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Schismatic family: Difference between revisions

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Comma list: 1375/1372, 4375/4356, 32805/32768
Comma list: 1375/1372, 4375/4356, 32805/32768


Mapping: [{{val|1 2 -1 -4 -7}}, {{val|0 -5 40 82 126}}]
Mapping: [{{val| 1 2 -1 -4 -7 }}, {{val| 0 -5 40 82 126 }}]


Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.616
Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.616
Line 1,663: Line 1,663:
Comma list: 1375/1372, 2080/2079, 4375/4356, 10648/10647
Comma list: 1375/1372, 2080/2079, 4375/4356, 10648/10647


Mapping: [{{val|1 2 -1 -4 -7 -9}}, {{val|0 -5 40 82 126 153}}]
Mapping: [{{val| 1 2 -1 -4 -7 -9 }}, {{val| 0 -5 40 82 126 153 }}]


Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.612
Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.612
Line 1,698: Line 1,698:


== Quintaschis ==
== Quintaschis ==
The ''quintaschis'' temperament (12&289) slices the fourth (4/3) into five semitones and tempers out 49009212/48828125 (quinzo-alegu) in the 7-limit.
The ''quintaschis'' temperament (12 & 289) slices the fourth (4/3) into five semitones and tempers out 49009212/48828125 in the 7-limit.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 32805/32768, 49009212/48828125
[[Comma list]]: 32805/32768, 49009212/48828125
Line 1,708: Line 1,708:
{{Multival|legend=1| 5 -40 -94 -75 -163 -106 }}
{{Multival|legend=1| 5 -40 -94 -75 -163 -106 }}


[[POTE generator]]: ~200/189 = 99.664
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~200/189 = 99.664


{{Val list|legend=1| 12, …, 289, 301, 590, 891, 1192 }}
{{Val list|legend=1| 12, …, 289, 301, 590, 891, 1192 }}
Line 1,721: Line 1,721:
Mapping: [{{val| 1 2 -1 -5 -8 }}, {{val| 0 -5 40 94 138 }}]
Mapping: [{{val| 1 2 -1 -5 -8 }}, {{val| 0 -5 40 94 138 }}]


POTE generator: ~35/33 = 99.653
Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.653


Optimal GPV sequence: {{Val list| 12, …, 277d, 289 }}
Optimal GPV sequence: {{Val list| 12, …, 277d, 289 }}
Line 1,734: Line 1,734:
Mapping: [{{val| 1 2 -1 -5 -8 -11 }}, {{val| 0 -5 40 94 138 177 }}]
Mapping: [{{val| 1 2 -1 -5 -8 -11 }}, {{val| 0 -5 40 94 138 177 }}]


POTE generator: ~35/33 = 99.658
Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 99.658


Optimal GPV sequence: {{Val list| 12f, …, 277dff, 289 }}
Optimal GPV sequence: {{Val list| 12f, …, 277dff, 289 }}
Line 1,747: Line 1,747:
Mapping: [{{val| 1 2 -1 -5 -8 -11 5 }}, {{val| 0 -5 40 94 138 177 -11 }}]
Mapping: [{{val| 1 2 -1 -5 -8 -11 5 }}, {{val| 0 -5 40 94 138 177 -11 }}]


POTE generator: ~18/17 = 99.656
Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.656


Optimal GPV sequence: {{Val list| 12f, 277dff, 289 }}
Optimal GPV sequence: {{Val list| 12f, 277dff, 289 }}
Line 1,760: Line 1,760:
Mapping: [{{val| 1 2 -1 -5 -8 -11 5 4 }}, {{val| 0 -5 40 94 138 177 -11 3 }}]
Mapping: [{{val| 1 2 -1 -5 -8 -11 5 4 }}, {{val| 0 -5 40 94 138 177 -11 3 }}]


POTE generator: ~18/17 = 99.659
Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.659


