Llywelynsmic clan: Difference between revisions

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[[Comma list]]: 4194304/4117715

: mapping generators: ~2, ~8/7

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[[Badness]] (Sintel): 2.06

Scales: [[Shoe5]], [[Shoe6]], [[Shoe11]], [[Shoe16]]

=== Overview to extensions ===

~~Full~~ 7-limit [[extension]]s of llywelyn ~~temperament~~ include:

Strong 7-limit [[extension]]s of llywelyn include gorgo (16 & 21), gorgik (21 & 37), and semaja (16 & 37). These temperaments are distributed into different family pages.

* [[Gorgo]] (+36/35) → [[Gamelismic clan #Gorgo|Gamelismic clan]]

* ''[[Gorgo]]'' (+36/35) → [[Gamelismic clan #Gorgo|Gamelismic clan]]

* ''[[Gorgik]]'' (+2401/2400) → [[Breedsmic temperaments #Gorgik|Breedsmic temperaments]]

* ''[[Semaja]]'' (+3125/3087) → [[Gariboh clan #Semaja|Gariboh clan]]

The rest are weak extensions. Misneb (21 & 32) splits 8/7 into two for 15/14~16/15 each. Ultrapyth (32 & 37) splits 16/7 into two for a perfect fifth. Buzzard (53 & 58) splits 16/7 into three, each for 21/16.

Discussed elsewhere are

* [[Ultrapyth]] (+64/63) → [[Archytas clan #Ultrapyth|Archytas clan]]

* ''[[Misneb]]'' (+225/224) → [[Marvel temperaments #Misneb|Marvel temperaments]]

* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan]]

* [[Semaja]] (+3125/3087) → [[Porwell temperaments #Semaja|Porwell temperaments]]

* [[Misneb]] (+225/224) → [[Marvel temperaments #Misneb|Marvel temperaments]]

* [[Gorgik]] (+2401/2400) → [[Breedsmic temperaments #Gorgik|Breedsmic temperaments]]

~~Discussed~~ immediately below is the canonical 2.5.7.11-subgroup to 2.5.7.11.13.17-subgroup extension.

Considered immediately below is the canonical 2.5.7.11-subgroup to 2.5.7.11.13.17-subgroup extension.

=== 2.5.7.11 subgroup ===

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Comma list: 176/175, 1310720/1294139

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 1 3 1 | 0 7 -1 13 }}

~~Gencom mapping:~~ {{~~mapping~~| 1 0 1 3 1 | 0 0 7 -1 13 }}

Optimal tunings:

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Comma list: 176/175, 640/637, 847/845

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 1 3 1 2 | 0 7 -1 13 9 }}

~~Gencom mapping:~~ {{~~mapping~~| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }}

Optimal tunings:

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Comma list: 176/175, 221/220, 640/637, 847/845

~~Subgroup-val mapping:~~ {{~~mapping~~| 1 1 3 1 2 2 | 0 7 -1 13 9 11 }}

~~Gencom mapping:~~ {{~~mapping~~| 1 0 1 3 1 2 2 | 0 0 7 -1 13 9 11 }}

Optimal tunings:

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Badness (Sintel): 0.458

[[Category:Llywelynsmic clan| ]]

[[Category:Temperament clans]]

[[Category:~~Llywelynsmic clan| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-2 temperaments]]

~~[[Category:Rank~~ 2]]

@@ Line 9: / Line 9: @@
 [[Comma list]]: 4194304/4117715
-{{Mapping|legend=2| 1 1 3 | 0 7 -1 }}
+{{Mapping|legend=3| 1 1 3 | 0 7 -1 }}
-{{Mapping|legend=3| 1 0 1 3 | 0 0 7 -1 }}
+{{Mapping|legend=5| 1 0 1 3 | 0 0 7 -1 }}
 : mapping generators: ~2, ~8/7
@@ Line 23: / Line 23: @@
 [[Badness]] (Sintel): 2.06
+Scales: [[Shoe5]], [[Shoe6]], [[Shoe11]], [[Shoe16]]
 === Overview to extensions ===
-Full 7-limit [[extension]]s of llywelyn temperament include:
+Strong 7-limit [[extension]]s of llywelyn include gorgo (16 & 21), gorgik (21 & 37), and semaja (16 & 37). These temperaments are distributed into different family pages.
-* [[Gorgo]] (+36/35) → [[Gamelismic clan #Gorgo|Gamelismic clan]]
+* ''[[Gorgo]]'' (+36/35) → [[Gamelismic clan #Gorgo|Gamelismic clan]]
+* ''[[Gorgik]]'' (+2401/2400) → [[Breedsmic temperaments #Gorgik|Breedsmic temperaments]]
+* ''[[Semaja]]'' (+3125/3087) → [[Gariboh clan #Semaja|Gariboh clan]]
+The rest are weak extensions. Misneb (21 & 32) splits 8/7 into two for 15/14~16/15 each. Ultrapyth (32 & 37) splits 16/7 into two for a perfect fifth. Buzzard (53 & 58) splits 16/7 into three, each for 21/16.
+Discussed elsewhere are
 * [[Ultrapyth]] (+64/63) → [[Archytas clan #Ultrapyth|Archytas clan]]
+* ''[[Misneb]]'' (+225/224) → [[Marvel temperaments #Misneb|Marvel temperaments]]
 * [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan]]
-* [[Semaja]] (+3125/3087) → [[Porwell temperaments #Semaja|Porwell temperaments]]
-* [[Misneb]] (+225/224) → [[Marvel temperaments #Misneb|Marvel temperaments]]
-* [[Gorgik]] (+2401/2400) → [[Breedsmic temperaments #Gorgik|Breedsmic temperaments]]
-Discussed immediately below is the canonical 2.5.7.11-subgroup to 2.5.7.11.13.17-subgroup extension.
+Considered immediately below is the canonical 2.5.7.11-subgroup to 2.5.7.11.13.17-subgroup extension.
 === 2.5.7.11 subgroup ===
@@ Line 40: / Line 46: @@
 Comma list: 176/175, 1310720/1294139
-Subgroup-val mapping: {{mapping| 1 1 3 1 | 0 7 -1 13 }}
+{{Mapping|legend=2| 1 1 3 1 | 0 7 -1 13 }}
-Gencom mapping: {{mapping| 1 0 1 3 1 | 0 0 7 -1 13 }}
+{{Mapping|legend=4| 1 0 1 3 1 | 0 0 7 -1 13 }}
 Optimal tunings:
@@ Line 57: / Line 63: @@
 Comma list: 176/175, 640/637, 847/845
-Subgroup-val mapping: {{mapping| 1 1 3 1 2 | 0 7 -1 13 9 }}
+{{Mapping|legend=2| 1 1 3 1 2 | 0 7 -1 13 9 }}
-Gencom mapping: {{mapping| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }}
+{{Mapping|legend=4| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }}
 Optimal tunings:
@@ Line 74: / Line 80: @@
 Comma list: 176/175, 221/220, 640/637, 847/845
-Subgroup-val mapping: {{mapping| 1 1 3 1 2 2 | 0 7 -1 13 9 11 }}
+{{Mapping|legend=2| 1 1 3 1 2 2 | 0 7 -1 13 9 11 }}
-Gencom mapping: {{mapping| 1 0 1 3 1 2 2 | 0 0 7 -1 13 9 11 }}
+{{Mapping|legend=4| 1 0 1 3 1 2 2 | 0 0 7 -1 13 9 11 }}
 Optimal tunings:
@@ Line 86: / Line 92: @@
 Badness (Sintel): 0.458
+[[Category:Llywelynsmic clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Llywelynsmic clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]