Llywelynsmic clan: Difference between revisions

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Created page with "The '''llywelyn clan''' tempers out the no-threes llywelyn comma, {{Monzo|22 0 -1 -7}} = 4194304/4117715. == Llywelyn == Subgroup: 2.5.7 Comma list: 4194304/4117715..."
 
 
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The '''llywelyn clan''' tempers out the no-threes llywelyn comma, {{Monzo|22 0 -1 -7}} = [[4194304/4117715]].  
{{Technical data page}}
The '''llywelyn clan''' tempers out the no-threes [[llywelyn comma]], {{monzo| 22 0 -1 -7 }} = 4194304/4117715.  


== Llywelyn ==
Full 7-limit [[extension]]s of llywelyn temperament include:
Subgroup: 2.5.7
* [[Gorgo]] (+36/35) → [[Gamelismic clan #Gorgo|Gamelismic clan]]
* [[Ultrapyth]] (+64/63) → [[Archytas clan #Ultrapyth|Archytas clan]]
* [[Buzzard]] (+1728/1715) → [[Vulture family]]
* [[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 below is the 2.5.7 subgroup temperament llywelyn a.k.a. shoe.
 
== Llywelyn a.k.a. shoe ==
Llywelyn a.k.a. shoe can be described as the 16 & 21 temperament, starting with the 2.5.7 subgroup up to the no-3 17-limit.
 
[[Subgroup]]: 2.5.7


[[Comma list]]: 4194304/4117715
[[Comma list]]: 4194304/4117715


[[Sval]] [[mapping]]: [{{Val| 1 1 3 }}, {{Val| 0 7 -1 }}]
{{Mapping|legend=2| 1 1 3 | 0 7 -1 }}


Mapping generators: 2, ~8/7
: mapping generators: ~2, ~8/7


Gencom mapping: [{{Val| 1 0 1 3 }}, {{Val| 0 0 7 -1 }}]
{{Mapping|legend=3| 1 0 1 3 | 0 0 7 -1 }}


[[Gencom]]: [2 8/7; 4194304/4117715]
: [[Gencom]]: [2 8/7; 4194304/4117715]


[[POTE generator]]: ~8/7 = 226.910
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 226.910


{{Val list|legend=1| 5, 11c, 16, 21, 37 }}
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }}


=== Extensions ===
=== 2.5.7.11 subgroup ===
Full 7-limit [[extension]]s of llywelyn temperament include:
Subgroup: 2.5.7.11
* [[Gorgo]], {36/35, 1029/1024} ([[Gamelismic clan #Gorgo|Gamelismic clan]])
 
* [[Ultrapyth]], {64/63, 6860/6561} ([[Archytas clan #Ultrapyth|Archytas clan]])
Comma list: 176/175, 1310720/1294139
* [[Buzzard]], {1728/1715, 5120/5103} ([[Vulture family|Vulture]]/[[Hemifamity temperaments #Buzzard|Hemifamity]])
 
* [[Semaja]], {3125/3087, 6144/6125} ([[Porwell temperaments #Semaja|Porwell temperaments]])
Sval mapping: {{mapping| 1 1 3 1 | 0 7 -1 13 }}
* [[Misneb]], {225/224, 4194304/4117715} ([[Marvel temperaments #Misneb|Marvel temperaments]])
 
* [[Gorgik]], {2401/2400, 28672/28125} ([[Breedsmic temperaments #Gorgik|Breedsmic temperaments]])
Gencom mapping: {{mapping| 1 0 1 3 1 | 0 0 7 -1 13 }}
 
: gencom: [2 8/7; 176/175 1310720/1294139]
 
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.114
 
{{Optimal ET sequence|legend=1| 16, 21, 37, 206cd }}
 
=== 2.5.7.11.13 subgroup ===
Subgroup: 2.5.7.11.13
 
Comma list: 176/175, 640/637, 847/845
 
Sval 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 }}
 
: gencom: [2 8/7; 176/175 640/637, 1304576/1294139]
 
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.108
 
{{Optimal ET sequence|legend=1| 16, 21, 37, 206cdf }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.5433 cents
 
=== 2.5.7.11.13.17 subgroup ===
Subgroup: 2.5.7.11.13.17
 
Comma list: 176/175, 221/220, 640/637, 847/845
 
Sval 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 tuning (POTE): ~2 = 1\1, ~8/7 = 227.242
 
{{Optimal ET sequence|legend=1| 16, 21, 37, 95 }}


[[Category:Regular temperament theory]]
[[Category:Temperament clans]]
[[Category:Temperament clan]]
[[Category:Pages with mostly numerical content]]
[[Category:Llywelynsmic clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 00:26, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The llywelyn clan tempers out the no-threes llywelyn comma, [22 0 -1 -7⟩ = 4194304/4117715.

Full 7-limit extensions of llywelyn temperament include:

Discussed below is the 2.5.7 subgroup temperament llywelyn a.k.a. shoe.

Llywelyn a.k.a. shoe

Llywelyn a.k.a. shoe can be described as the 16 & 21 temperament, starting with the 2.5.7 subgroup up to the no-3 17-limit.

Subgroup: 2.5.7

Comma list: 4194304/4117715

Subgroup-val mapping: [⟨1 1 3], ⟨0 7 -1]]

mapping generators: ~2, ~8/7

Gencom mapping: [⟨1 0 1 3], ⟨0 0 7 -1]]

Gencom: [2 8/7; 4194304/4117715]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 226.910

Optimal ET sequence: 5, 11c, 16, 21, 37, 164d

2.5.7.11 subgroup

Subgroup: 2.5.7.11

Comma list: 176/175, 1310720/1294139

Sval mapping: [⟨1 1 3 1], ⟨0 7 -1 13]]

Gencom mapping: [⟨1 0 1 3 1], ⟨0 0 7 -1 13]]

gencom: [2 8/7; 176/175 1310720/1294139]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.114

Optimal ET sequence: 16, 21, 37, 206cd

2.5.7.11.13 subgroup

Subgroup: 2.5.7.11.13

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

Sval mapping: [⟨1 1 3 1 2], ⟨0 7 -1 13 9]]

Gencom mapping: [⟨1 0 1 3 1 2], ⟨0 0 7 -1 13 9]]

gencom: [2 8/7; 176/175 640/637, 1304576/1294139]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.108

Optimal ET sequence: 16, 21, 37, 206cdf

RMS error: 0.5433 cents

2.5.7.11.13.17 subgroup

Subgroup: 2.5.7.11.13.17

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

Sval mapping: [⟨1 1 3 1 2 2], ⟨0 7 -1 13 9 11]]

Gencom mapping: [⟨1 0 1 3 1 2 2], ⟨0 0 7 -1 13 9 11]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.242

Optimal ET sequence: 16, 21, 37, 95

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