Optimal GPV sequence: {{Val list| 12f, 289 }}
Optimal GPV sequence: {{Val list| 12f, 289 }}
Line 1,773: Line 1,773:
Mapping: [{{val| 1 2 -1 -5 -9 }}, {{val| 0 -5 40 94 150 }}]
Mapping: [{{val| 1 2 -1 -5 -9 }}, {{val| 0 -5 40 94 150 }}]


POTE generator: ~200/189 = 99.671
Optimal tuning (POTE): ~2 = 1\1, ~200/189 = 99.671


Optimal GPV sequence: {{Val list| 12, …, 289e, 301, 915 }}
Optimal GPV sequence: {{Val list| 12, …, 289e, 301, 915 }}
Line 1,786: Line 1,786:
Mapping: [{{val| 1 2 -1 -5 -9 -11 }}, {{val| 0 -5 40 94 150 177 }}]
Mapping: [{{val| 1 2 -1 -5 -9 -11 }}, {{val| 0 -5 40 94 150 177 }}]


POTE generator: ~200/189 = 99.661
Optimal tuning (POTE): ~2 = 1\1, ~200/189 = 99.661


Optimal GPV sequence: {{Val list| 12f, …, 289e, 301 }}
Optimal GPV sequence: {{Val list| 12f, …, 289e, 301 }}
Line 1,799: Line 1,799:
Mapping: [{{val| 1 2 -1 -5 -9 -11 5 }}, {{val| 0 -5 40 94 150 177 -11 }}]
Mapping: [{{val| 1 2 -1 -5 -9 -11 5 }}, {{val| 0 -5 40 94 150 177 -11 }}]


POTE generator: ~18/17 = 99.665
Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.665


Optimal GPV sequence: {{Val list| 12f, 289e, 301 }}
Optimal GPV sequence: {{Val list| 12f, 289e, 301 }}
Line 1,812: Line 1,812:
Mapping: [{{val| 1 2 -1 -5 -9 -11 5 4 }}, {{val| 0 -5 40 94 150 177 -11 3 }}]
Mapping: [{{val| 1 2 -1 -5 -9 -11 5 4 }}, {{val| 0 -5 40 94 150 177 -11 3 }}]


POTE generator: ~18/17 = 99.668
Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.668


Optimal GPV sequence: {{Val list| 12f, 301 }}
Optimal GPV sequence: {{Val list| 12f, 301 }}
Line 1,825: Line 1,825:
Mapping: [{{val| 1 2 -1 -5 -9 14 }}, {{val| 0 -5 40 94 150 -124 }}]
Mapping: [{{val| 1 2 -1 -5 -9 14 }}, {{val| 0 -5 40 94 150 -124 }}]


POTE generator: ~200/189 = 99.672
Optimal tuning (POTE): ~2 = 1\1, ~200/189 = 99.672


Optimal GPV sequence: {{Val list| 12, 301, 614, 915 }}
Optimal GPV sequence: {{Val list| 12, 301, 614, 915 }}
Line 1,838: Line 1,838:
Mapping: [{{val| 1 2 -1 -5 -9 14 5 }}, {{val| 0 -5 40 94 150 -124 -11 }}]
Mapping: [{{val| 1 2 -1 -5 -9 14 5 }}, {{val| 0 -5 40 94 150 -124 -11 }}]


POTE generator: ~18/17 = 99.671
Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.671


Optimal GPV sequence: {{Val list| 12, 301 }}
Optimal GPV sequence: {{Val list| 12, 301 }}
Line 1,851: Line 1,851:
Mapping: [{{val| 1 2 -1 -5 -9 14 5 4 }}, {{val| 0 -5 40 94 150 -124 -11 3 }}]
Mapping: [{{val| 1 2 -1 -5 -9 14 5 4 }}, {{val| 0 -5 40 94 150 -124 -11 3 }}]


POTE generator: ~18/17 = 99.672
Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 99.672


Optimal GPV sequence: {{Val list| 12, 301 }}
Optimal GPV sequence: {{Val list| 12, 301 }}
Line 1,858: Line 1,858:


