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Archytas clan: Difference between revisions

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+CTE tunings. Review optimal ET sequences.
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: [[gencom]]: [2 3/2; 64/63]
: [[gencom]]: [2 3/2; 64/63]


[[Optimal tuning]] ([[POTE]]): ~3/2 = 709.321
[[Optimal tuning]]s:
* [[CTE]]: ~3/2 = 709.5948
* [[POTE]]: ~3/2 = 709.321


{{Optimal ET sequence|legend=1| 2, 3, 5, 12, 17, 22, 137bdd, 159bddd, 181bbddd }}
{{Optimal ET sequence|legend=1| 2, 3, 5, 12, 17, 22, 137bdd, 159bddd, 181bbddd }}
[[Badness]]: 0.00464


Scales: [[archy5]], [[archy7]], [[archy12]]
Scales: [[archy5]], [[archy7]], [[archy12]]
Line 54: Line 58:
: gencom: [2 3/2; 64/63 99/98]
: gencom: [2 3/2; 64/63 99/98]


Optimal tuning (POTE): ~3/2 = 707.192
Optimal tunings:
* CTE: ~3/2 = 708.4564
* POTE: ~3/2 = 707.192


{{Optimal ET sequence|legend=1| 5, 12, 17, 39d, 56d }}
Optimal ET sequence: {{Optimal ET sequence| 5, 12, 17, 39d, 56d }}
 
Badness: 0.00933


Scales: [[supra7]], [[supra12]]
Scales: [[supra7]], [[supra12]]
Line 71: Line 79:
: gencom: [2 3/2; 64/63 78/77 99/98]
: gencom: [2 3/2; 64/63 78/77 99/98]


Optimal tuning (POTE): ~3/2 = 706.137
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 707.3440
* POTE: ~2 = 1\1, ~3/2 = 706.137
 
Optimal ET sequence: {{Optimal ET sequence| 12f, 17 }}


{{Optimal ET sequence|legend=1| 12f, 17 }}
Badness: 0.0111


Scales: [[supra7]], [[supra12]]
Scales: [[supra7]], [[supra12]]
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{{Mapping|legend=1| 1 0 -12 | 0 1 9 }}
{{Mapping|legend=1| 1 0 -12 | 0 1 9 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 710.078
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 709.3933
* [[POTE]]: ~2 = 1\1, ~3/2 = 710.078


{{Optimal ET sequence|legend=1| 5, 17, 22, 49, 120b, 169bbc }}
{{Optimal ET sequence|legend=1| 5, 17, 22, 49, 120b, 169bbc }}
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{{Multival|legend=1| 1 9 -2 12 -6 -30 }}
{{Multival|legend=1| 1 9 -2 12 -6 -30 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 710.291
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 709.5907
* [[POTE]]: ~2 = 1\1, ~3/2 = 710.291


{{Optimal ET sequence|legend=1| 5, 17, 22, 27, 49 }}
{{Optimal ET sequence|legend=1| 5, 17, 22, 27, 49, 174bbcddd }}


[[Badness]]: 0.032318
[[Badness]]: 0.032318
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Mapping: {{mapping| 1 0 -12 6 -22 | 0 1 9 -2 16 }}
Mapping: {{mapping| 1 0 -12 6 -22 | 0 1 9 -2 16 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 710.175
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 709.5143
* POTE: ~2 = 1\1, ~3/2 = 710.175


{{Optimal ET sequence|legend=1| 22, 27e, 49 }}
Optimal ET sequence: {{Optimal ET sequence| 22, 27e, 49 }}


Badness: 0.024976
Badness: 0.024976
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Mapping: {{mapping| 1 0 -12 6 -22 -17 | 0 1 9 -2 16 13 }}
Mapping: {{mapping| 1 0 -12 6 -22 -17 | 0 1 9 -2 16 13 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 710.479
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 709.8362
* POTE: ~2 = 1\1, ~3/2 = 710.479


{{Optimal ET sequence|legend=1| 22, 27e, 49, 76bcde }}
Optimal ET sequence: {{Optimal ET sequence| 22, 27e, 49, 76bcde }}


