Llywelynsmic clan: Difference between revisions

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{{Technical data page}}
The '''llywelyn clan''' tempers out the no-threes [[llywelyn comma]], {{monzo| 22 0 -1 -7 }} = 4194304/4117715.  
The '''llywelyn clan''' tempers out the no-threes [[llywelyn comma]], {{monzo| 22 0 -1 -7 }} = 4194304/4117715.  


Full 7-limit [[extension]]s of llywelyn temperament include:
Full 7-limit [[extension]]s of llywelyn temperament include:
* [[Gorgo]], {36/35, 1029/1024} → [[Gamelismic clan #Gorgo|Gamelismic clan]]
* [[Gorgo]] (+36/35) → [[Gamelismic clan #Gorgo|Gamelismic clan]]
* [[Ultrapyth]], {64/63, 6860/6561} → [[Archytas clan #Ultrapyth|Archytas clan]]
* [[Ultrapyth]] (+64/63) → [[Archytas clan #Ultrapyth|Archytas clan]]
* [[Buzzard]], {1728/1715, 5120/5103} → [[Vulture family]] / [[Hemifamity temperaments #Buzzard|Hemifamity temperaments]]
* [[Buzzard]] (+1728/1715) → [[Vulture family]]
* [[Semaja]], {3125/3087, 6144/6125} → [[Porwell temperaments #Semaja|Porwell temperaments]]
* [[Semaja]] (+3125/3087) → [[Porwell temperaments #Semaja|Porwell temperaments]]
* [[Misneb]], {225/224, 4194304/4117715} → [[Marvel temperaments #Misneb|Marvel temperaments]]
* [[Misneb]] (+225/224) → [[Marvel temperaments #Misneb|Marvel temperaments]]
* [[Gorgik]], {2401/2400, 28672/28125} → [[Breedsmic temperaments #Gorgik|Breedsmic temperaments]]
* [[Gorgik]] (+2401/2400) → [[Breedsmic temperaments #Gorgik|Breedsmic temperaments]]


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


== Llywelyn aka shoe ==
== Llywelyn a.k.a. shoe ==
{{See also| Chromatic pairs #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
[[Subgroup]]: 2.5.7
Line 18: Line 19:
[[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]


[[Optimal tuning]] ([[POTE]]): ~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 }}


=== 2.5.7.11 subgroup ===
=== 2.5.7.11 subgroup ===
Line 35: Line 36:
Comma list: 176/175, 1310720/1294139
Comma list: 176/175, 1310720/1294139


Sval mapping: [{{val| 1 1 3 1 }}, {{val| 0 7 -1 13 }}]
Sval mapping: {{mapping| 1 1 3 1 | 0 7 -1 13 }}


Gencom: [2 8/7; 176/175 1310720/1294139]
Gencom mapping: {{mapping| 1 0 1 3 1 | 0 0 7 -1 13 }}


Gencom mapping: [{{val| 1 0 1 3 1 }}, {{val| 0 0 7 -1 13 }}]
: gencom: [2 8/7; 176/175 1310720/1294139]


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


Optimal GPV sequence: {{Val list| 16, 21, 37 }}
{{Optimal ET sequence|legend=1| 16, 21, 37, 206cd }}


=== 2.5.7.11.13 subgroup ===
=== 2.5.7.11.13 subgroup ===
Line 50: Line 51:
Comma list: 176/175, 640/637, 847/845
Comma list: 176/175, 640/637, 847/845


Sval mapping: [{{val| 1 1 3 1 2 }}, {{val| 0 7 -1 13 9 }}]
Sval mapping: {{mapping| 1 1 3 1 2 | 0 7 -1 13 9 }}


Gencom: [2 8/7; 176/175 640/637, 1304576/1294139]
Gencom mapping: {{mapping| 1 0 1 3 1 2 | 0 0 7 -1 13 9 }}


Gencom mapping: [{{val| 1 0 1 3 1 2 }}, {{val| 0 0 7 -1 13 9 }}]
: gencom: [2 8/7; 176/175 640/637, 1304576/1294139]


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


Optimal GPV sequence: {{Val list| 16, 21, 37 }}
{{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 ===
=== 2.5.7.11.13.17 subgroup ===
Subgroup: 2.5.7.11.13.17
Subgroup: 2.5.7.11.13.17


Comma list: 176/175, 221/200, 640/637, 833/832
Comma list: 176/175, 221/220, 640/637, 847/845
 
Sval mapping: [{{val| 1 1 3 1 2 2 }}, {{val| 0 7 -1 13 9 11 }}]


Gencom: [2 8/7; 176/175 221/200, 640/637, 833/832]
Sval mapping: {{mapping| 1 1 3 1 2 2 | 0 7 -1 13 9 11 }}


Gencom mapping: [{{val| 1 0 1 3 1 2 2 }}, {{val| 0 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): ~8/7 = 227.242
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.242


Optimal GPV sequence: {{Val list| 16, 21, 37 }}
{{Optimal ET sequence|legend=1| 16, 21, 37, 95 }}


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

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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