Aberschismic family: Difference between revisions
→Laka: delete 17-limit laka, as the current structure doesn't make sense |
Move counterpyth to subgroup extensions section as it skips multiple primes |
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{{ | {{Interwiki | ||
| en = | | en = | ||
| de = Hemifamity | | de = Hemifamity | ||
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{{Mapping|legend=1| 1 0 0 10 | 0 1 0 -6 | 0 0 1 1 }} | {{Mapping|legend=1| 1 0 0 10 | 0 1 0 -6 | 0 0 1 1 }} | ||
: mapping generators: ~2, ~3, ~5 | : mapping generators: ~2, ~3, ~5 | ||
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==== Subgroup extensions ==== | ==== Subgroup extensions ==== | ||
A notable 2.3.5.7.19 subgroup extension, counterpyth, is | A notable 2.3.5.7.19-subgroup extension, counterpyth, is considered in [[#Subgroup extensions]]. | ||
== Pele == | == Pele == | ||
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== Lono == | == Lono == | ||
Lono tempers out [[176/175]] and may be described as the {{nowrap| 46 & 53 & 58 }} temperament, finding the interval class of 11 at the triple-down augmented fourth (C–v<sup>3</sup>F#). [[111edo]] is a great tuning for it. [[157edo]] is a viable alternative, which is almost as good. | Lono tempers out [[176/175]] and may be described as the {{nowrap| 46 & 53 & 58 }} temperament, finding the interval class of 11 at the triple-down augmented fourth (C–v<sup>3</sup>F#). It notably also tempers out [[8019/8000]], thus setting 11/10, 10/9, 9/8, and 8/7 a comma apart from each other. [[111edo]] is a great tuning for it. [[157edo]] is a viable alternative, which is almost as good. | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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Badness (Sintel): 0.731 | Badness (Sintel): 0.731 | ||
== Subgroup extensions == | |||
=== Counterpyth (2.3.5.7.19) === | |||
{{Main| Counterpyth }} | |||
Developed analogous to [[parapyth]], counterpyth is an extension of hemifamity with an even milder fifth, as it finds [[19/15]] at the major third (C–E) and [[19/10]] at the major seventh (C–B). Notice the factorization {{nowrap| 5120/5103 {{=}} ([[400/399]])⋅([[1216/1215]]) }}. Other important ratios are [[21/19]] at the diminished third (C–Ebb) and [[19/14]] at the augmented third (C–E#). | |||
It can be further extended via the mappings of laka or akea, while working less well with pele or lono due to their much sharper fifths. | |||
Subgroup: 2.3.5.7.19 | |||
Comma list: 400/399, 1216/1215 | |||
Mapping: {{mapping| 1 0 0 10 -6 | 0 1 0 -6 5 | 0 0 1 1 1 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.6953{{c}}, ~3/2 = 702.5169{{c}}, ~5/4 = 386.2648{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6771{{c}}, ~5/4 = 386.0544{{c}} | |||
{{Optimal ET sequence|legend=0| 12, 29, 41, 53, 94, 99, 140, 152, 292h, 444dh }} | |||
Badness (Sintel): 0.347 | |||
== References == | == References == | ||