== Sextilififths ==
== Sextilififths ==
The sextilififths (130&159, also known as ''sextilischis'') slices the fourth (4/3) into six small semitones, which serves as both 21/20 and 22/21.
The sextilififths (130 & 159, also known as ''sextilischis'') slices the fourth (4/3) into six small semitones, which serves as both 21/20 and 22/21.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 32768/32805, 235298/234375
[[Comma list]]: 32768/32805, 235298/234375
Line 1,870: Line 1,870:
{{Multival|legend=1| 6 -48 -55 -90 -104 7 }}
{{Multival|legend=1| 6 -48 -55 -90 -104 7 }}


[[POTE generator]]: ~21/20 = 83.053
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 83.053


{{Val list|legend=1| 29, 72cd, 101, 130, 289, 419 }}
{{Val list|legend=1| 29, 72cd, 101, 130, 289, 419 }}
Line 1,883: Line 1,883:
Mapping: [{{val| 1 2 -1 -1 0 }}, {{val| 0 -6 48 55 50 }}]
Mapping: [{{val| 1 2 -1 -1 0 }}, {{val| 0 -6 48 55 50 }}]


POTE generator: ~21/20 = 83.049
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.049


Optimal GPV sequence: {{Val list| 29, 72cde, 101e, 130, 289 }}
Optimal GPV sequence: {{Val list| 29, 72cde, 101e, 130, 289 }}
Line 1,896: Line 1,896:
Mapping: [{{val| 1 2 -1 -1 0 1 }}, {{val| 0 -6 48 55 50 39 }}]
Mapping: [{{val| 1 2 -1 -1 0 1 }}, {{val| 0 -6 48 55 50 39 }}]


POTE generator: ~21/20 = 83.049
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.049


Optimal GPV sequence: {{Val list| 29, 72cdef, 101e, 130, 289 }}
Optimal GPV sequence: {{Val list| 29, 72cdef, 101e, 130, 289 }}
Line 1,903: Line 1,903:


== Septiquarschis ==
== Septiquarschis ==
The ''septiquarschis'' temperament (89&94) splits septimal minor seventh ([[7/4]]) into four generators and tempers out 829440/823543 (''mynaslender'' comma, sepru-ayo) and 67108864/66706983 (''[[Septiness clan|septiness]]'' comma, sasasepru).
The ''septiquarschis'' temperament (89 & 94) splits septimal minor seventh ([[7/4]]) into four generators and tempers out 829440/823543 (mynaslender comma) and 67108864/66706983 (septiness comma).


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 32805/32768, 829440/823543
[[Comma list]]: 32805/32768, 829440/823543
Line 1,913: Line 1,913:
{{Multival|legend=1| 7 56 -4 231 -26 -76 }}
{{Multival|legend=1| 7 56 -4 231 -26 -76 }}


[[POTE generator]]: ~147/128 = 242.614
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~147/128 = 242.614


{{Val list|legend=1| 89, 94, 183, 460d, 643d, 1103dd }}
{{Val list|legend=1| 89, 94, 183, 460d, 643d, 1103dd }}
Line 1,926: Line 1,926:
Mapping: [{{val| 1 3 -9 2 -2 }}, {{val| 0 -7 -56 4 27 }}]
Mapping: [{{val| 1 3 -9 2 -2 }}, {{val| 0 -7 -56 4 27 }}]


POTE generator: ~147/128 = 242.616
Optimal tuning (POTE): ~2 = 1\1, ~147/128 = 242.616


Optimal GPV sequence: {{Val list| 89, 94, 183, 460d, 643d, 826dd }}
Optimal GPV sequence: {{Val list| 89, 94, 183, 460d, 643d, 826dd }}
Line 1,939: Line 1,939:
Mapping: [{{val| 1 3 -9 2 -2 13 }}, {{val| 0 -7 -56 4 27 -46 }}]
Mapping: [{{val| 1 3 -9 2 -2 13 }}, {{val| 0 -7 -56 4 27 -46 }}]


