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Amity family: Difference between revisions

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Re-sort the amicable extensions as amorous is more notable
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Amicable tempers out the [[breedsma]] as well as the [[canousma]], and may be described as the {{nowrap| 99 & 311 }} temperament.  
Amicable tempers out the [[breedsma]] as well as the [[canousma]], and may be described as the {{nowrap| 99 & 311 }} temperament.  


While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.  
There are multiple reasonable places for primes 11 and 13 in the interval chain. Amorous (99ef & 311) has these primes placed on the same side of the interval chain so it blends smarter with the lower harmonics. Amical (99 & 311) shows a slightly more accurate but much more complex alternative. Pseudoamorous (99ef & 113) and pseudoamical (99 & 113) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semi-octave period and the ~21/20 generator with [[harry]], but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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[[Badness]] (Sintel): 1.15
[[Badness]] (Sintel): 1.15
=== Amorous ===
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 6250/6237, 19712/19683
Mapping: {{mapping| 1 -17 -46 -26 -135 | 0 20 52 31 149 }}
Optimal tunings:
* WE: ~2 = 1200.0380{{c}}, ~40/21 = 1115.1458{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1109{{c}}
{{Optimal ET sequence|legend=0| 99e, 212, 311, 1145c, 1456cd }}
Badness (Sintel): 1.62
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
apping: {{mapping| 1 -17 -46 -26 -135 -171 | 0 20 52 31 149 188 }}
Optimal tunings:
* WE: ~2 = 1200.0543{{c}}, ~40/21 = 1115.1594{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1095{{c}}
{{Optimal ET sequence|legend=0| 99ef, 212, 311, 834, 1145c }}
Badness (Sintel): 1.43


=== Amical ===
=== Amical ===
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Optimal tunings:
Optimal tunings:
* WE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1094{{c}}
* WE: ~2 = 1199.9926{{c}}, ~40/21 = 1115.1094{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1162{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1162{{c}}


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Badness (Sintel): 2.06
Badness (Sintel): 2.06


=== Amorous ===
=== Pseudoamorous ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 2401/2400, 6250/6237, 19712/19683
Comma list: 243/242, 441/440, 980000/970299


Mapping: {{mapping| 1 -17 -46 -26 -135 | 0 20 52 31 149 }}
Mapping: {{mapping| 1 -17 -46 -26 -43 | 0 20 52 31 50 }}


Optimal tunings:
Optimal tunings:
* WE: ~2 = 1200.0380{{c}}, ~40/21 = 1115.1458{{c}}
* WE: ~2 = 1199.8269{{c}}, ~21/11 = 1114.9475{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1109{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1115.1038{{c}}
 
{{Optimal ET sequence|legend=0| 99e, 212e }} *


{{Optimal ET sequence|legend=0| 99e, 212, 311, 1145c, 1456cd }}
<nowiki/>* optimal patent val: [[113edo|113]]


Badness (Sintel): 1.62
Badness (Sintel): 1.87


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


Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
Comma list: 243/242, 364/363, 441/440, 1875/1859


apping: {{mapping| 1 -17 -46 -26 -135 -171 | 0 20 52 31 149 188 }}
Mapping: {{mapping| 1 -17 -46 -26 -43 -79 | 0 20 52 31 50 89 }}


Optimal tunings:
Optimal tunings:
* WE: ~2 = 1200.0543{{c}}, ~40/21 = 1115.1594{{c}}
* WE: ~2 = 1200.0182{{c}}, ~40/21 = 1115.1005{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1095{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.0840{{c}}


{{Optimal ET sequence|legend=0| 99ef, 212, 311, 834, 1145c }}
{{Optimal ET sequence|legend=0| 99ef, 113, 212ef }}


Badness (Sintel): 1.43
Badness (Sintel): 1.77


=== Pseudoamical ===
=== Pseudoamical ===
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Badness (Sintel): 1.94
Badness (Sintel): 1.94
=== Pseudoamorous ===
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 980000/970299
Mapping: {{mapping| 1 -17 -46 -26 -43 | 0 20 52 31 50 }}
Optimal tunings:
* WE: ~2 = 1199.8269{{c}}, ~21/11 = 1114.9475{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1115.1038{{c}}
{{Optimal ET sequence|legend=0| 99e, 212e }} *
* optimal patent val: [[113edo|113]]
Badness (Sintel): 1.87
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 441/440, 1875/1859
Mapping: {{mapping| 1 -17 -46 -26 -43 -79 | 0 20 52 31 50 89 }}
Optimal tunings:
* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9153{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9164{{c}}
{{Optimal ET sequence|legend=0| 99ef, 113, 212ef }}
Badness (Sintel): 1.77


=== Floral ===
=== Floral ===
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Optimal tunings:
Optimal tunings:
* WE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1257{{c}}
* WE: ~99/70 = 600.0052{{c}}, ~66/49 = 515.1257{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1215{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1215{{c}}


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