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Archytas clan: Difference between revisions

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Line 51: Line 51:
POTE generator: ~3/2 = 707.192
POTE generator: ~3/2 = 707.192


Vals: {{Val list| 5, 12, 17, 39d, 56d }}
Optimal GPV sequence: {{Val list| 5, 12, 17, 39d, 56d }}


Scales: [[supra7]], [[supra12]]
Scales: [[supra7]], [[supra12]]
Line 70: Line 70:
POTE generator: ~3/2 = 706.137
POTE generator: ~3/2 = 706.137


Vals: {{Val list| 12f, 17 }}
Optimal GPV sequence: {{Val list| 12f, 17 }}


Scales: [[supra7]], [[supra12]]
Scales: [[supra7]], [[supra12]]
Line 89: Line 89:
POTE generator: ~11/9 = 353.958
POTE generator: ~11/9 = 353.958


Vals: {{Val list| 7, 10, 17, 44e, 61de }}
Optimal GPV sequence: {{Val list| 7, 10, 17, 44e, 61de }}


Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]
Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]
Line 108: Line 108:
POTE generator: ~11/9 = 353.775
POTE generator: ~11/9 = 353.775


Vals: {{Val list| 7, 10, 17, 44e, 61de }}
Optimal GPV sequence: {{Val list| 7, 10, 17, 44e, 61de }}


Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]
Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]
Line 115: Line 115:
{{main| Superpyth }}
{{main| Superpyth }}


In the 5-limit, superpyth tempers out 20480/19683 (sayo comma). This temperament has a fifth generator of ~3/2 = ~710¢ and 5/4 is equated to nine generators minus 5 octaves. A weak extension [[Jubilismic clan #Bipyth|bipyth]] (10cd&22) tempers out the same 5-limit comma as the superpyth, but with a half-octave period and the jubilisma (50/49) rather than the Archytas comma tempered out.
Subgroup: 2.3.5
[[Comma list]]: 20480/19683
[[Mapping]]: [{{val| 1 0 -12 }}, {{val| 0 1 9 }}]
[[POTE generator]]: ~3/2 = 710.078
{{Val list|legend=1| 5, 17, 22, 49, 120b, 169bbc }}
[[Badness]]: 0.135141
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 138: Line 153:
POTE generator: ~3/2 = 710.175
POTE generator: ~3/2 = 710.175


Vals: {{Val list| 22, 27e, 49 }}
Optimal GPV sequence: {{Val list| 22, 27e, 49 }}


Badness: 0.024976
Badness: 0.024976
Line 151: Line 166:
POTE generator: ~3/2 = 710.479
POTE generator: ~3/2 = 710.479


Vals: {{Val list| 22, 27e, 49, 76bcde }}
Optimal GPV sequence: {{Val list| 22, 27e, 49, 76bcde }}


Badness: 0.024673
Badness: 0.024673
Line 164: Line 179:
POTE generator: ~3/2 = 709.495
POTE generator: ~3/2 = 709.495


Vals: {{Val list| 5, 12c, 17, 22 }}
Optimal GPV sequence: {{Val list| 5, 12c, 17, 22 }}


Badness: 0.032768
Badness: 0.032768
Line 177: Line 192:
POTE generator: ~3/2 = 708.703
POTE generator: ~3/2 = 708.703


Vals: {{Val list| 17, 22, 83cdf }}
Optimal GPV sequence: {{Val list| 17, 22, 83cdf }}


Badness: 0.036336
Badness: 0.036336
Line 207: Line 222:
POTE generator: ~3/2 = 708.205
POTE generator: ~3/2 = 708.205


Vals: {{Val list| 17c, 22, 39d, 61d }}
Optimal GPV sequence: {{Val list| 17c, 22, 39d, 61d }}


Badness: 0.032203
Badness: 0.032203
Line 220: Line 235:
POTE generator: ~3/2 = 708.004
POTE generator: ~3/2 = 708.004


Vals: {{Val list| 17c, 22, 39d, 61df, 100bcdf }}
Optimal GPV sequence: {{Val list| 17c, 22, 39d, 61df, 100bcdf }}


Badness: 0.030219
Badness: 0.030219
Line 233: Line 248:
POTE generator: ~3/2 = 709.021
POTE generator: ~3/2 = 709.021


Vals: {{Val list| 5ce, 17ce, 22 }}
Optimal GPV sequence: {{Val list| 5ce, 17ce, 22 }}


Badness: 0.083490
Badness: 0.083490
Line 262: Line 277:
Mapping: [{{val| 1 0 -20 6 -25 }}, {{val| 0 1 14 -2 18 }}]
Mapping: [{{val| 1 0 -20 6 -25 }}, {{val| 0 1 14 -2 18 }}]


POTE generator: ~3/2 = 713.7453
POTE generator: ~3/2 = 713.745


Vals: {{Val list| 5, 32, 37, 79bc }}
Optimal GPV sequence: {{Val list| 5, 32, 37, 79bc }}


