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Chromatic pairs: Difference between revisions

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Cleanup (8/)
Cleanup (9/)
Line 755: Line 755:
[[Comma list]]: 126/125
[[Comma list]]: 126/125


Mapping: [<1 0 -1|, <0 1 3|]
{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}


Gencom mapping: [<1 -1 0 1|, <0 4/3 1/3 -5/3|]
{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}


[[Gencom|Gencom]]: [2 6/5; 126/125]
: [[gencom]]: [2 6/5; 126/125]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 311.154
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 311.154
Line 780: Line 780:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/11 = 279.318
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/11 = 279.318


Mapping: [<1 1 0|, <0 2 3|]
{{Mapping|legend=2| 1 1 0 | 0 2 3 }}


Gencom mapping: [<1 0 0 0 3 3|, <0 0 0 0 2 3|]
{{Mapping|legend=3| 1 0 0 0 3 3 | 0 0 0 0 2 3 }}


[[Gencom|Gencom]]: [2 13/11; 1352/1331]
: [[gencom]]: [2 13/11; 1352/1331]


{{Optimal ET sequence|legend=1| 13, 30, 43, 73, 116b }}
{{Optimal ET sequence|legend=1| 13, 30, 43, 73, 116b }}
Line 803: Line 803:
[[Comma list]]: 29282/28561
[[Comma list]]: 29282/28561


Mapping: [<4 0 1|, <0 1 1|]
{{Mapping|legend=2| 4 0 1 | 0 1 1 }}


Gencom mapping: [<4 0 0 0 12 13|, <0 0 0 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]
: [[gencom]]: [13/11 11/8; 29282/28561]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 546.660
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 546.660
Line 828: Line 828:
[[Comma list]]: 144/143, 176/175, 196/195
[[Comma list]]: 144/143, 176/175, 196/195


Mapping: [<1 0 2 -2 6|, <0 3 -1 5 -5|]
{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}


Gencom mapping: [<1 -5/4 3 -1/4 7/4 -1/4|, <0 -1/4 -3 3/4 -21/4 19/4|]
{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}


[[Gencom|Gencom]]: [2 7/6; 144/143 176/175 196/195]
: [[gencom]]: [2 7/6; 144/143 176/175 196/195]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300
Line 864: Line 864:
[[Comma list]]: 121/120, 126/125
[[Comma list]]: 121/120, 126/125


Mapping: [<1 1 2 2|, <0 -2 -6 -1|]
{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1}}


Gencom mapping: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|]
{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}


[[Gencom|Gencom]]: [2 11/10; 121/120 126/125]
: [[gencom]]: [2 11/10; 121/120 126/125]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~11/10 = 155.776
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~11/10 = 155.776
Line 892: Line 892:
[[Comma list]]: 121/120, 169/168, 275/273
[[Comma list]]: 121/120, 169/168, 275/273


Mapping: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]
{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}


Gencom mapping: [<1 -3 0 2 0 1|, <0 24/5 -6/5 -26/5 9/5 -1/5|]
{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}


[[Gencom|Gencom]]: [2 13/10; 121/120 169/168 275/273]
: [[gencom]]: [2 13/10; 121/120 169/168 275/273]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 453.242
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 453.242
Line 919: Line 919:
[[Comma list]]: 99/98
[[Comma list]]: 99/98


Mapping: [<1 0 1|, <0 1 2|]
{{Mapping|legend=2| 1 0 1 | 0 1 2 }}


Gencom mapping: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|]
{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}


[[Gencom|Gencom]]: [2 7/6; 99/98]
: [[gencom]]: [2 7/6; 99/98]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 273.174
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 273.174
Line 944: Line 944:
[[Comma list]]: 99/98, 176/175
[[Comma list]]: 99/98, 176/175


Mapping: [<1 0 5 -9|, <0 1 -2 4|]
{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}


Gencom mapping: [<1 4/9 2 -1/9 -1/9|, <0 -4/3 1 -2/3 4/3|]
{{Mapping|legend=3| 1 4/9 2 -1/9 -1/9 | 0 -4/3 1 -2/3 4/3 }}


[[Gencom|Gencom]]: [2 5/4; 99/98 176/175]
: [[gencom]]: [2 5/4; 99/98 176/175]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~5/4 = 386.558
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~5/4 = 386.558
Line 969: Line 969:
[[Comma list]]: 99/98, 243/242
[[Comma list]]: 99/98, 243/242


Mapping: [<1 3 6 7|, <0 -4 -9 -10|]
{{Mapping|legend=2| 1 3 6 7 | 0 -4 -9 -10 }}


Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10|]
{{Mapping|legend=3| 1 3 0 6 7 | 0 -4 0 -9 -10 }}


[[Gencom|Gencom]]: [2 9/7; 99/98 243/242]
: [[gencom]]: [2 9/7; 99/98 243/242]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.244
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.244
Line 1,049: Line 1,049:
[[Comma list]]: 100/99, 245/242
[[Comma list]]: 100/99, 245/242


Mapping: [<1 1 1 0|, <0 -2 3 4|]
{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}


