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Breedsmic temperaments: Difference between revisions

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== Surmarvelpyth ==
== Surmarvelpyth ==
Named because the generator fifth, 675/448 is 225/224 (marvel comma) sharp of 3/2. Defined as the 311 & 742 temperament starting with the 7-limit to the 19-limit.
''Surmarvelpyth'' is named for the generator fifth, 675/448 being 225/224 (marvel comma) sharp of 3/2. It can be described as the 311 & 431 temperament, starting with the 7-limit to the 19-limit.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


Comma list: 2401/2400, {{monzo|88 -33 -19 3}}
[[Comma list]]: 2401/2400, {{monzo| 93 -32 -17 -1 }}


Mapping: {{val|1 43 -74 -25}}, {{val|0 -70 129 47}}
[[Mapping]]: {{val| 1 43 -74 -25 }}, {{val| 0 -70 129 47 }}


Optimal tuning (CTE): ~675/448 = 709.972
Mapping generators: ~2, ~675/448
 
[[Optimal tuning]] ([[CTE]]): ~675/448 = 709.9719
 
{{Val list|legend=1| 120, 191, 311, 742, 1053, 2848, 3901 }}
 
[[Badness]]: 0.202


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 2401/2400, 820125/819896, 22478848/22460625
Comma list: 2401/2400, 820125/819896, 2097152/2096325
 
Mapping: {{val| 1 43 -74 -25 36 }}, {{val| 0 -70 129 47 -55 }}


Mapping: {{val|1 43 -74 -25 36}}, {{val|0 -70 129 47 -55}}
Optimal tuning (CTE): ~675/448 = 709.9720


Optimal tuning (CTE): ~675/448 = 709.972
Optimal GPV sequence: {{val list| 120, 191, 311, 742, 1053, 1795 }}
 
Badness: 0.0523


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 2401/2400, 4096/4095, 6656/6655, 59535/59488
Comma list: 2401/2400, 4096/4095, 6656/6655, 24192/24167
 
Mapping: {{val| 1 43 -74 -25 36 25 }}, {{val| 0 -70 129 47 -55 -36 }}
 
Optimal tuning (CTE): ~98/65 = 709.9723


Mapping: {{val|1 43 -74 -25 36 25}}, {{val|0 -70 129 47 -55 -36}}
Optimal GPV sequence: {{val list| 120, 191, 311, 742, 1053, 1795f }}


Optimal tuning (CTE): ~98/65 = 709.972
Badness: 0.0325


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 2401/2400, 4096/4095, 11016/11011, 12376/12375, 14400/14399
Comma list: 2401/2400, 2601/2600, 4096/4095, 6656/6655, 8624/8619
 
Mapping: {{val| 1 43 -74 -25 36 25 -103 }}, {{val| 0 -70 129 47 -55 -36 181 }}
 
Optimal tuning (CTE): ~98/65 = 709.9722


Mapping: {{val|1 43 -74 -25 36 25 -103}}, {{val|0 -70 129 47 -55 -36 181}}
Optimal GPV sequence: {{val list| 120g, 191g, 311, 431, 742, 1795f }}


Optimal tuning (CTE): ~98/65 = 709.972
Badness: 0.0325


===19-limit===
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 2926/2925, 4096/4095, 3136/3135, 12376/12375, 5985/5984, 11016/11011
Comma list: 2401/2400, 2601/2600, 2926/2925, 3136/3135, 3213/3211, 5985/5984
 
Mapping: {{val| 1 43 -74 -25 36 25 -103 -49 }}, {{val| 0 -70 129 47 -55 -36 181 90 }}
 
Optimal tuning (CTE): ~98/65 = 709.9722
 
Optimal GPV sequence: {{val list| 120g, 191g, 311, 431, 742, 1795f }}


Mapping: {{val|1 43 -74 -25 36 25 -103 -49}}, {{val|0 -70 129 47 -55 -36 181 90}}
Badness: 0.0138


Optimal tuning (CTE): ~675/448 = 709.972
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Breedsmic temperaments| ]] <!-- main article -->
[[Category:Breedsmic temperaments| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
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