POTE generator: ~147/128 = 242.610
Optimal tuning (POTE): ~2 = 1\1, ~147/128 = 242.610


Optimal GPV sequence: {{Val list| 89, 94, 183, 277, 460d }}
Optimal GPV sequence: {{Val list| 89, 94, 183, 277, 460d }}
Line 1,946: Line 1,946:


== Tsaharuk ==
== Tsaharuk ==
{{See also|Tsaharuk}}
{{Main| Tsaharuk }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 32805/32768, 420175/419904
[[Comma list]]: 32805/32768, 420175/419904
Line 1,958: Line 1,958:
{{Multival|legend=1| 5 -40 24 -75 24 168 }}
{{Multival|legend=1| 5 -40 24 -75 24 168 }}


[[POTE generator]]: ~243/224 = 140.350
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/224 = 140.350


{{Val list|legend=1| 17, 60c, 77, 94, 171 }}
{{Val list|legend=1| 17, 60c, 77, 94, 171 }}
Line 1,971: Line 1,971:
Mapping: [{{val| 1 1 7 0 1 }}, {{val| 0 5 -40 24 21 }}]
Mapping: [{{val| 1 1 7 0 1 }}, {{val| 0 5 -40 24 21 }}]


POTE generator: ~88/81 = 140.365
Optimal tuning (POTE): ~2 = 1\1, ~88/81 = 140.365


Optimal GPV sequence: {{Val list| 17, 60ce, 77, 94, 171e, 265e, 436ee }}
Optimal GPV sequence: {{Val list| 17, 60ce, 77, 94, 171e, 265e, 436ee }}
Line 1,984: Line 1,984:
Mapping: [{{val| 1 1 7 0 1 3 }}, {{val| 0 5 -40 24 21 6 }}]
Mapping: [{{val| 1 1 7 0 1 3 }}, {{val| 0 5 -40 24 21 6 }}]


POTE generator: ~13/12 = 140.363
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.363


Optimal GPV sequence: {{Val list| 17, 60ce, 77, 94, 171e, 436ee }}
Optimal GPV sequence: {{Val list| 17, 60ce, 77, 94, 171e, 436ee }}
Line 1,991: Line 1,991:


== Quanharuk ==
== Quanharuk ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16875/16807, 32805/32768
[[Comma list]]: 16875/16807, 32805/32768
Line 2,001: Line 2,001:
{{Multival|legend=1| 5 -40 -29 -75 -60 45 }}
{{Multival|legend=1| 5 -40 -29 -75 -60 45 }}


[[POTE generator]]: ~56/45 = 380.355
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~56/45 = 380.355


{{Val list|legend=1| 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd }}
{{Val list|legend=1| 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd }}
Line 2,016: Line 2,016:
Mapping generators: ~2, ~56/45
Mapping generators: ~2, ~56/45


POTE generator: ~56/45 = 380.352
Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 380.352


Optimal GPV sequence: {{Val list| 41, 142, 183, 224, 631d, 855d, 1079d }}
Optimal GPV sequence: {{Val list| 41, 142, 183, 224, 631d, 855d, 1079d }}
Line 2,031: Line 2,031:
Mapping generators: ~2, ~56/45
Mapping generators: ~2, ~56/45


POTE generator: ~56/45 = 380.351
Optimal tuning (POTE): ~2 = 1\1, ~56/45 = 380.351


Optimal GPV sequence: {{Val list| 41, 142, 183, 224, 631d, 855d }}
Optimal GPV sequence: {{Val list| 41, 142, 183, 224, 631d, 855d }}
Line 2,038: Line 2,038:


== Quadrant ==
== Quadrant ==
The ''quadrant'' temperament (12&224) has a period of quarter octave and tempers out the [[dimcomp comma]], 390625/388962. In this temperament, 25/21 is mapped into quarter octave.
The ''quadrant'' temperament (12 & 224) has a period of quarter octave and tempers out the [[dimcomp comma]], 390625/388962. In this temperament, 25/21 is mapped into quarter octave.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 32805/32768, 390625/388962
[[Comma list]]: 32805/32768, 390625/388962
Line 2,050: Line 2,050:
{{Multival|legend=1| 4 -32 -68 -60 -119 -68 }}
{{Multival|legend=1| 4 -32 -68 -60 -119 -68 }}