Gencom mapping: [<1 1/10 -4/5 11/10 1/5|, <0 -3/2 -1 3/2 1|]
{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}


[[Gencom|Gencom]]: [2 21/20; 100/99 245/242]
: [[gencom]]: [2 21/20; 100/99 245/242]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892
Line 1,070: Line 1,070:
[[Comma list]]: 343/338, 847/832
[[Comma list]]: 343/338, 847/832


Mapping: [<1 1 3 1|, <0 4 1 6|]
{{Mapping|legend=2| 1 1 3 1 | 0 4 1 6 }}


Gencom mapping: [<1 0 0 1 3 1|, <0 0 0 4 1 6|]
{{Mapping|legend=3| 1 0 0 1 3 1| 0 0 0 4 1 6 }}


[[Gencom|Gencom]]: [2 11/8; 343/338 847/832]
: [[gencom]]: [2 11/8; 343/338 847/832]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 540.099
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 540.099
Line 1,150: Line 1,150:
[[Comma list]]: 99/98, 9317/9216
[[Comma list]]: 99/98, 9317/9216


Mapping: [<1 0 1 3|, <0 7 4 1|]
{{Mapping|legend=2| 1 0 1 3 | 0 7 4 1 }}


Gencom mapping: [<1 0 0 1 3|, <0 7/2 0 4 1|]
{{Mapping|legend=3| 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]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents
Line 1,189: Line 1,189:
[[Comma list]]: 100/99, 105/104, 144/143, 196/195
[[Comma list]]: 100/99, 105/104, 144/143, 196/195


Mapping: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]
{{Mapping|legend=2| 1 0 2 -1 6 -2 | 0 5 3 6 -4 9 }}


Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|]
{{Mapping|legend=3| 1 5/2 5/2 5 2 7 | 0 -5/2 -1/2 -6 4 -9 }}


[[Gencom|Gencom]]: [2 9/7; 100/99 105/104 144/143 196/195]
: [[gencom]]: [2 9/7; 100/99 105/104 144/143 196/195]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~9/7 = 439.146
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~9/7 = 439.146
Line 1,216: Line 1,216:
[[Comma list]]: 78/77, 99/98, 144/143
[[Comma list]]: 78/77, 99/98, 144/143


Mapping: [<1 1 2 3 3|, <0 5 7 4 6|]
{{Mapping|legend=2| 1 1 2 3 3 | 0 5 7 4 6 }}


Gencom mapping: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]
{{Mapping|legend=3| 1 1 0 2 3 3 | 0 5 0 7 4 6 }}


[[Gencom|Gencom]]: [2 13/12; 78/77 99/98 144/143]
: [[gencom]]: [2 13/12; 78/77 99/98 144/143]


[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990
[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990


EDOs: [[17edo|17]], [[43edo|43]], [[60edo|60c]]
{{Optimal ET sequence|legend=1| 17, 43, 60c }}


[[Tp tuning #T2 tuning|RMS error]]: 1.752 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.752 cents
Line 1,245: Line 1,245:
[[Comma list]]: 65/64, 170/169, 221/220
[[Comma list]]: 65/64, 170/169, 221/220


Mapping: [<1 0 15 6 11|, <0 1 -5 -1 -3|]
{{Mapping|legend=2| 1 0 15 6 11 | 0 1 -5 -1 -3 }}


Gencom mapping: [<1 0 2 0 5 4 5|, <0 0 1 0 -5 -1 -3|]
{{Mapping|legend=3| 1 0 2 0 5 4 5 | 0 0 1 0 -5 -1 -3 }}


[[Gencom|Gencom]]: [2 5/4; 65/64 170/169 221/220]
: [[gencom]]: [2 5/4; 65/64 170/169 221/220]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 372.236
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 372.236
Line 1,301: Line 1,301:
[[Comma list]]: 64/63, 99/98
[[Comma list]]: 64/63, 99/98


Mapping: [<1 0 6 13|, <0 1 -1 -3|]
{{Mapping|legend=2| 1 0 6 13 | 0 1 -1 -3 }}


Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]
{{Mapping|legend=3| 1 3/2 0 3 4 | 0 1/2 0 -1 -3 }}


[[Gencom|Gencom]]: [2 9/8; 64/63 99/98]
: [[gencom]]: [2 9/8; 64/63 99/98]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 214.384
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 214.384
Line 1,328: Line 1,328:
[[Comma list]]: 65/64, 81/80, 91/90
[[Comma list]]: 65/64, 81/80, 91/90


Mapping: [<1 0 -4 -13 10|, <0 1 2 5 -2|]
{{Mapping|legend=2| 1 0 -4 -13 10 | 0 1 2 5 -2 }}


Gencom mapping: [<1 3/2 2 2 0 4|, <0 1/2 2 5 0 -2|]
{{Mapping|legend=3| 1 3/2 2 2 0 4 | 0 1/2 2 5 0 -2 }}


