Schismatic family: Difference between revisions
→Subgroup extensions: normalize mappings and generators |
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[[Badness]]: 0.045817 | [[Badness]]: 0.045817 | ||
=== 2.3.5.7.13.19.23 subgroup === | |||
Subgroup: 2.3.5.7.13.19.23 | |||
Comma list: 351/350, 456/455, 513/512, 576/575, 676/675 | |||
Mapping: {{mapping| 1 0 15 -17 14 9 -24 | 0 2 -16 25 -13 -6 36 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.783 | |||
{{Optimal ET sequence|legend=1| 24i, 53, 130 }} <!-- 443h is not a GPV --> | |||
Badness: 0.583 (Sintel) | |||
=== 11-limit === | === 11-limit === | ||
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=== 13-limit === | === 13-limit === | ||
Its S-expression-based comma list is {[[540/539|S12/S14]], [[676/675|S13/S15 = S26]], [[729/728|S27]], [[4096/4095|S64]](, [[4225/4224|S65]])}. Tempering [[169/168|S13]], [[225/224|S15]] or [[625/624|S25]] leads to [[53edo]] (through [[Catakleismic]]) while tempering [[24192/24167|S12/S13]], [[10985/10976|S13/S14]], [[43904/43875|S14/S15]] or [[2401/2400|S49]] ( | Its S-expression-based comma list is {[[540/539|S12/S14]], [[676/675|S13/S15 = S26]], [[729/728|S27]], [[4096/4095|S64]](, [[4225/4224|S65]])}. Tempering out [[169/168|S13]], [[225/224|S15]] or [[625/624|S25]] leads to [[53edo]] (through [[Catakleismic]]) while tempering out [[24192/24167|S12/S13]], [[10985/10976|S13/S14]], [[43904/43875|S14/S15]] or [[2401/2400|S49]] (implying S12 = S13 = S14 = S15) leads to [[130edo]]. | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.810 | Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.810 | ||
{{Optimal ET sequence|legend=1| 53, 130, 183, | {{Optimal ET sequence|legend=1| 53, 130, 183, 496d }} <!-- 679df is not a GPV --> | ||
Badness: 0.021073 | Badness: 0.021073 | ||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 351/350, 442/441, 456/455, 561/560, 676/675, 4096/4095 | |||
Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 | 0 2 -16 25 -60 -13 67 -6 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.809 | |||
{{Optimal ET sequence|legend=1| 53, 130, 183, 313h }} <!-- 496dh is not a GPV --> | |||
Badness: 1.111 (Sintel) | |||
=== 23-limit === | |||
Subgroup: 2.3.5.7.11.13.17.19.23 | |||
Comma list: 351/350, 442/441, 456/455, 561/560, 676/675, 736/735, 4096/4095 | |||
Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 -24 | 0 2 -16 25 -60 -13 67 -6 36 }} | |||
Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.807 | |||
{{Optimal ET sequence|legend=1| 53, 130, 183, 313h }} <!-- 496dh is not a GPV --> | |||
Badness: 1.061 (Sintel) | |||
; Music | ; Music | ||