Gamelismic clan: Difference between revisions

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==== Subgroup extensions ====

No-5 subgroup extensions of slendric include radon, a 2.3.7.11-subgroup extension that may be viewed as no-5 rodan~~, considered below~~, euslendric, a 2.3.7.13-subgroup extension, baladic, a weak 2.3.7.13-subgroup extension, trisect, a weak 2.3.7.11/5-subgroup extension, and gigapyth, a 2.3.7.85-subgroup extension, considered in [[#~~Other subgroup extensions]].~~

No-5 subgroup extensions of slendric include radon, a 2.3.7.11-subgroup extension that may be viewed as no-5 rodan, euslendric, a 2.3.7.13-subgroup extension, baladic, a weak 2.3.7.13-subgroup extension, trisect, a weak 2.3.7.11/5-subgroup extension, and gigapyth, a 2.3.7.85-subgroup extension, considered in [[#Subgroup extensions_2|#Subgroup extensions]].

~~=== Radon ===~~

~~{{See also~~|~~Chromatic pairs~~ #~~Radon}}~~

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

~~Subgroup: 2.3.7.11~~

~~Comma list: 896/891, 1029/1024~~

~~{{Mapping|legend=2| 1 1 3 6 | 0 3 -1 -13 }}~~

~~{{Mapping|legend=4| 1 1 0 3 6 | 0 3 0 -1 -13 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.9708{{c}}, ~8/7 = 234.3748{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.3813{{c}}

~~{{Optimal ET sequence|legend=0| 5, …, 36, 41, 87, 128 }}~~

~~Badness (Sintel): 0~~.~~619~~

== Mothra ==

Line 1,936:

Line 1,915:

Badness (Sintel): 0.894

== ~~Other subgroup~~ extensions ==

== Subgroup extensions ==

=== Radon (2.3.7.11) ===

Radon is the no-5's version of [[rodan]], equating the diatonic major third to [[14/11]].

Subgroup: 2.3.7.11

Comma list: 896/891, 1029/1024

Optimal tunings:

* WE: ~2 = 1199.9708{{c}}, ~8/7 = 234.3748{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.3813{{c}}

Badness (Sintel): 0.619

=== 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 46: / Line 46: @@
 ==== Subgroup extensions ====
-No-5 subgroup extensions of slendric include radon, a 2.3.7.11-subgroup extension that may be viewed as no-5 rodan, considered below, euslendric, a 2.3.7.13-subgroup extension, baladic, a weak 2.3.7.13-subgroup extension, trisect, a weak 2.3.7.11/5-subgroup extension, and gigapyth, a 2.3.7.85-subgroup extension, considered in [[#Other subgroup extensions]].
+No-5 subgroup extensions of slendric include radon, a 2.3.7.11-subgroup extension that may be viewed as no-5 rodan, euslendric, a 2.3.7.13-subgroup extension, baladic, a weak 2.3.7.13-subgroup extension, trisect, a weak 2.3.7.11/5-subgroup extension, and gigapyth, a 2.3.7.85-subgroup extension, considered in [[#Subgroup extensions_2|#Subgroup extensions]].
-=== Radon ===
-{{See also|Chromatic pairs #Radon}}
-Radon is the no-fives version of [[rodan]], equating the diatonic major third to [[14/11]].
-Subgroup: 2.3.7.11
-Comma list: 896/891, 1029/1024
-{{Mapping|legend=2| 1 1 3 6 | 0 3 -1 -13 }}
-{{Mapping|legend=4| 1 1 0 3 6 | 0 3 0 -1 -13 }}
-Optimal tunings:
-* WE: ~2 = 1199.9708{{c}}, ~8/7 = 234.3748{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.3813{{c}}
-{{Optimal ET sequence|legend=0| 5, …, 36, 41, 87, 128 }}
-Badness (Sintel): 0.619
 == Mothra ==
@@ Line 1,936: / Line 1,915: @@
 Badness (Sintel): 0.894
-== Other subgroup extensions ==
+== Subgroup extensions ==
+=== Radon (2.3.7.11) ===
+{{See also|Chromatic pairs #Radon}}
+Radon is the no-5's version of [[rodan]], equating the diatonic major third to [[14/11]].
+Subgroup: 2.3.7.11
+Comma list: 896/891, 1029/1024
+{{Mapping|legend=2| 1 1 3 6 | 0 3 -1 -13 }}
+{{Mapping|legend=4| 1 1 0 3 6 | 0 3 0 -1 -13 }}
+Optimal tunings:
+* WE: ~2 = 1199.9708{{c}}, ~8/7 = 234.3748{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.3813{{c}}
+{{Optimal ET sequence|legend=0| 5, …, 36, 41, 87, 128 }}
+Badness (Sintel): 0.619
 === 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.