | ||
{{Mapping|legend= | {{Mapping|legend=3| 2 0 3 | 0 1 1 }} | ||
: sval mapping generators: ~26/21, ~7 | : sval mapping generators: ~26/21, ~7 | ||
| Line 2,015: | Line 2,015: | ||
[[Comma list]]: {{monzo| 11 1 -5 }} | [[Comma list]]: {{monzo| 11 1 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 4 3 | 0 -5 -1 }} | ||
: [[gencom]]: [5/2 125/88; 341796875/329832448] | : [[gencom]]: [5/2 125/88; 341796875/329832448] | ||
| Line 2,026: | Line 2,026: | ||
= Related temperament collections = | = Related temperament collections = | ||
* [[Dual-fifth temperaments]] | * [[Dual-fifth temperaments]] | ||
* [[Irrational-subgroup temperaments]] | |||
* [[Equalizer subgroup]] temperaments | * [[Equalizer subgroup]] temperaments | ||
* [[Substitute harmonic]] temperaments | * [[Substitute harmonic]] temperaments | ||