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: ''For the 5-limit version of this temperament, see [[High badness temperaments #Emka]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Emka]].''


[[Emka]] tempers out {{monzo| -50 -8 27 }} in the 5-limit. This temperament can be described as 37 & 50 temperament, which tempers out the hemimean and 84035/82944 (quinzo-ayo). Alternative extension [[Horwell temperaments #Emkay|emkay]] (87 & 224) tempers out the same 5-limit comma as the emka, but with the horwell (65625/65536) rather than the hemimean tempered out.
Emka tempers out {{monzo| -50 -8 27 }} in the 5-limit. This temperament can be described as 37 & 50 temperament, which tempers out the hemimean and 84035/82944 (quinzo-ayo). Alternative extension [[Horwell temperaments #Emkay|emkay]] (87 & 224) tempers out the same 5-limit comma as the emka, but with the horwell (65625/65536) rather than the hemimean tempered out.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 511: Line 511:


== Decipentic ==
== Decipentic ==
The generator for the ''decipentic'' temperament (43&amp;56) is tenth root of fifth harmonic ([[5/1]], pentave), 5<sup>1/10</sup>, tuned between [[75/64]] and [[20/17]] (close to 27/23). Aside from the hemimean comma, this temperament tempers out the [[Bronzismic temperaments|bronzisma]], 2097152/2083725 (satriru-agugu). [[99edo|99EDO]] is a good tuning for decipentic, with generator 23\99, and MOS of 9, 13, 17, 30, 43 or 56 notes are available.
The generator for the decipentic temperament (43 &amp; 56) is the tenth root of the [[5/1|5th harmonic (5/1)]], 5<sup>1/10</sup>, tuned between [[75/64]] and [[20/17]] (close to [[27/23]]). Aside from the hemimean comma, this temperament tempers out the [[bronzisma]], 2097152/2083725. [[99edo]] is a good tuning for decipentic, with generator 23\99, and [[mos scale]]s of 9, 13, 17, 30, 43 or 56 notes are available.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125, 2097152/2083725
[[Comma list]]: 3136/3125, 2097152/2083725


[[Mapping]]: [{{val| 1 6 0 -3 }}, {{val| 0 -19 10 25 }}]
{{Mapping|legend=1| 1 6 0 -3 | 0 -19 10 25 }}


{{Multival|legend=1| 19 -10 -25 -60 -93 -30 }}
{{Multival|legend=1| 19 -10 -25 -60 -93 -30 }}


[[POTE generator]]: ~75/64 = 278.800
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~75/64 = 278.800


{{Optimal ET sequence|legend=1| 13, 43, 56, 99 }}
{{Optimal ET sequence|legend=1| 13, 43, 56, 99 }}
Line 532: Line 532:
Comma list: 441/440, 1344/1331, 3136/3125
Comma list: 441/440, 1344/1331, 3136/3125


Mapping: [{{val| 1 6 0 -3 3 }}, {{val| 0 -19 10 25 2 }}]
Mapping: {{mapping| 1 6 0 -3 3 | 0 -19 10 25 2 }}


POTE generator: ~75/64 = 278.799
Optimal tuning (POTE): ~2 = 1\1, ~75/64 = 278.799


{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
Line 545: Line 545:
Comma list: 169/168, 441/440, 832/825, 975/968
Comma list: 169/168, 441/440, 832/825, 975/968


Mapping: [{{val| 1 6 0 -3 3 3 }}, {{val| 0 -19 10 25 2 3 }}]
Mapping: {{mapping| 1 6 0 -3 3 3 | 0 -19 10 25 2 3 }}


POTE generator: ~13/11 = 278.802
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 278.802


{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
Line 558: Line 558:
Comma list: 169/168, 221/220, 256/255, 273/272, 375/374
Comma list: 169/168, 221/220, 256/255, 273/272, 375/374


Mapping: [{{val| 1 6 0 -3 3 3 2 }}, {{val| 0 -19 10 25 2 3 9 }}]
Mapping: {{mapping| 1 6 0 -3 3 3 2 | 0 -19 10 25 2 3 9 }}


