Gamelismic clan: Difference between revisions

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

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

* ''[[~~Blacksmith~~]]'' (+28/27) → [[Limmic temperaments #~~Blacksmith~~|Limmic temperaments]]

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

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

* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]

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=== Euslendric ===

Forms of slendric in the most optimal range for the 2.3.7 temperament (36 & 77) lack an obvious strong mapping of prime 5 or prime 11. However, slendric can extend well to ~~2.3.7.13.17.19.~~29 by tempering out [[273/272]], [[343/342]], [[378/377]], [[513/512]], and [[729/728]], or a comma basis defined in terms of [[S-expression]]s as {S7/S8, S14/S16, S15/S20, S27, S28}.

Forms of slendric in the most optimal range for the 2.3.7 temperament (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.

==== 2.3.7.13 ====

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Badness (Dirichlet): 0.339

==== 2.3.7.13.17 ====

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Badness (Dirichlet): 0.332

==== 2.3.7.13.17.19 ====

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==== 2.3.7.13.17.19.29 ====

Badness (Dirichlet): 0.380

Subgroup: 2.3.7.13.17.19.29

==== 2.3.7.13.17.19.23 ====

Subgroup: 2.3.7.13.17.19.23

Comma list: 273/272, 343/342, 392/391, 513/512, 729/728

Sval mapping: [{{val|1 1 3 0 0 6 9}}, {{val|0 3 -1 19 21 -9 -23}}]

Optimal tunings:

* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.624

* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.607

Badness (Dirichlet): 0.474

==== 2.3.7.13.17.19.23.29 ====

Subgroup: 2.3.7.13.17.19.23.29

Comma list: 273/272, 343/342, 378/377, 513/512, ~~729~~/~~728~~

Comma list: 273/272, 343/342, 378/377, 392/391, 513/512, 609/608

Sval mapping: [{{val|1 1 3 0 0 6 7}}, {{val|0 3 -1 19 21 -9 -11}}]

Sval mapping: [{{val|1 1 3 0 0 6 9 7}}, {{val|0 3 -1 19 21 -9 -23 -11}}]

Optimal tunings:

* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.~~655~~

* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.626

* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.~~629~~

* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.620

Badness (Dirichlet): 0.473

=== Radon ===

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=== Baladic ===

Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. It tempers out {{S|13}} = [[169/168]], 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]]~[[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 {{S|13}} = [[169/168]], 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.

==== 2.3.7.13 ====

@@ Line 9: / Line 9: @@
 * [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
 * ''[[Echidnic]]'' (+686/675} → [[Diaschismic family #Echidnic|Diaschismic family]]
-* ''[[Blacksmith]]'' (+28/27) → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
+* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood|Limmic temperaments]]
 * ''[[Trismegistus]]'' (+3125/3072) → [[Magic family #Trismegistus|Magic family]]
 * [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]
@@ Line 46: / Line 46: @@
 === Euslendric ===
-Forms of slendric in the most optimal range for the 2.3.7 temperament (36 & 77) lack an obvious strong mapping of prime 5 or prime 11. However, slendric can extend well to 2.3.7.13.17.19.29 by tempering out [[273/272]], [[343/342]], [[378/377]], [[513/512]], and [[729/728]], or a comma basis defined in terms of [[S-expression]]s as {S7/S8, S14/S16, S15/S20, S27, S28}.
+Forms of slendric in the most optimal range for the 2.3.7 temperament (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.
 ==== 2.3.7.13 ====
@@ Line 60: / Line 60: @@
 {{Optimal ET sequence|legend=1| 5, ..., 31f, 36, 77, 113 }}
+Badness (Dirichlet): 0.339
 ==== 2.3.7.13.17 ====
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 {{Optimal ET sequence|legend=1| 5g, ..., 31fg, 36, 113, 149 }}
+Badness (Dirichlet): 0.332
 ==== 2.3.7.13.17.19 ====
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 {{Optimal ET sequence|legend=1| 5g, ..., 36, 77, 113 }}
-==== 2.3.7.13.17.19.29 ====
+Badness (Dirichlet): 0.380
-Subgroup: 2.3.7.13.17.19.29
+==== 2.3.7.13.17.19.23 ====
+Subgroup: 2.3.7.13.17.19.23
+Comma list: 273/272, 343/342, 392/391, 513/512, 729/728
+Sval mapping: [{{val|1 1 3 0 0 6 9}}, {{val|0 3 -1 19 21 -9 -23}}]
+Optimal tunings:
+* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.624
+* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.607
+{{Optimal ET sequence|legend=1| 5gi, ..., 36, 77, 113 }}
+Badness (Dirichlet): 0.474
+==== 2.3.7.13.17.19.23.29 ====
+Subgroup: 2.3.7.13.17.19.23.29
-Comma list: 273/272, 343/342, 378/377, 513/512, 729/728
+Comma list: 273/272, 343/342, 378/377, 392/391, 513/512, 609/608
-Sval mapping: [{{val|1 1 3 0 0 6 7}}, {{val|0 3 -1 19 21 -9 -11}}]
+Sval mapping: [{{val|1 1 3 0 0 6 9 7}}, {{val|0 3 -1 19 21 -9 -23 -11}}]
 Optimal tunings:
-* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.655
+* [[CTE]]: ~2/1 = 1200.000, ~8/7 = 233.626
-* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.629
+* [[POTE]]: ~2/1 = 1200.000, ~8/7 = 233.620
-{{Optimal ET sequence|legend=1| 5g, ..., 36, 77, 113 }}
+{{Optimal ET sequence|legend=1| 5gi, ..., 36, 77, 113 }}
+Badness (Dirichlet): 0.473
 === Radon ===
@@ Line 122: / Line 145: @@
 === Baladic ===
-Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. It tempers out {{S|13}} = [[169/168]], 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]]~[[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 {{S|13}} = [[169/168]], 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.
 ==== 2.3.7.13 ====