Gamelismic clan: Difference between revisions
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==== Subgroup extensions ==== | ==== Subgroup extensions ==== | ||
No-five subgroup extensions of slendric include radon, a 2.3.7.11-subgroup extension that may be viewed as no-five rodan, considered below, euslendric, a 2.3.7.13-subgroup extension, | No-five subgroup extensions of slendric include radon, a 2.3.7.11-subgroup extension that may be viewed as no-five rodan, considered below, euslendric, a 2.3.7.13-subgroup extension, baladic, a weak 2.3.7.13.17-subgroup extension, and gigapyth, a 2.3.7.85-subgroup extension, considered in [[#Other subgroup extensions]]. Dicussed elsewhere is [[Subgroup temperaments #Trisect|trisect]] in the 2.3.7.11/5 subgroup. | ||
=== Radon === | === Radon === | ||
{{See also|Chromatic pairs #Radon}} | |||
Radon is the no-fives version of [[rodan]], equating the diatonic major third to [[14/11]]. | Radon is the no-fives version of [[rodan]], equating the diatonic major third to [[14/11]]. | ||
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== Other subgroup extensions == | == Other subgroup extensions == | ||
=== Euslendric === | === Euslendric (2.3.7.13) === | ||
Forms of slendric in the most optimal range for the 2.3.7 temperament ({{nowrap| 36 & 77 }}) lack an obvious strong mapping of prime 5 or prime 11. However, slendric can extend well to the no-fives no-elevens [[29-limit]] by tempering out [[273/272]], [[343/342]], [[378/377]], [[392/391]], [[513/512]], and [[729/728]], or a comma basis defined in terms of [[S-expression]]s as {S7/S8, S14/S16, S15/S20, S24/S26, S27, S28}. [[113edo]] is an obvious tuning. | Forms of slendric in the most optimal range for the 2.3.7 temperament ({{nowrap| 36 & 77 }}) lack an obvious strong mapping of prime 5 or prime 11. However, slendric can extend well to the no-fives no-elevens [[29-limit]] by tempering out [[273/272]], [[343/342]], [[378/377]], [[392/391]], [[513/512]], and [[729/728]], or a comma basis defined in terms of [[S-expression]]s as {S7/S8, S14/S16, S15/S20, S24/S26, S27, S28}. [[113edo]] is an obvious tuning. | ||
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Badness (Sintel): 0.473 | Badness (Sintel): 0.473 | ||
=== Baladic === | === Baladic (2.3.7.13) === | ||
Baladic is a 2.3.7.13.17-subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. It tempers out [[169/168]] ({{S|13}}), which splits [[7/6]] in half ([[13/12]]~[[14/13]]) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]]. 36edo is an excellent baladic tuning. | Baladic is a 2.3.7.13.17-subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. It tempers out [[169/168]] ({{S|13}}), which splits [[7/6]] in half ([[13/12]]~[[14/13]]) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]]. 36edo is an excellent baladic tuning. | ||
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Badness (Sintel): 0.253 | Badness (Sintel): 0.253 | ||
=== Gigapyth (2.3.7.85) === | |||
Subgroup: 2.3.7.85 | |||
Comma list: 1029/1024, 7225/7203 | |||
Subgroup-val mapping: {{mapping| 1 -2 4 7 | 0 6 -2 -1 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1200.8295{{c}}, ~128/85 = 717.2597{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~128/85 = 716.7933{{c}} | |||
{{Optimal ET sequence|legend=0| 5, 42*, 47, 52, 57, 62, 67, 72, 149*, 370d***, 519bdd***** }} | |||
<nowiki/>* Wart for 85 | |||
== References == | == References == | ||