Llywelynsmic clan: Difference between revisions

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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
{{Mapping|legend=3| 1 0 1 3 | 0 0 7 -1 }}


Gencom mapping: [{{Val| 1 0 1 3 }}, {{Val| 0 0 7 -1 }}]
: [[Gencom]]: [2 8/7; 4194304/4117715]


[[Gencom]]: [2 8/7; 4194304/4117715]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 226.910


[[POTE generator]]: ~8/7 = 226.910
{{Optimal ET sequence|legend=1| 5, 11c, 16, 21, 37, 164d }}


{{Val list|legend=1| 5, 11c, 16, 21, 37 }}
=== 2.5.7.11 subgroup ===
====2.5.7.11====
Subgroup: 2.5.7.11
Subgroup: 2.5.7.11


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


[[Mapping|Sval mapping]]: [{{val|1 1 3 1}}, {{val|0 7 -1 13}}]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.114


[[Tp tuning|POL2 generator]]: ~8/7 = 227.114
{{Optimal ET sequence|legend=1| 16, 21, 37, 206cd }}


{{Val list|legend=1| 16, 21, 37 }}
=== 2.5.7.11.13 subgroup ===
====2.5.7.11.13====
Subgroup: 2.5.7.11.13
Subgroup: 2.5.7.11.13


[[Comma]]: 176/175, 640/637, 1304576/1294139
Comma list: 176/175, 640/637, 847/845


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


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


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


[[Tp tuning|POL2 generator]]: ~8/7 = 227.108
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.108


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


====2.5.7.11.13.17====
[[Tp tuning #T2 tuning|RMS error]]: 0.5433 cents
 
=== 2.5.7.11.13.17 subgroup ===
Subgroup: 2.5.7.11.13.17
Subgroup: 2.5.7.11.13.17


[[Comma]]: 176/175, 221/200, 640/637, 833/832
Comma list: 176/175, 221/220, 640/637, 847/845


[[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|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 }}


[[Mapping|Sval mapping]]: [{{val|1 1 3 1 2 2}}, {{val|0 7 -1 13 9 11}}]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.242


[[Tp tuning|POL2 generator]]: ~8/7 = 227.242
{{Optimal ET sequence|legend=1| 16, 21, 37, 95 }}
 
{{Val list|legend=1| 16, 21, 37 }}
 
=== Extensions ===
Full 7-limit [[extension]]s of llywelyn temperament include:
* [[Gorgo]], {36/35, 1029/1024} ([[Gamelismic clan #Gorgo|Gamelismic clan]])
* [[Ultrapyth]], {64/63, 6860/6561} ([[Archytas clan #Ultrapyth|Archytas clan]])
* [[Buzzard]], {1728/1715, 5120/5103} ([[Vulture family|Vulture]]/[[Hemifamity temperaments #Buzzard|Hemifamity]])
* [[Semaja]], {3125/3087, 6144/6125} ([[Porwell temperaments #Semaja|Porwell temperaments]])
* [[Misneb]], {225/224, 4194304/4117715} ([[Marvel temperaments #Misneb|Marvel temperaments]])
* [[Gorgik]], {2401/2400, 28672/28125} ([[Breedsmic temperaments #Gorgik|Breedsmic temperaments]])


[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[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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