Archytas clan: Difference between revisions
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==== Subgroup extensions ==== | ==== Subgroup extensions ==== | ||
Omitting prime 5, archy can be extended to the [[2.3.7.11 subgroup]] by identifying 11/8 as a diminished | Omitting prime 5, archy can be extended to the [[2.3.7.11 subgroup]] by identifying 11/8 as a diminished fifth (C–G♭). This is called supra, given in [[#Subgroup extensions_2|#Subgroup extensions]]. Discussed elsewhere are [[suhajira]] of the [[rastmic clan #Suhajira|rastmic clan]], and [[the Archipelago#crete|crete]]. | ||
== Superpyth == | == Superpyth == | ||
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Scales: [[supra7]], [[supra12]] | Scales: [[supra7]], [[supra12]] | ||
=== Preflutterpyth (2.3.7.11) === | |||
This temperament is the no-5 restriction of 11-limit [[#Ultrapyth|ultrapyth]], which maps 11/8 to the diminished sixth (C–A𝄫). Its main extension is flutterpyth, a temperament found to yield [[blackdye]] tunings where [[aberrisma|aberrisma-altered]] minor and major thirds become tempered [[13/11]][[~]][[19/16]] and [[14/11]]. | |||
Subgroup: 2.3.7.11 | |||
Comma list: 64/63, 2744/2673 | |||
{{Mapping|legend=0| 1 0 6 21 | 0 1 -2 -11 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1196.7477{{c}}, ~3/2 = 710.3039{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 712.4735{{c}} | |||
{{Optimal ET sequence|legend=0| 27e, 32, 91bdee, 123bbdee }} | |||
Badness (Sintel): 1.02 | |||
==== Flutterpyth ==== | |||
Subgroup: 2.3.7.11.13 | |||
Comma list: 64/63, 364/363, 1078/1053 | |||
{{Mapping|legend=0| 1 0 6 21 34 | 0 1 -2 -11 -19 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1196.9412{{c}}, ~3/2 = 711.0195{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 713.0039{{c}} | |||
{{Optimal ET sequence|legend=0| 32f, 69bf, 101beff }} | |||
Badness (Sintel): 1.52 | |||
===== 2.3.7.11.13.19 subgroup ===== | |||
Subgroup: 2.3.7.11.13.19 | |||
Comma list: 64/63, 209/208, 343/342, 364/363 | |||
{{Mapping|legend=0| 1 0 6 21 34 17 | 0 1 -2 -11 -19 -8 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1197.4072{{c}}, ~3/2 = 711.2733{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 712.9612{{c}} | |||
{{Optimal ET sequence|legend=0| 32f, 69bf }} | |||
Badness (Sintel): 1.28 | |||
=== Oceanfront (2.3.7.13/5) === | === Oceanfront (2.3.7.13/5) === | ||