Gamelismic clan: Difference between revisions

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* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]

* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]

* ''[[Trisected]]'' (+128/125) → [[Augmented family #Trisected|Augmented family]]

* [[Trisected]] (+128/125) → [[Augmented family #Trisected|Augmented family]]

* ''[[Echidnic]]'' (+686/675) → [[Diaschismic family #Echidnic|Diaschismic family]]

* [[Trismegistus]] (+3125/3072) → [[Magic family #Trismegistus|Magic family]]

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==== 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, ~~and~~ baladic, a weak 2.3.7.13.17-subgroup extension, considered in [[#Other subgroup extensions]]. Dicussed elsewhere is [[~~No-fives subgroup~~ temperaments #~~Gigapyth~~|~~gigapyth~~]] in the 2.3.7.85 subgroup.

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 is the no-fives version of [[rodan]], equating the diatonic major third to [[14/11]].

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Badness (Sintel): 0.990

~~; Music~~

* ''Prelude for solo piano'' (2014) by [[Chris Vaisvil]] – [https://web.archive.org/web/20201127013310/http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 play] | [https://www.chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ blog] – in Mothra[16], brat 4 tuning

==== 17-limit ====

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== 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.

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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.

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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 ==

@@ Line 33: / Line 33: @@
 * [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
 * [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
-* ''[[Trisected]]'' (+128/125) → [[Augmented family #Trisected|Augmented family]]
+* [[Trisected]] (+128/125) → [[Augmented family #Trisected|Augmented family]]
 * ''[[Echidnic]]'' (+686/675) → [[Diaschismic family #Echidnic|Diaschismic family]]
 * [[Trismegistus]] (+3125/3072) → [[Magic family #Trismegistus|Magic family]]
@@ Line 46: / Line 46: @@
 ==== 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, and baladic, a weak 2.3.7.13.17-subgroup extension, considered in [[#Other subgroup extensions]]. Dicussed elsewhere is [[No-fives subgroup temperaments #Gigapyth|gigapyth]] in the 2.3.7.85 subgroup.
+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 ===
+{{See also|Chromatic pairs #Radon}}
 Radon is the no-fives version of [[rodan]], equating the diatonic major third to [[14/11]].
@@ Line 130: / Line 132: @@
 Badness (Sintel): 0.990
-; Music
-* ''Prelude for solo piano'' (2014) by [[Chris Vaisvil]] – [https://web.archive.org/web/20201127013310/http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 play] | [https://www.chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ blog] – in Mothra[16], brat 4 tuning
 ==== 17-limit ====
@@ Line 1,936: / Line 1,935: @@
 == 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.
@@ Line 2,023: / Line 2,022: @@
 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.
@@ Line 2,059: / Line 2,058: @@
 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 ==