Subgroup temperaments: Difference between revisions
Added antikythera, tutone, greeley and pepperoni from Chromatic pairs |
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Optimal tuning (CTE): ~3575/3528 = 23.477 | Optimal tuning (CTE): ~3575/3528 = 23.477 | ||
=== Antikythera === | |||
Subgroup: 2.9.5.7 | |||
Commas: 50/49, 64/63 | |||
Related temperament: [[pajara|pajara]] | |||
[[Tp_tuning|POT2 generator]]: ~8/7 = 214.095 | |||
[[Gencom|Gencom]]: [7/5 8/7; 50/49 64/63] | |||
Gencom mapping: [<2 3 5 6|, <0 1/2 -1 -1|] | |||
Mapping: [<2 0 11 12|, <0 1 -1 -1|] | |||
EDOS: 4, 6, 10, 16, 22, 28 | |||
[[Tp_tuning#T2 tuning|RMS error]]: 2.572 cents | |||
== 2.9.5.7.11 subgroup == | |||
=== Tutone === | |||
Subgroup: 2.9.5.7.11 | |||
Commas: 81/80, 99/98, 126/125 | |||
Related temperaments: [[Meantone_family|meantone]], [[Hemimean_family#Belobog|belobog]], hemithirds, hemiwürschmidt | |||
[[Tp_tuning|POT2 generator]]: ~9/8 = 193.937 | |||
[[Gencom|Gencom]]: [2 9/8; 81/80 99/98 126/125] | |||
Gencom mapping: [<1 3/2 2 2 2|, <0 1/2 2 5 9|] | |||
Mapping: [<1 0 -4 -13 -25|, <0 1 2 5 9|] | |||
EDOs: 25, 31, 68b, 99b | |||
[[Tp_tuning#T2 tuning|RMS error]]: 1.439 cents | |||
== 2.9.7.11 subgroup == | == 2.9.7.11 subgroup == | ||
| Line 300: | Line 339: | ||
[[Optimal GPV sequence]]: [[8edf]], [[11edf]] | [[Optimal GPV sequence]]: [[8edf]], [[11edf]] | ||
=== Greeley === | |||
Subgroup: 2.5/3.7/3.11/3 | |||
Commas: 121/120, 126/125 | |||
Related temperament: [[Porcupine_family#Opossum|Opossum]], [[Starling_temperaments#Nusecond temperament|Nusecond]] | |||
[[Tp_tuning|POT2 generator]]: ~11/10 = 155.776 | |||
[[Gencom|Gencom]]: [2 11/10; 121/120 126/125] | |||
Gencom mapping: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|] | |||
Mapping: [<1 1 2 2|, <0 -2 -6 -1|] | |||
EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd | |||
[[Tp_tuning#T2 tuning|RMS error]]: 1.034 cents | |||
=== Pepperoni === | |||
Subgroup: 2.3.11/7.13/7 | |||
Commas: 352/351, 364/363 | |||
Sval name: 5&12 | |||
Related temperament: The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name. | |||
[[Tp_tuning|POT2 generator]]: ~3/2 = 703.856 | |||
[[Gencom|Gencom]]: [2 3/2; 352/351 364/363] | |||
Gencom mapping: [<1 1 0 -8/3 1/3 7/3|, <0 1 0 11/3 -1/3 -10/3|] | |||
Mapping: [<1 0 7 12|, <0 1 -4 -7|] | |||
EDOs: 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd | |||
[[Tp_tuning#T2 tuning|RMS error]]: 0.3789 cents | |||
[[Category:Subgroup temperaments| ]] <!-- main article --> | [[Category:Subgroup temperaments| ]] <!-- main article --> | ||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||