Subgroup temperaments: Difference between revisions
m the canon name of the 2.75.85 temp is archagall as named by scott dakota; the extension to 9/7 is both simple and harmonically obvious |
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 | ||
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[[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 | ||
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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 | ||
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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] | ||
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[[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] | ||
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[[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] | ||
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[[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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== 2.75.85 subgroup == | == 2.75.85 subgroup == | ||
=== Archagall === | === Archagall === | ||
{{ See also | Fifthplus }} | {{See also| Fifthplus }} | ||
By tempering out the comma [[24576/24565]] in the 2.75.85 subgroup, we have three [[85/64]]'s up and one octave down as a [[75/64]] and we have two [[128/85]]'s up and one octave down as a [[17/15]] whole tone. It is because of this combination of accuracy, efficiency and mapping-wise simplicity and its corresponding explanatory power in what this comma does that the comma has been named the ''archagallisma''. The ''MVP'' stands for ''minimum viable product'', as this is the core of what the archagall logic achieves, with further extensions adding to the subgroup while avoiding significantly impacting its accuracy. This is a highly accurate temperament that could be considered to be encoding the "high-accuracy logic" of [[superpyth]] and which is inescapably related to the [[17L 5s]] scale form as it is the 17 & 22 temperament (or less accurately, the 5 & 17 temperament) in the 2.75.85 subgroup. | By tempering out the comma [[24576/24565]] in the 2.75.85 subgroup, we have three [[85/64]]'s up and one octave down as a [[75/64]] and we have two [[128/85]]'s up and one octave down as a [[17/15]] whole tone. It is because of this combination of accuracy, efficiency and mapping-wise simplicity and its corresponding explanatory power in what this comma does that the comma has been named the ''archagallisma''. The ''MVP'' stands for ''minimum viable product'', as this is the core of what the archagall logic achieves, with further extensions adding to the subgroup while avoiding significantly impacting its accuracy. This is a highly accurate temperament that could be considered to be encoding the "high-accuracy logic" of [[superpyth]] and which is inescapably related to the [[17L 5s]] scale form as it is the 17 & 22 temperament (or less accurately, the 5 & 17 temperament) in the 2.75.85 subgroup. | ||
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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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{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 61, 83, 310, 393, 476, 1345, 1821, 4118*, 5939*, 7760* }} | {{Optimal ET sequence|legend=1| 5, 12, 17, 22, 61, 83, 310, 393, 476, 1345, 1821, 4118*, 5939*, 7760* }} | ||
=== 2.75 | ==== 2.75.9/7.85 subgroup ==== | ||
A fairly natural way to extend archagall is by tempering out [[2025/2023]] ([[S-expression|S15/S17]]), which equates a stack of two [[17/15]]'s with [[9/7]] without much damage. As 9/7 was not previously in the subgroup, this does not decrease the rank of the temperament and qualifies a proper and natural extension. We can equally get the same temperament by tempering out S15/S16 instead (equating a stack of three [[16/15]]'s with [[17/14]]); however, [[16/15]] is not in the subgroup, so it is preferred to think of it as adding 2025/2023. | A fairly natural way to extend archagall is by tempering out [[2025/2023]] ([[S-expression|S15/S17]]), which equates a stack of two [[17/15]]'s with [[9/7]] without much damage. As 9/7 was not previously in the subgroup, this does not decrease the rank of the temperament and qualifies a proper and natural extension. We can equally get the same temperament by tempering out S15/S16 instead (equating a stack of three [[16/15]]'s with [[17/14]]); however, [[16/15]] is not in the subgroup, so it is preferred to think of it as adding 2025/2023. | ||
Subgroup: 2.75 | Subgroup: 2.75.9/7.85 | ||
Comma list: 2025/2023 ({{monzo| 2 -2 0 | Comma list: 2025/2023 ({{monzo| 2 -2 1 0 }}), 24576/24565 ({{monzo| 13 1 0 -3 }}) | ||
{{Mapping|legend= | {{Mapping|legend=2| 1 2 6 5 | 0 3 -4 1 }} | ||
Optimal tunings: | |||
* | * Subgroup WE: ~2 = 1200.0241{{c}}, ~85/64 = 491.3358{{c}} | ||
* | * Subgroup CWE: ~2 = 1200.0000{{c}}, ~85/64 = 491.3290{{c}} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 5, 12, 17, 22, 83, 105, 127, 403, 530, 657, 784, 1441* }} | ||
== 4.3.5 subgroup == | == 4.3.5 subgroup == | ||
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[[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 | ||
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[[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 | ||
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[[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 | ||
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[[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 | ||
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[[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] | ||
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[[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] | ||
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[[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] | ||
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[[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] | ||
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[[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] | ||
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[[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] | ||
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[[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] | ||
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[[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] | ||
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[[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] | ||
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[[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] | ||
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[[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 | ||
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[[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] | ||
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[[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 | ||
| Line 1,366: | Line 1,366: | ||
[[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 | ||
| Line 1,811: | Line 1,811: | ||
[[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 | ||
| Line 1,831: | Line 1,831: | ||
[[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 | ||