Badness: 0.024673
Badness: 0.024673
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Mapping: {{mapping| 1 1 -3 4 -6 4 | 0 2 18 -4 32 -1 }}
Mapping: {{mapping| 1 1 -3 4 -6 4 | 0 2 18 -4 32 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 355.036
Optimal tunings:
* CTE: ~2 = 1\1, ~16/13 = 354.7594
* POTE: ~2 = 1\1, ~16/13 = 355.036


{{Optimal ET sequence|legend=1| 17e, 27e, 44, 71d }}
Optimal ET sequence: {{Optimal ET sequence| 27e, 44, 71d, 98bde }}


Badness: 0.049183
Badness: 0.049183
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Mapping: {{mapping| 1 0 -12 6 13 | 0 1 9 -2 -6 }}
Mapping: {{mapping| 1 0 -12 6 13 | 0 1 9 -2 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 709.495
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 709.3561
* POTE: ~2 = 1\1, ~3/2 = 709.495


{{Optimal ET sequence|legend=1| 5, 12c, 17, 22 }}
Optimal ET sequence: {{Optimal ET sequence| 5, 17, 22 }}


Badness: 0.032768
Badness: 0.032768
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Mapping: {{mapping| 1 0 -12 6 13 18 | 0 1 9 -2 -6 -9 }}
Mapping: {{mapping| 1 0 -12 6 13 18 | 0 1 9 -2 -6 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 708.703
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 708.7020
* POTE: ~2 = 1\1, ~3/2 = 708.703


{{Optimal ET sequence|legend=1| 17, 22, 83cdf }}
Optimal ET sequence: {{Optimal ET sequence| 5f, 17, 22 }}


Badness: 0.036336
Badness: 0.036336
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{{Multival|legend=1| 1 -13 -2 -23 -6 32 }}
{{Multival|legend=1| 1 -13 -2 -23 -6 32 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 708.328
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 708.7690
* [[POTE]]: ~2 = 1\1, ~3/2 = 708.328


{{Optimal ET sequence|legend=1| 17c, 22, 61d }}
{{Optimal ET sequence|legend=1| 17c, 22, 61d }}
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Mapping: {{mapping| 1 0 23 6 13 | 0 1 -13 -2 -6 }}
Mapping: {{mapping| 1 0 23 6 13 | 0 1 -13 -2 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 708.205
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 708.7131
* POTE: ~2 = 1\1, ~3/2 = 708.205


{{Optimal ET sequence|legend=1| 17c, 22, 39d, 61d }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 22, 39d, 61d }}


Badness: 0.032203
Badness: 0.032203
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Mapping: {{mapping| 1 0 23 6 13 18 | 0 1 -13 -2 -6 -9 }}
Mapping: {{mapping| 1 0 23 6 13 18 | 0 1 -13 -2 -6 -9 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 708.004
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 708.4106
* POTE: ~2 = 1\1, ~3/2 = 708.004


{{Optimal ET sequence|legend=1| 17c, 22, 39d, 61df, 100bcdf }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 22, 39d, 61df, 100bcdf }}


Badness: 0.030219
Badness: 0.030219
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Mapping: {{mapping| 1 0 23 6 -22 | 0 1 -13 -2 16 }}
Mapping: {{mapping| 1 0 23 6 -22 | 0 1 -13 -2 16 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 709.021
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 709.0435
* POTE: ~2 = 1\1, ~3/2 = 709.021


{{Optimal ET sequence|legend=1| 5ce, 17ce, 22 }}
Optimal ET sequence: {{Optimal ET sequence| 22 }}


Badness: 0.083490
Badness: 0.083490
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{{Multival|legend=1| 1 14 -2 20 -6 -44 }}
{{Multival|legend=1| 1 14 -2 20 -6 -44 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 713.651
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 713.2179
* [[POTE]]: ~2 = 1\1, ~3/2 = 713.651


