Chromatic pairs: Difference between revisions
Cleanup (7/) |
Cleanup (8/) |
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[[Comma list]]: 126/125 | [[Comma list]]: 126/125 | ||
[ | Mapping: [<1 0 -1|, <0 1 3|] | ||
Gencom mapping: [<1 -1 0 1|, <0 4/3 1/3 -5/3|] | |||
[[Gencom|Gencom]]: [2 6/5; 126/125] | [[Gencom|Gencom]]: [2 6/5; 126/125] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 311.154 | |||
{{Optimal ET sequence|legend=1| 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b }} | {{Optimal ET sequence|legend=1| 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b }} | ||
| 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|] | ||
Gencom mapping: [<1 0 0 0 3 3|, <0 0 0 0 2 3|] | Gencom mapping: [<1 0 0 0 3 3|, <0 0 0 0 2 3|] | ||
[[Gencom|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|] | ||
Gencom mapping: [<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 ET sequence|legend=1| 4, 16, 20, 24, 44, 68, 112c, 180bc }} | {{Optimal ET sequence|legend=1| 4, 16, 20, 24, 44, 68, 112c, 180bc }} | ||
| 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|] | ||
Gencom mapping: [<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|Gencom]]: [2 7/6; 144/143 176/175 196/195] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300 | |||
{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 58, 156bde, 205bde }} | {{Optimal ET sequence|legend=1| 9, 31, 40, 49, 58, 156bde, 205bde }} | ||
| 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|] | ||
Gencom mapping: <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|Gencom]]: [2 11/10; 121/120 126/125] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~11/10 = 155.776 | |||
{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131d, 208bd }} | {{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131d, 208bd }} | ||
| 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|] | ||
Gencom mapping: [<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|Gencom]]: [2 13/10; 121/120 169/168 275/273] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 453.242 | |||
{{Optimal ET sequence|legend=1| 5, 8, 13, 21, 29, 37, 44, 45, 188bde }} | {{Optimal ET sequence|legend=1| 5, 8, 13, 21, 29, 37, 44, 45, 188bde }} | ||
| Line 919: | Line 919: | ||
[[Comma list]]: 99/98 | [[Comma list]]: 99/98 | ||
[ | Mapping: [<1 0 1|, <0 1 2|] | ||
Gencom mapping: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|] | |||
[[Gencom|Gencom]]: [2 7/6; 99/98] | [[Gencom|Gencom]]: [2 7/6; 99/98] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 273.174 | |||
{{Optimal ET sequence|legend=1| 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc }} | {{Optimal ET sequence|legend=1| 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc }} | ||
| 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|] | ||
Gencom mapping: [<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|Gencom]]: [2 5/4; 99/98 176/175] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~5/4 = 386.558 | |||
{{Optimal ET sequence|legend=1| 22, 25, 28, 31, 59, 90c, 149c }} | {{Optimal ET sequence|legend=1| 22, 25, 28, 31, 59, 90c, 149c }} | ||
| 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|] | ||
Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10|] | |||
[[Gencom|Gencom]]: [2 9/7; 99/98 243/242] | [[Gencom|Gencom]]: [2 9/7; 99/98 243/242] | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.244 | |||
{{Optimal ET sequence|legend=1| 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd }} | {{Optimal ET sequence|legend=1| 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd }} | ||
| 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|] | ||
Gencom mapping: [<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|Gencom]]: [2 21/20; 100/99 245/242] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892 | |||
{{Optimal ET sequence|legend=1| 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd }} | {{Optimal ET sequence|legend=1| 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd }} | ||
| 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|] | ||
Gencom mapping: [<1 0 0 1 3 1|, <0 0 0 4 1 6|] | |||
[[Gencom|Gencom]]: [2 11/8; 343/338 847/832] | [[Gencom|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 }} | {{Optimal ET sequence|legend=1| 5, 7, 9, 11, 20 }} | ||
| 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|] | ||
Gencom mapping: [<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 ET sequence|legend=1| 11, 20, 31, 42, 115bd, 157bd }} | {{Optimal ET sequence|legend=1| 11, 20, 31, 42, 115bd, 157bd }} | ||
| 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|] | ||