[[POTE generator]]: ~3/2 = 701.8234
[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~3/2 = 701.8234


{{Val list|legend=1| 212, 224, 436, 660, 1096c }}
{{Val list|legend=1| 212, 224, 436, 660, 1096c }}
Line 2,063: Line 2,063:
Mapping: [{{val| 4 0 60 119 185 }}, {{val| 0 1 -8 -17 -27 }}]
Mapping: [{{val| 4 0 60 119 185 }}, {{val| 0 1 -8 -17 -27 }}]


POTE generator: ~3/2 = 701.8176
Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 701.8176


Optimal GPV sequence: {{Val list| 212, 224, 436, 660 }}
Optimal GPV sequence: {{Val list| 212, 224, 436, 660 }}
Line 2,076: Line 2,076:
Mapping: [{{val| 4 0 60 119 185 224 }}, {{val| 0 1 -8 -17 -27 -33 }}]
Mapping: [{{val| 4 0 60 119 185 224 }}, {{val| 0 1 -8 -17 -27 -33 }}]


POTE generator: ~3/2 = 701.8158
Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 701.8158


Optimal GPV sequence: {{Val list| 212, 224, 436, 660 }}
Optimal GPV sequence: {{Val list| 212, 224, 436, 660 }}
Line 2,083: Line 2,083:


== Septant ==
== Septant ==
The ''septant'' temperament (224&301) has a period of 1/7 octave and tempers out the [[akjaysma]], {{monzo|47 -7 -7 -7}}.
The ''septant'' temperament (224 & 301) has a period of 1/7 octave and tempers out the [[akjaysma]], {{monzo| 47 -7 -7 -7 }}.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 32805/32768, 516560652/514714375
[[Comma list]]: 32805/32768, 516560652/514714375
Line 2,095: Line 2,095:
{{Multival|legend=1| 7 -56 49 -105 58 271 }}
{{Multival|legend=1| 7 -56 49 -105 58 271 }}


[[POTE generator]]: ~3/2 = 701.702
[[Optimal tuning]] ([[POTE]]): ~8575/7776 = 1\7, ~3/2 = 701.702


{{Val list|legend=1| 77, 147, 224, 301, 525, 826, 1351 }}
{{Val list|legend=1| 77, 147, 224, 301, 525, 826, 1351 }}
Line 2,108: Line 2,108:
Mapping: [{{val| 7 0 105 -56 -120 }}, {{val| 0 1 -8 7 13 }}]
Mapping: [{{val| 7 0 105 -56 -120 }}, {{val| 0 1 -8 7 13 }}]


POTE generator: ~3/2 = 701.719
Optimal tuning (POTE): ~495/448 = 1\7, ~3/2 = 701.719


Optimal GPV sequence: {{Val list| 77, 147, 224, 301, 525 }}
Optimal GPV sequence: {{Val list| 77, 147, 224, 301, 525 }}
Line 2,121: Line 2,121:
Mapping: [{{val| 7 0 105 -56 -120 37 }}, {{val| 0 1 -8 7 13 -1 }}]
Mapping: [{{val| 7 0 105 -56 -120 37 }}, {{val| 0 1 -8 7 13 -1 }}]


POTE generator: ~3/2 = 701.724
Optimal tuning (POTE): ~495/448 = 1\7, ~3/2 = 701.724


Optimal GPV sequence: {{Val list| 77, 147, 224, 525 }}
Optimal GPV sequence: {{Val list| 77, 147, 224, 525 }}
Line 2,128: Line 2,128:


== Octant ==
== Octant ==
The octant temperament (224&472) has a period of 1/8 octave. In this temperament, 12/11, 35/27, and 99/70 are mapped into 1\8, 3\8, and 4\8 respectively.
The octant temperament (224 & 472) has a period of 1/8 octave. In this temperament, 12/11, 35/27, and 99/70 are mapped into 1\8, 3\8, and 4\8 respectively.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 32805/32768, 2259436291848/2251875390625
[[Comma list]]: 32805/32768, 2259436291848/2251875390625
Line 2,140: Line 2,140:
{{Multival|legend=1| 8 -64 88 -120 117 384 }}
{{Multival|legend=1| 8 -64 88 -120 117 384 }}


[[POTE generator]]: ~3/2 = 701.713
[[Optimal tuning]] ([[POTE]]): ~42875/39366 = 1\8, ~3/2 = 701.713


{{Val list|legend=1| 24, 224, 472, 696, 1168 }}
{{Val list|legend=1| 24, 224, 472, 696, 1168 }}
Line 2,153: Line 2,153:
Mapping: [{{val| 8 0 120 -117 15 }}, {{val| 0 1 -8 11 1 }}]
Mapping: [{{val| 8 0 120 -117 15 }}, {{val| 0 1 -8 11 1 }}]


Mapping generators: ~12/11, ~3
Optimal tuning (POTE): ~12/11 = 1\8, ~3/2 = 701.713
 
POTE generator: ~3/2 = 701.713


Optimal GPV sequence: {{Val list| 24, 224, 472, 696, 1168 }}
Optimal GPV sequence: {{Val list| 24, 224, 472, 696, 1168 }}
Line 2,168: Line 2,166:
Mapping: [{{val| 8 0 120 -117 15 93 }}, {{val| 0 1 -8 11 1 -5 }}]
Mapping: [{{val| 8 0 120 -117 15 93 }}, {{val| 0 1 -8 11 1 -5 }}]


Mapping generators: ~12/11, ~3
Optimal tuning (POTE): ~12/11 = 1\8, ~3/2 = 701.725
 
POTE generator: ~3/2 = 701.725


Optimal GPV sequence: {{Val list| 24, 224, 472, 696 }}
Optimal GPV sequence: {{Val list| 24, 224, 472, 696 }}
Line 2,179: Line 2,175:
''Tridecafifths'' divides the perfect 3/2 into 13 quartertones.  
''Tridecafifths'' divides the perfect 3/2 into 13 quartertones.  


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Comma list: 32805/32768, 96889010407/96000000000
[[Comma list]]: 32805/32768, {{monzo| -14 -1 -9 13 }}


Mapping: [{{val|1 1 7 6}}, {{val|0 13 -104 -71}}]
[[Mapping]]: [{{val| 1 1 7 6 }}, {{val| 0 13 -104 -71 }}]


Mapping generators: ~2, ~1323/1280
Mapping generators: ~2, ~1323/1280


Optimal tuning (CTE): ~1323/1280 = 53.974
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~1323/1280 = 53.9741
 
{{Val list|legend=1| 89, 200, 289 }}


Vals: {{EDOs|89, 200, 289, 378}}, ...
[[Badness]]: 0.433


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 441/440, 200704/200475, 55296000/55240493
Comma list: 441/440, 32805/32768, 55296000/55240493
 
Mapping: [{{val| 1 1 7 6 4 }}, {{val| 0 13 -104 -71 -12 }}]


Mapping: [{{val|1 1 7 6 4}}, {{val|0 13 -104 -71 -12}}]
Optimal tuning (CTE): ~2 = 1\1, ~33/32 = 53.9744


Mapping generators: ~2, ~33/32
Optimal GPV sequence: {{Val list| 89, 200, 289 }}


Optimal tuning (CTE): ~33/32 = 53.974
Badness: 0.128


Vals: {{EDOs|89, 200, 289, 378}}, ...
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Schismatic]]
[[Category:Schismatic]]
[[Category:Schismatic family| ]] <!-- main article -->
[[Category:Schismatic family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Schismatic_family"