[[Gencom|Gencom]]: [2 9/8; 65/64 81/80 91/90]
: [[gencom]]: [2 9/8; 65/64 81/80 91/90]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 191.059
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 191.059
Line 1,368: Line 1,368:
[[Comma list]]: 56/55, 91/90, 100/99
[[Comma list]]: 56/55, 91/90, 100/99


Mapping: [<1 0 -1 2 2|, <0 1 3 2 -2|]
{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}


Gencom mapping: [<1 -3/7 4/7 11/7 4 -6/7|, <0 0 -1 -3 -2 2|]
{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}


[[Gencom|Gencom]]: [2 6/5; 56/55 91/90 100/99]
: [[gencom]]: [2 6/5; 56/55 91/90 100/99]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 313.842
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 313.842
Line 1,393: Line 1,393:
[[Comma list]]: 56/55, 128/125
[[Comma list]]: 56/55, 128/125


Mapping: [<3 7 0 2|, <0 0 1 1|]
{{Mapping|legend=2| 3 7 0 2 | 0 0 1 1 }}


Gencom mapping: [<3 0 7 9 11|, <0 0 0 -1 -1|]
{{Mapping|legend=3| 3 0 7 9 11| 0 0 0 -1 -1 }}


[[Gencom|Gencom]]: [5/4 8/7; 56/55 128/125]
: [[gencom]]: [5/4 8/7; 56/55 128/125]


[[Optimal tuning]] ([[POTE]]): ~5/4 = 1\3, ~8/7 = 228.275
[[Optimal tuning]] ([[POTE]]): ~5/4 = 1\3, ~8/7 = 228.275
Line 1,431: Line 1,431:
[[Comma list]]: 56/55, 78/77, 91/90
[[Comma list]]: 56/55, 78/77, 91/90


Mapping: [<1 2 1 2 2|, <0 -3 -2 1 -1|]
{{Mapping|legend=2| 1 2 1 2 2 | 0 -3 -2 1 -1 }}


Gencom mapping: [<1 -5/4 2 -1/4 3/4 3/4|, <0 -1/2 3 3/2 -3/2 1/2|]
{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}


[[Gencom|Gencom]]: [2 13/12; 56/55 78/77 91/90]
: [[gencom]]: [2 13/12; 56/55 78/77 91/90]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/12 = 132.428
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/12 = 132.428
Line 1,454: Line 1,454:
[[Comma list]]: 55/54, 64/63, 100/99
[[Comma list]]: 55/54, 64/63, 100/99


Mapping: [<1 1 1 5 2|, <0 3 4 -3 2|]
{{Mapping|legend=2| 1 1 1 5 2 | 0 3 4 -3 2 }}


Gencom mapping: [<1 2 3 2 4|, <0 -3/2 -5/2 3 -2|]
{{Mapping|legend=3| 1 2 3 2 4 | 0 -3/2 -5/2 3 -2 }}


[[Gencom|Gencom]]: [2 6/5; 55/54 64/63 100/99]
: [[gencom]]: [2 6/5; 55/54 64/63 100/99]


[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495
Line 1,479: Line 1,479:
[[Comma list]]: 50/49, 64/63
[[Comma list]]: 50/49, 64/63


Mapping: [<2 0 11 12|, <0 1 -1 -1|]
{{Mapping|legend=2| 2 0 11 12 | 0 1 -1 -1 }}


Gencom mapping: [<2 3 5 6|, <0 1/2 -1 -1|]
{{Mapping|legend=3| 2 3 5 6 | 0 1/2 -1 -1 }}


[[Gencom|Gencom]]: [7/5 8/7; 50/49 64/63]
: [[gencom]]: [7/5 8/7; 50/49 64/63]


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 214.095
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 214.095
Line 1,504: Line 1,504:
[[Comma list]]: 45/44, 65/64, 81/80
[[Comma list]]: 45/44, 65/64, 81/80


Mapping: [<1 0 -4 -6 10|, <0 1 2 3 -2|]
{{Mapping|legend=2| 1 0 -4 -6 10 | 0 1 2 3 -2 }}


Gencom mapping: [<1 3/2 2 0 3 4|, <0 1/2 2 0 3 -2|]
{{Mapping|legend=3| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }}


[[Gencom|Gencom]]: [2 9/8; 45/44 65/64 81/80]
: [[gencom]]: [2 9/8; 45/44 65/64 81/80]


[[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151
[[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151
Line 1,529: Line 1,529:
[[Comma list]]: 45/44, 56/55, 81/80
[[Comma list]]: 45/44, 56/55, 81/80


Mapping: [<1 0 -4 -13 -6|, <0 1 2 5 3|]
{{Mapping|legend=2| 1 0 -4 -13 -6 | 0 1 2 5 3 }}


Gencom mapping: [<1 3/2 2 2 3|, <0 1/2 2 5 3|]
{{Mapping|legend=3| 1 3/2 2 2 3 | 0 1/2 2 5 3 }}


[[Gencom|Gencom]]: [2 9/8; 45/44 56/55 81/80]
: [[gencom]]: [2 9/8; 45/44 56/55 81/80]


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 192.500
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 192.500
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