Gencom mapping: [<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|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 ET sequence|legend=1| 11, 30, 41, 153cdef, 194cdef, 235cdef }} | {{Optimal ET sequence|legend=1| 11, 30, 41, 153cdef, 194cdef, 235cdef }} | ||
| 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|] | ||
Gencom mapping: [<1 1 0 2 3 3|, <0 5 0 7 4 6|] | |||
[[Gencom|Gencom]]: [2 13/12; 78/77 99/98 144/143] | [[Gencom|Gencom]]: [2 13/12; 78/77 99/98 144/143] | ||
[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990 | |||
EDOs: [[17edo|17]], [[43edo|43]], [[60edo|60c]] | EDOs: [[17edo|17]], [[43edo|43]], [[60edo|60c]] | ||
| 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|] | ||
Gencom mapping: [<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|Gencom]]: [2 5/4; 65/64 170/169 221/220] | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 372.236 | |||
{{Optimal ET sequence|legend=1| 10, 13, 16, 29 }} | {{Optimal ET sequence|legend=1| 10, 13, 16, 29 }} | ||
| 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|] | ||
Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|] | |||
[[Gencom|Gencom]]: [2 9/8; 64/63 99/98] | [[Gencom|Gencom]]: [2 9/8; 64/63 99/98] | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 214.384 | |||
{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }} | {{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }} | ||
| 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|] | ||
Gencom mapping: [<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|Gencom]]: [2 9/8; 65/64 81/80 91/90] | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 191.059 | |||
{{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25e, 44de }} | {{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25e, 44de }} | ||
| 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|] | ||
Gencom mapping: [<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|Gencom]]: [2 6/5; 56/55 91/90 100/99] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 313.842 | |||
{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }} | {{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }} | ||
| 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|] | ||
Gencom mapping: [<3 0 7 9 11|, <0 0 0 -1 -1|] | |||
[[Gencom|Gencom]]: [5/4 8/7; 56/55 128/125] | [[Gencom|Gencom]]: [5/4 8/7; 56/55 128/125] | ||
[[Optimal tuning]] ([[POTE]]): ~5/4 = 1\3, ~8/7 = 228.275 | |||
{{Optimal ET sequence|legend=1| 3, 6, 9, 15, 21 }} | {{Optimal ET sequence|legend=1| 3, 6, 9, 15, 21 }} | ||
| 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|] | ||
Gencom mapping: [<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|Gencom]]: [2 13/12; 56/55 78/77 91/90] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/12 = 132.428 | |||
{{Optimal ET sequence|legend=1| 9, 63, 82bd, 91bde }} | {{Optimal ET sequence|legend=1| 9, 63, 82bd, 91bde }} | ||
| 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|] | ||
Gencom mapping: [<1 2 3 2 4|, <0 -3/2 -5/2 3 -2|] | |||
[[Gencom|Gencom]]: [2 6/5; 55/54 64/63 100/99] | [[Gencom|Gencom]]: [2 6/5; 55/54 64/63 100/99] | ||
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495 | |||
{{Optimal ET sequence|legend=1| 7, 11, 37b, 48b, 59b }} | {{Optimal ET sequence|legend=1| 7, 11, 37b, 48b, 59b }} | ||
| 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|] | ||
Gencom mapping: [<2 3 5 6|, <0 1/2 -1 -1|] | |||
[[Gencom|Gencom]]: [7/5 8/7; 50/49 64/63] | [[Gencom|Gencom]]: [7/5 8/7; 50/49 64/63] | ||
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 214.095 | |||
{{Optimal ET sequence|legend=1| 4, 6, 10, 16, 22, 28 }} | {{Optimal ET sequence|legend=1| 4, 6, 10, 16, 22, 28 }} | ||
| 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|] | ||
Gencom mapping: [<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|Gencom]]: [2 9/8; 45/44 65/64 81/80] | ||
[[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151 | |||
{{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }} | {{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }} | ||
| 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|] | ||
Gencom mapping: [<1 3/2 2 2 3|, <0 1/2 2 5 3|] | |||
[[Gencom|Gencom]]: [2 9/8; 45/44 56/55 81/80] | [[Gencom|Gencom]]: [2 9/8; 45/44 56/55 81/80] | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 192.500 | |||
{{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25, 31, 56, 81 }} | {{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25, 31, 56, 81 }} | ||
| Line 1,543: | Line 1,543: | ||
[[File:leantone_81edo.png|alt=leantone_81edo.png|leantone_81edo.png]] | [[File:leantone_81edo.png|alt=leantone_81edo.png|leantone_81edo.png]] | ||
Scales: | |||
* [[leantone6|Six note haplotonic scale]] | * [[leantone6|Six note haplotonic scale]] | ||
* [[leantone7|Seven note albitonic scale]] | * [[leantone7|Seven note albitonic scale]] | ||