POTE generator: ~13/11 = 278.798
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 278.798


{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
Line 571: Line 571:
Comma list: 169/168, 210/209, 221/220, 256/255, 273/272, 286/285
Comma list: 169/168, 210/209, 221/220, 256/255, 273/272, 286/285


Mapping: [{{val| 1 6 0 -3 3 3 2 1 }}, {{val| 0 -19 10 25 2 3 9 14 }}]
Mapping: {{mapping| 1 6 0 -3 3 3 2 1 | 0 -19 10 25 2 3 9 14 }}


POTE generator: ~13/11 = 278.790
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 278.790


{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
{{Optimal ET sequence|legend=1| 13, 43, 56, 99e }}
Line 584: Line 584:
Comma list: 3136/3125, 15488/15435, 16384/16335
Comma list: 3136/3125, 15488/15435, 16384/16335


Mapping: [{{val| 1 6 0 -3 3 }}, {{val| 0 -38 20 50 47 }}]
Mapping: {{mapping| 1 6 0 -3 3 | 0 -38 20 50 47 }}


POTE generator: ~896/825 = 139.403
Optimal tuning (POTE): ~2 = 1\1, ~896/825 = 139.403


{{Optimal ET sequence|legend=1| 43, 112, 155, 198, 439cd, 637cd }}
{{Optimal ET sequence|legend=1| 43, 112, 155, 198, 439cd, 637cd }}
Line 597: Line 597:
Comma list: 676/675, 1001/1000, 3136/3125, 15488/15435
Comma list: 676/675, 1001/1000, 3136/3125, 15488/15435


Mapping: [{{val| 1 6 0 -3 3 8 }}, {{val| 0 -38 20 50 47 -37 }}]
Mapping: {{mapping| 1 6 0 -3 3 8 | 0 -38 20 50 47 -37 }}


POTE generator: ~13/12 = 139.403
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 139.403


{{Optimal ET sequence|legend=1| 43, 155, 198, 439cdf, 637cdf }}
{{Optimal ET sequence|legend=1| 43, 155, 198, 439cdf, 637cdf }}
Line 606: Line 606:


== Sengagen ==
== Sengagen ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125, 420175/419904
[[Comma list]]: 3136/3125, 420175/419904


[[Mapping]]: [{{val| 1 1 2 2 }}, {{val| 0 29 16 40 }}]
{{Mapping|legend=1| 1 1 2 2 | 0 29 16 40 }}


{{Multival|legend=1| 29 16 40 -42 -18 48 }}
{{Multival|legend=1| 29 16 40 -42 -18 48 }}


[[POTE generator]]: ~686/675 = 24.217
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~686/675 = 24.217


{{Optimal ET sequence|legend=1| 49, 50, 99, 248, 347, 446 }}
{{Optimal ET sequence|legend=1| 49, 50, 99, 248, 347, 446 }}
Line 625: Line 625:
Comma list: 540/539, 1344/1331, 3136/3125
Comma list: 540/539, 1344/1331, 3136/3125


Mapping: [{{val| 1 1 2 2 3 }}, {{val| 0 29 16 40 23 }}]
Mapping: {{mapping| 1 1 2 2 3 | 0 29 16 40 23 }}


POTE generator: ~99/98 = 24.235
Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 24.235


{{Optimal ET sequence|legend=1| 49, 50, 99e }}
{{Optimal ET sequence|legend=1| 49, 50, 99e }}
Line 638: Line 638:
Comma list: 351/350, 540/539, 975/968, 1344/1331
Comma list: 351/350, 540/539, 975/968, 1344/1331


Mapping: [{{val| 1 1 2 2 3 4 }}, {{val| 0 29 16 40 23 -15 }}]
Mapping: {{mapping| 1 1 2 2 3 4 | 0 29 16 40 23 -15 }}


POTE generator: ~99/98 = 24.181
Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 24.181


