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Subgroup temperaments: Difference between revisions

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-tutone (addressed in hemimean clan); cleanup (2/)
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Badness: 0.0564
Badness: 0.0564
== 2.9.5.7.11 subgroup ==
=== Tutone ===
{{See also| Hemimean clan }}
Related temperaments: [[meantone]], [[belobog]], [[hemithirds]], [[hemiwürschmidt]]
[[Subgroup]]: 2.9.5.7.11
[[Comma list]]: 81/80, 99/98, 126/125
{{Mapping|legend=2| 1 0 -4 -13 -25 | 0 1 2 5 9 }}
: mapping generators: ~2, ~9
{{Mapping|legend=3| 1 3/2 2 2 2 | 0 1/2 2 5 9 }}
: [[gencom]]: [2 9/8; 81/80 99/98 126/125]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 193.937
{{Optimal ET sequence|legend=1| 25, 31, 68b, 99b }}
[[Badness]]: 0.00536


== 2.9.7.11 subgroup ==
== 2.9.7.11 subgroup ==
Line 105: Line 81:
[[Comma list]]: 64/63, 99/98
[[Comma list]]: 64/63, 99/98


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


[[Gencom]]: [2 8/7; 64/63 99/98]
: sval mapping generators: ~2, ~9


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


[[Optimal tuning]] ([[POTE]]): ~8/7 = 214.384
: [[gencom]]: [2 8/7; 64/63 99/98]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 216.9128


{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }}
{{Optimal ET sequence|legend=1| 5, 6, 11, 17, 28 }}


[[Tp tuning #T2 tuning|RMS error]]: 1.977 cents
[[Badness]]: 0.00233


=== Mechanism ===
=== Mechanism ===
Line 122: Line 100:
[[Comma list]]: 896/891, 26411/26244
[[Comma list]]: 896/891, 26411/26244


[[Sval]] [[mapping]]: [{{val| 1 5 5 2 }}, {{val| 0 -5 -6 4 }}]
{{Mapping|legend=2| 1 0 -1 6 | 0 5 6 -4 }}


[[Gencom]]: [2 9/7; 896/891 26411/26244]
: sval mapping generators: ~2, ~14/9


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


[[Optimal tuning]] ([[POTE]]): ~9/7 = 438.465
: [[gencom]]: [2 9/7; 896/891 26411/26244]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/9 = 761.3782


{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
[[Badness]]: 0.00439


=== Apparatus ===
=== Apparatus ===
Line 139: Line 119:
[[Comma list]]: 41503/41472, 322102/321489
[[Comma list]]: 41503/41472, 322102/321489


[[Sval]] [[mapping]]: [{{val| 1 5 3 5 }}, {{val| 0 -19 -2 -16 }}]
{{Mapping|legend=2| 1 5 3 5 | 0 -19 -2 -16 }}


[[Gencom]]: [2 77/72; 41503/41472 322102/321489]
: mapping generators: ~2, ~77/72


[[Gencom]] [[mapping]]: [{{val| 1 5/2 0 3 5}}, {{val| 0 -19/2 0 -2 -16 }}]
{{Mapping|legend=3| 1 5/2 0 3 5 | 0 -19/2 0 -2 -16 }}


[[Optimal tuning]] ([[POTE]]): ~77/72 = 115.570
: [[gencom]]: [2 77/72; 41503/41472 322102/321489]


{{Optimal ET sequence|legend=1| 10, 21, 31, 52, 83, 135, 353, 488, 623 }}
[[Optimal tuning]] ([[CTE]]): ~77/72 = 115.5685


[[Tp tuning #T2 tuning|RMS error]]: 0.0673 cents
{{Optimal ET sequence|legend=1| 10e, 21, 31, 52, 83, 135, 353, 488, 623 }}
 
[[Badness]]: 0.00263


== 2.9.15.7 subgroup ==
== 2.9.15.7 subgroup ==
Line 157: Line 139:
[[Comma list]]: 225/224, 245/243
[[Comma list]]: 225/224, 245/243


[[Sval]] [[mapping]]: [{{val| 1 0 2 -1 }}, {{val| 0 5 3 6 }}]
{{Mapping|legend=2| 1 0 2 -1 | 0 5 3 6 }}
 
: sval mapping generators: ~2, ~14/9


[[Gencom]]: [2 9/7; 225/224 245/243]
{{Mapping|legend=3| 1 5/2 5/2 5 | 0 -5/2 -1/2 -6 }}


[[Gencom]] [[mapping]]: [{{val| 1 5/2 5/2 5 }}, {{val| 0 -5/2 -1/2 -6 }}]
: [[gencom]]: [2 9/7; 225/224 245/243]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~9/7 = 439.296
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~14/9 = 760.704


{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 71, 93, 112c, 134c, 175c }}
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 71, 93, 112c, 134c, 175c }}
Line 174: Line 158:
Comma list: 100/99, 225/224, 245/243
Comma list: 100/99, 225/224, 245/243


Sval mapping: [{{val| 1 0 2 -1 6 }}, {{val| 0 5 3 6 -4 }}]
Sval mapping: {{mapping| 1 0 2 -1 6 | 0 5 3 6 -4 }}


Gencom: [2 9/7; 100/99 225/224 245/243]
Gencom mapping: {{mapping| 1 5/2 5/2 5 2 | 0 -5/2 -1/2 -6 4 }}


Gencom mapping: [{{val| 1 5/2 5/2 5 2 }}, {{val| 0 -5/2 -1/2 -6 4 }}]
: gencom: [2 9/7; 100/99 225/224 245/243]


Optimal tuning (subgroup POTE): ~9/7 = 438.607
Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.393


{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52, 93, 145, 342bce }}
{{Optimal ET sequence|legend=1| 8, 11, 30, 41, 52, 93, 145, 342bce }}
Line 191: Line 175:
Comma list: 100/99, 105/104, 144/143, 196/195
Comma list: 100/99, 105/104, 144/143, 196/195


Sval mapping: [{{val| 1 0 2 -1 6 -2 }}, {{val| 0 5 3 6 -4 9 }}]
Sval mapping: {{mapping| 1 0 2 -1 6 -2 | 0 5 3 6 -4 9 }}


Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
Gencom mapping: {{mapping| 1 5/2 5/2 5 2 7 | 0 -5/2 -1/2 -6 4 -9 }}


Gencom mapping: [{{val| 1 5/2 5/2 5 2 7 }}, {{val| 0 -5/2 -1/2 -6 4 -9 }}]
: gencom: [2 9/7; 100/99 105/104 144/143 196/195]


Optimal tuning (subgroup POTE): ~9/7 = 438.977
Optimal tuning (subgroup POTE): ~2 = 1\1, ~14/9 = 761.023


{{Optimal ET sequence|legend=1| 11, 30, 41, 153cdef, 194cdef, 235cdef }}
{{Optimal ET sequence|legend=1| 11, 30, 41, 153cdef, 194cdef, 235cdef }}
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