{{Optimal ET sequence|legend=1| 5, 32, 37 }}
{{Optimal ET sequence|legend=1| 5, 27c, 32, 37 }}


[[Badness]]: 0.108466
[[Badness]]: 0.108466
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Mapping: {{mapping| 1 0 -20 6 21 | 0 1 14 -2 -11 }}
Mapping: {{mapping| 1 0 -20 6 21 | 0 1 14 -2 -11 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 713.395
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 713.2816
* POTE: ~2 = 1\1, ~3/2 = 713.395


{{Optimal ET sequence|legend=1| 5, 32, 37 }}
Optimal ET sequence: {{Optimal ET sequence| 5, 32, 37 }}


Badness: 0.068238
Badness: 0.068238
Line 273: Line 311:
Mapping: {{mapping| 1 0 -20 6 21 -25 | 0 1 14 -2 -11 18 }}
Mapping: {{mapping| 1 0 -20 6 21 -25 | 0 1 14 -2 -11 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 713.500
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 713.3086
* POTE: ~2 = 1\1, ~3/2 = 713.500


{{Optimal ET sequence|legend=1| 5, 32, 37 }}
Optimal ET sequence: {{Optimal ET sequence| 5, 32, 37 }}


Badness: 0.049172
Badness: 0.049172
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Mapping: {{mapping| 1 0 -20 6 -38 | 0 1 14 -2 26 }}
Mapping: {{mapping| 1 0 -20 6 -38 | 0 1 14 -2 26 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 713.791
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 713.3952
* POTE: ~2 = 1\1, ~3/2 = 713.791


{{Optimal ET sequence|legend=1| 5e, 32e, 37, 79bce, 116bbce }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 32e, 37, 79bce }}


Badness: 0.078068
Badness: 0.078068
Line 299: Line 341:
Mapping: {{mapping| 1 0 -20 6 -38 -25 | 0 1 14 -2 26 18 }}
Mapping: {{mapping| 1 0 -20 6 -38 -25 | 0 1 14 -2 26 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 713.811
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 713.7079
* POTE: ~2 = 1\1, ~3/2 = 713.811


{{Optimal ET sequence|legend=1| 5e, 32e, 37, 79bcef, 116bbcef }}
Optimal ET sequence: {{Optimal ET sequence| 5e, 32e, 37, 79bcef }}


Badness: 0.045653
Badness: 0.045653
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{{See also| Schismatic family #Schism }}
{{See also| Schismatic family #Schism }}


Schism tempers out the [[schisma]], mapping the ~5/4 to -8 fifths as a diminished fourth (C-Fb) as does any schismic temperament.  
Schism tempers out the [[schisma]], mapping the ~5/4 to -8 fifths as a diminished fourth (C-Fb) as does any schismic temperament. 12edo is recommendable tuning, though 29edo (29d val), 41edo (41d val), and 53edo (53d val) can be used.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 1 0 15 6 | 0 1 -8 -2 }}
{{Mapping|legend=1| 1 0 15 6 | 0 1 -8 -2 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.556
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.2696
* [[POTE]]: ~2 = 1\1, ~3/2 = 701.556


{{Multival|legend=1| 1 -8 -2 -15 -6 18 }}
{{Multival|legend=1| 1 -8 -2 -15 -6 18 }}


{{Optimal ET sequence|legend=1| 12, 29d, 41d, 53d }}
{{Optimal ET sequence|legend=1| 5c, 7c, 12 }}


[[Badness]]: 0.056648
[[Badness]]: 0.056648
Line 350: Line 396:
Mapping: {{mapping| 1 0 15 6 13 | 0 1 -8 -2 -6 }}
Mapping: {{mapping| 1 0 15 6 13 | 0 1 -8 -2 -6 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.136
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 703.3833
* POTE: ~2 = 1\1, ~3/2 = 702.136


{{Optimal ET sequence|legend=1| 12, 29de, 41de }}
Optimal ET sequence: {{Optimal ET sequence| 5c, 7ce, 12, 29de }}


Badness: 0.037482
Badness: 0.037482
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