{{Optimal ET sequence|legend=1| 49, 50, 99e, 149e }}
{{Optimal ET sequence|legend=1| 49, 50, 99e, 149e }}
Line 651: Line 651:
Comma list: 144/143, 196/195, 364/363, 625/624
Comma list: 144/143, 196/195, 364/363, 625/624


Mapping: [{{val| 1 1 2 2 3 3 }}, {{val| 0 29 16 40 23 35 }}]
Mapping: {{mapping| 1 1 2 2 3 3 | 0 29 16 40 23 35 }}


POTE generator: ~99/98 = 24.234
Optimal tuning (POTE): ~2 = 1\1, ~99/98 = 24.234


{{Optimal ET sequence|legend=1| 49f, 50, 99ef }}
{{Optimal ET sequence|legend=1| 49f, 50, 99ef }}
Line 662: Line 662:
{{See also| Sensipent family }}
{{See also| Sensipent family }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125, 19683/19600
[[Comma list]]: 3136/3125, 19683/19600


[[Mapping]]: [{{val| 1 6 8 17 }}, {{val| 0 -14 -18 -45 }}]
{{Mapping|legend=1| 1 6 8 17 | 0 -14 -18 -45 }}


{{Multival|legend=1| 14 18 45 -4 32 54 }}
{{Multival|legend=1| 14 18 45 -4 32 54 }}


[[POTE generator]]: ~56/45 = 378.467
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~56/45 = 378.467


{{Optimal ET sequence|legend=1| 19, 111, 130, 929c, 1059c, 1189bc, 1319bc }}
{{Optimal ET sequence|legend=1| 19, 111, 130, 929c, 1059c, 1189bc, 1319bc }}
Line 681: Line 681:
Comma list: 540/539, 3136/3125, 8019/8000
Comma list: 540/539, 3136/3125, 8019/8000


Mapping: [{{val| 1 6 8 17 -6 }}, {{val| 0 -14 -18 -45 30 }}]
Mapping: {{mapping| 1 6 8 17 -6 | 0 -14 -18 -45 30 }}


POTE generator: ~56/45 = 378.440
Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 378.440


{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce, 501cde, 872cde }}
{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce, 501cde, 872cde }}
Line 694: Line 694:
Comma list: 351/350, 540/539, 676/675, 3136/3125
Comma list: 351/350, 540/539, 676/675, 3136/3125


Mapping: [{{val| 1 6 8 17 -6 16 }}, {{val| 0 -14 -18 -45 30 -39 }}]
Mapping: {{mapping| 1 6 8 17 -6 16 | 0 -14 -18 -45 30 -39 }}


POTE generator: ~56/45 = 378.437
Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 378.437


{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce }}
{{Optimal ET sequence|legend=1| 19, 111, 130, 241, 371ce }}
Line 703: Line 703:


== Mowglic ==
== Mowglic ==
The ''mowglic'' temperament (19&amp;161) is an extension of the [[Syntonic-enneadecal equivalence continuum|mowgli temperament]] which tempers out the hemimean comma and the secanticornisma (177147/175000, laruquingu) in the 7-limit.
The mowglic temperament (19 &amp; 161) is an extension of the [[Syntonic-enneadecal equivalence continuum|mowgli temperament]] which tempers out the hemimean comma and the secanticornisma (177147/175000, laruquingu) in the 7-limit.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125, 177147/175000
[[Comma list]]: 3136/3125, 177147/175000


[[Mapping]]: [{{val| 1 0 0 -3 }}, {{val| 0 15 22 55 }}]
{{Mapping|legend=1| 1 0 0 -3 | 0 15 22 55 }}


{{Multival|legend=1| 15 22 55 0 45 66 }}
{{Multival|legend=1| 15 22 55 0 45 66 }}


[[POTE generator]]: ~27/25 = 126.706
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~27/25 = 126.706


{{Optimal ET sequence|legend=1| 19, 123d, 142, 161 }}
{{Optimal ET sequence|legend=1| 19, 123d, 142, 161 }}
Line 724: Line 724:
Comma list: 540/539, 3136/3125, 72171/71680
Comma list: 540/539, 3136/3125, 72171/71680


