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]].  
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, 1029/1024} → [[Gamelismic clan #Gorgo|Gamelismic clan]]
* [[Ultrapyth]], {64/63, 6860/6561} → [[Archytas clan #Ultrapyth|Archytas clan]]
* [[Buzzard]], {1728/1715, 5120/5103} → [[Vulture family]] / [[Hemifamity temperaments #Buzzard|Hemifamity temperaments]]
* [[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]]
 
Discussed below is the 2.5.7 subgroup temperament llywelyn aka shoe.
 
== Llywelyn aka shoe ==
[[Subgroup]]: 2.5.7


[[Comma list]]: 4194304/4117715
[[Comma list]]: 4194304/4117715
Line 10: Line 20:
Mapping generators: 2, ~8/7
Mapping generators: 2, ~8/7


Gencom mapping: [{{Val| 1 0 1 3 }}, {{Val| 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]


[[POTE generator]]: ~8/7 = 226.910
[[Optimal tuning]] ([[POTE]]): ~8/7 = 226.910


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


[[Comma]]: 176/175, 1310720/1294139
Comma list: 176/175, 1310720/1294139


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


[[Tp tuning|POL2 generator]]: ~8/7 = 227.114
Optimal tuning (POTE): ~8/7 = 227.114


{{Val list|legend=1| 16, 21, 37 }}
Optimal GPV sequence: {{Val list| 16, 21, 37 }}
====2.5.7.11.13====
 
=== 2.5.7.11.13 subgroup ===
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: [{{val| 1 1 3 1 2 }}, {{val| 0 7 -1 13 9 }}]


[[Gencom|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]


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


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


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


====2.5.7.11.13.17====
=== 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, 221/200, 640/637, 833/832


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


[[Mapping|Sval mapping]]: [{{val|1 1 3 1 2 2}}, {{val|0 7 -1 13 9 11}}]
Gencom mapping: [{{val| 1 0 1 3 1 2 2 }}, {{val| 0 0 7 -1 13 9 11 }}]


[[Tp tuning|POL2 generator]]: ~8/7 = 227.242
Optimal tuning (POTE): ~8/7 = 227.242


{{Val list|legend=1| 16, 21, 37 }}
Optimal GPV sequence: {{Val list| 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:Rank 2]]
[[Category:Rank 2]]
[[Category:Llywelyn clan| ]] <!-- main article -->

Revision as of 16:14, 30 August 2022

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 aka shoe.

Llywelyn aka shoe

Subgroup: 2.5.7

Comma list: 4194304/4117715

Sval 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): ~8/7 = 226.910

Template:Val list

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

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

Optimal tuning (POTE): ~8/7 = 227.114

Optimal GPV sequence: Template:Val list

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

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

Optimal tuning (POTE): ~8/7 = 227.108

Optimal GPV sequence: Template:Val list

2.5.7.11.13.17 subgroup

Subgroup: 2.5.7.11.13.17

Comma list: 176/175, 221/200, 640/637, 833/832

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

Gencom: [2 8/7; 176/175 221/200, 640/637, 833/832]

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

Optimal tuning (POTE): ~8/7 = 227.242

Optimal GPV sequence: Template:Val list

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