Badness: 0.0547
Badness: 0.0547
Line 277: Line 292:
POTE generator: ~3/2 = 713.395
POTE generator: ~3/2 = 713.395


Vals: {{Val list| 5, 32, 37 }}
Optimal GPV sequence: {{Val list| 5, 32, 37 }}


Badness: 0.068238
Badness: 0.068238
Line 290: Line 305:
POTE generator: ~3/2 = 713.500
POTE generator: ~3/2 = 713.500


Vals: {{Val list| 5, 32, 37 }}
Optimal GPV sequence: {{Val list| 5, 32, 37 }}


Badness: 0.049172
Badness: 0.049172
Line 303: Line 318:
POTE generator: ~3/2 = 713.791
POTE generator: ~3/2 = 713.791


Vals: {{Val list| 5e, 32e, 37, 79bce, 116bbce }}
Optimal GPV sequence: {{Val list| 5e, 32e, 37, 79bce, 116bbce }}


Badness: 0.078068
Badness: 0.078068
Line 316: Line 331:
POTE generator: ~3/2 = 713.811
POTE generator: ~3/2 = 713.811


Vals: {{Val list| 5e, 32e, 37, 79bcef, 116bbcef }}
Optimal GPV sequence: {{Val list| 5e, 32e, 37, 79bcef, 116bbcef }}


Badness: 0.045653
Badness: 0.045653
Line 346: Line 361:
POTE generator: ~3/2 = 702.136
POTE generator: ~3/2 = 702.136


Vals: {{Val list| 12, 29de, 41de }}
Optimal GPV sequence: {{Val list| 12, 29de, 41de }}


Badness: 0.037482
Badness: 0.037482
Line 379: Line 394:
POTE generator: ~49/40 = 356.140
POTE generator: ~49/40 = 356.140


Vals: {{Val list| 27e, 37, 64be, 91bcde }}
Optimal GPV sequence: {{Val list| 27e, 37, 64be, 91bcde }}


Badness: 0.045639
Badness: 0.045639
Line 392: Line 407:
POTE generator: ~16/13 = 356.229
POTE generator: ~16/13 = 356.229


Vals: {{Val list| 27e, 37, 64be }}
Optimal GPV sequence: {{Val list| 27e, 37, 64be }}


Badness: 0.030161
Badness: 0.030161
Line 405: Line 420:
POTE generator: ~11/9 = 355.419
POTE generator: ~11/9 = 355.419


Vals: {{Val list| 10, 17c, 27e }}
Optimal GPV sequence: {{Val list| 10, 17c, 27e }}


Badness: 0.032863
Badness: 0.032863
Line 418: Line 433:
POTE generator: ~11/9 = 355.456
POTE generator: ~11/9 = 355.456


Vals: {{Val list| 10, 17c, 27e }}
Optimal GPV sequence: {{Val list| 10, 17c, 27e }}


Badness: 0.022619
Badness: 0.022619
Line 431: Line 446:
POTE generator: ~49/40 = 356.710
POTE generator: ~49/40 = 356.710


Vals: {{Val list| 10, 27, 37 }}
Optimal GPV sequence: {{Val list| 10, 27, 37 }}


Badness: 0.058084
Badness: 0.058084
Line 444: Line 459:
POTE generator: ~16/13 = 356.701
POTE generator: ~16/13 = 356.701


Vals: {{Val list| 10, 27, 37 }}
Optimal GPV sequence: {{Val list| 10, 27, 37 }}


Badness: 0.033971
Badness: 0.033971
Line 474: Line 489:
POTE generator: ~7/5 = 577.850
POTE generator: ~7/5 = 577.850


Vals: {{Val list| 2, 25e, 27e }}
Optimal GPV sequence: {{Val list| 2, 25e, 27e }}


Badness: 0.052054
Badness: 0.052054
Line 487: Line 502:
POTE generator: ~7/5 = 578.060
POTE generator: ~7/5 = 578.060


Vals: {{Val list| 2f, 25ef, 27e }}
Optimal GPV sequence: {{Val list| 2f, 25ef, 27e }}


Badness: 0.039705
Badness: 0.039705
Line 517: Line 532:
POTE generator: ~7/5 = 562.085
POTE generator: ~7/5 = 562.085


Vals: {{Val list| 2, 13, 15, 32c, 47bc, 79bcce }}
Optimal GPV sequence: {{Val list| 2, 13, 15, 32c, 47bc, 79bcce }}


Badness: 0.031036
Badness: 0.031036
Line 530: Line 545:
POTE generator: ~7/5 = 562.365
POTE generator: ~7/5 = 562.365


Vals: {{Val list| 15, 17c, 32cf }}
Optimal GPV sequence: {{Val list| 15, 17c, 32cf }}


Badness: 0.026214
Badness: 0.026214
Line 543: Line 558:
POTE generator: ~7/5 = 563.239
POTE generator: ~7/5 = 563.239


Vals: {{Val list| 15f, 17c, 32c, 49c }}
Optimal GPV sequence: {{Val list| 15f, 17c, 32c, 49c }}


Badness: 0.032721
Badness: 0.032721
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