Mapping: [{{val| 1 0 0 -3 8 }}, {{val| 0 15 22 55 -43 }}]
Mapping: {{mapping| 1 0 0 -3 8 | 0 15 22 55 -43 }}


POTE generator: ~27/25 = 126.711
Optimal tuning (POTE): ~2 = 1\1, ~27/25 = 126.711


{{Optimal ET sequence|legend=1| 19, 123de, 142, 161 }}
{{Optimal ET sequence|legend=1| 19, 123de, 142, 161 }}
Line 737: Line 737:
Comma list: 351/350, 540/539, 1701/1690, 3136/3125
Comma list: 351/350, 540/539, 1701/1690, 3136/3125


Mapping: [{{val| 1 0 0 -3 8 -2 }}, {{val| 0 15 22 55 -43 54 }}]
Mapping: {{mapping| 1 0 0 -3 8 -2 | 0 15 22 55 -43 54 }}


POTE generator: ~14/13 = 126.705
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.705


{{Optimal ET sequence|legend=1| 19, 123def, 142f, 161 }}
{{Optimal ET sequence|legend=1| 19, 123def, 142f, 161 }}
Line 750: Line 750:
Comma list: 351/350, 540/539, 833/832, 1701/1690, 3136/3125
Comma list: 351/350, 540/539, 833/832, 1701/1690, 3136/3125


Mapping: [{{val| 1 0 0 -3 8 -2 10 }}, {{val| 0 15 22 55 -43 54 -56 }}]
Mapping: {{mapping| 1 0 0 -3 8 -2 10 | 0 15 22 55 -43 54 -56 }}


POTE generator: ~14/13 = 126.703
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.703


{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
Line 763: Line 763:
Comma list: 351/350, 476/475, 495/494, 513/512, 540/539, 1701/1690
Comma list: 351/350, 476/475, 495/494, 513/512, 540/539, 1701/1690


Mapping: [{{val| 1 0 0 -3 8 -2 10 9 }}, {{val| 0 15 22 55 -43 54 -56 -45 }}]
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 | 0 15 22 55 -43 54 -56 -45 }}


POTE generator: ~14/13 = 126.705
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.705


{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
Line 776: Line 776:
Comma list: 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539
Comma list: 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539


Mapping: [{{val| 1 0 0 -3 8 -2 10 9 6 }}, {{val| 0 15 22 55 -43 54 -56 -45 -14 }}]
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 6 | 0 15 22 55 -43 54 -56 -45 -14 }}


POTE generator: ~14/13 = 126.703
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.703


{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
Line 789: Line 789:
Comma list: 261/260, 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539
Comma list: 261/260, 276/275, 351/350, 476/475, 495/494, 513/512, 529/528, 540/539


Mapping: [{{val| 1 0 0 -3 8 -2 10 9 6 0 }}, {{val| 0 15 22 55 -43 54 -56 -45 -14 46 }}]
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 6 0 | 0 15 22 55 -43 54 -56 -45 -14 46 }}


POTE generator: ~14/13 = 126.704
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.704


{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
{{Optimal ET sequence|legend=1| 19, 123defg, 142f, 161 }}
Line 802: Line 802:
Comma list: 261/260, 276/275, 351/350, 435/434, 476/475, 495/494, 513/512, 529/528, 540/539
Comma list: 261/260, 276/275, 351/350, 435/434, 476/475, 495/494, 513/512, 529/528, 540/539


Mapping: [{{val| 1 0 0 -3 8 -2 10 9 6 0 2 }}, {{val| 0 15 22 55 -43 54 -56 -45 -14 46 28 }}]
Mapping: {{mapping| 1 0 0 -3 8 -2 10 9 6 0 2 | 0 15 22 55 -43 54 -56 -45 -14 46 28 }}


POTE generator: ~14/13 = 126.703
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 126.703


{{Optimal ET sequence|legend=1| 19, 123defgk, 142fk, 161 }}
{{Optimal ET sequence|legend=1| 19, 123defgk, 142fk, 161 }}
Line 811: Line 811:


== Tremka ==
== Tremka ==
The name "tremka" is initially used for [[No-sevens subgroup temperaments|no-sevens version]] of 50&amp;111 (especially in the 2.3.5.11.13 subgroup), but extending to full 13-limit or higher prime limit does no significant tuning damage, so for that we keep the 2.3.5.11.13 label tremka.
The name ''tremka'' was initially used for [[No-sevens subgroup temperaments|no-sevens version]] of 50 &amp; 111 (especially in the 2.3.5.11.13 subgroup), but extending to full 13-limit or higher prime limit does no significant tuning damage, so for that we keep the 2.3.5.11.13 label tremka.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125, 2125764/2100875
[[Comma list]]: 3136/3125, 2125764/2100875


[[Mapping]]: [{{val|1 -4 -2 -8}}, {{val|0 31 24 60}}]
{{Mapping|legend=1| 1 -4 -2 -8 | 0 31 24 60 }}


{{Multival|legend=1|31 24 60 -34 8 72}}
{{Multival|legend=1| 31 24 60 -34 8 72 }}


[[POTE generator]]: ~4375/3888 = 216.173
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~4375/3888 = 216.173


{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
Line 832: Line 832:
Comma list: 540/539, 3136/3125, 35937/35840
Comma list: 540/539, 3136/3125, 35937/35840


Mapping: [{{val|1 -4 -2 -8 4}}, {{val|0 31 24 60 -3}}]
Mapping: {{mapping| 1 -4 -2 -8 4 | 0 31 24 60 -3 }}


POTE generator: ~112/99 = 216.168
Optimal tuning (POTE): ~2 = 1\1, ~112/99 = 216.168


{{Optimal ET sequence|legend=1| 50, 111, 161, 272, 433c }}
{{Optimal ET sequence|legend=1| 50, 111, 161, 272, 433c }}
Line 845: Line 845:
Comma list: 351/350, 540/539, 847/845, 3136/3125
Comma list: 351/350, 540/539, 847/845, 3136/3125


Mapping: [{{val|1 -4 -2 -8 4 1}}, {{val|0 31 24 60 -3 15}}]
Mapping: {{mapping| 1 -4 -2 -8 4 1 | 0 31 24 60 -3 15 }}


POTE generator: ~112/99 = 216.172
Optimal tuning (POTE): ~2 = 1\1, ~112/99 = 216.172


{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
Line 858: Line 858:
Comma list: 351/350, 540/539, 561/560, 847/845, 1089/1088
Comma list: 351/350, 540/539, 561/560, 847/845, 1089/1088


Mapping: [{{val|1 -4 -2 -8 4 1 -6}}, {{val|0 31 24 60 -3 15 56}}]
Mapping: {{mapping| 1 -4 -2 -8 4 1 -6 | 0 31 24 60 -3 15 56 }}


POTE generator: ~17/15 = 216.172
Optimal tuning (POTE): ~2 = 1\1, ~17/15 = 216.172


{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
{{Optimal ET sequence|legend=1| 50, 111, 161, 272 }}
Line 871: Line 871:
Comma list: 324/323, 351/350, 456/455, 476/455, 495/494, 540/539
Comma list: 324/323, 351/350, 456/455, 476/455, 495/494, 540/539


Mapping: [{{val|1 -4 -2 -8 4 1 -6 -8}}, {{val|0 31 24 60 -3 15 56 68}}]
Mapping: {{mapping| 1 -4 -2 -8 4 1 -6 -8 | 0 31 24 60 -3 15 56 68 }}


POTE generator: ~17/15 = 216.170
Optimal tuning (POTE): ~2 = 1\1, ~17/15 = 216.170


{{Optimal ET sequence|legend=1| 50, 111, 161, 272h, 433cfh, 705ccdffhh }}
{{Optimal ET sequence|legend=1| 50, 111, 161, 272h, 433cfh, 705ccdffhh }}
Line 880: Line 880:


== Undetrita ==
== Undetrita ==
The ''undetrita'' temperament (111&amp;118) tempers out the hemimean comma (3136/3125) and [[skeetsma]] (14348907/14336000) in the 7-limit; 3025/3024, 3388/3375, and 8019/8000 in the 11-limit. This temperament is related to [[11edt|11EDT]] tuning, and the name ''undetrita'' is a play on the words "undecimus" (Latin for "eleventh") and "[[tritave]]" (third harmonic). It is also related to the [[Subgroup temperaments #No-sevens subgroup|twentcufo temperament]], which is no-sevens version of 111&amp;118.
The undetrita temperament (111 &amp; 118) tempers out the hemimean comma (3136/3125) and [[skeetsma]] (14348907/14336000) in the 7-limit; 3025/3024, 3388/3375, and 8019/8000 in the 11-limit. This temperament is related to [[11edt]], and the name ''undetrita'' is a play on the words ''undecimus'' (Latin for "eleventh") and ''[[tritave]]'' (3rd harmonic). It is also related to the [[Subgroup temperaments #No-sevens subgroup|twentcufo temperament]], which is no-sevens version of 111 &amp; 118.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125, 14348907/14336000
[[Comma list]]: 3136/3125, 14348907/14336000


[[Mapping]]: [{{val|1 0 -2 -8}}, {{val|0 11 30 75}}]
{{Mapping|legend=1| 1 0 -2 -8 | 0 11 30 75 }}


{{Multival|legend=1|11 30 75 22 88 90}}
{{Multival|legend=1| 11 30 75 22 88 90 }}


[[POTE generator]]: ~448/405 = 172.917
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~448/405 = 172.917


{{Optimal ET sequence|legend=1| 111, 118, 229, 347, 576c }}
{{Optimal ET sequence|legend=1| 111, 118, 229, 347, 576c }}
Line 901: Line 901:
Comma list: 3025/3024, 3136/3125, 8019/8000
Comma list: 3025/3024, 3136/3125, 8019/8000


Mapping: [{{val|1 0 -2 -8 0}}, {{val|0 11 30 75 24}}]
Mapping: {{mapping| 1 0 -2 -8 0 | 0 11 30 75 24 }}


POTE generator: ~400/363 = 172.912
Optimal tuning (POTE): ~2 = 1\1, ~400/363 = 172.912


{{Optimal ET sequence|legend=1| 111, 118, 229, 347 }}
{{Optimal ET sequence|legend=1| 111, 118, 229, 347 }}
Line 914: Line 914:
Comma list: 352/351, 729/728, 1001/1000, 3025/3024
Comma list: 352/351, 729/728, 1001/1000, 3025/3024


Mapping: [{{val|1 0 -2 -8 0 5}}, {{val|0 11 30 75 24 -9}}]
Mapping: {{mapping| 1 0 -2 -8 0 5 | 0 11 30 75 24 -9 }}


POTE generator: ~72/65 = 172.930
Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 172.930


{{Optimal ET sequence|legend=1| 111, 229f }}
{{Optimal ET sequence|legend=1| 111, 229f }}
Line 927: Line 927:
Comma list: 351/350, 1573/1568, 2080/2079, 3136/3125
Comma list: 351/350, 1573/1568, 2080/2079, 3136/3125


Mapping: [{{val|1 0 -2 -8 0 -11}}, {{val|0 11 30 75 24 102}}]
Mapping: {{mapping| 1 0 -2 -8 0 -11 | 0 11 30 75 24 102 }}


POTE generator: ~400/363 = 172.933
Optimal tuning (POTE): ~2 = 1\1, ~400/363 = 172.933


{{Optimal ET sequence|legend=1| 111, 229 }}
{{Optimal ET sequence|legend=1| 111, 229 }}
Line 977: Line 977:
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Hemimean clan| ]] <!-- main article -->
[[Category:Hemimean clan| ]] <!-- main article -->
[[Category:Hemimean]]
[[Category:Hemimean| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Hemimean_clan"