Breedsmic temperaments: Difference between revisions

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 == Amicable ==
 {{see also| Amity family }}
+The amicable temperament tempers out the [[amity comma]] and the [[canousma]] in addition to the breedsma, and is closely associated with the canou 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.
 Subgroup: 2.3.5.7
@@ Line 570: / Line 574: @@
 [[Badness]]: 0.045473
+=== Amical ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 131072/130977, 1600000/1594323
+Mapping: [{{val| 1 3 6 5 -8 }}, {{val| 0 -20 -52 -31 162 }}]
+Vals: {{val list| 99, 212e, 311, 410, 721, 1032, 1343 }}
+Badness: 0.101
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206
+Mapping: [{{val| 1 3 6 5 -8 -5 }}, {{val| 0 -20 -52 -31 162 123 }}]
+Vals: {{val list| 99, 212ef, 311, 410, 721, 1032 }}
+Badness: 0.0499
+=== Amorous ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 6250/6237, 19712/19683
+Mapping: [{{val| 1 3 6 5 14 }}, {{val| 0 -20 -52 -31 -149 }}]
+POTE generator: ~21/20 = 84.8896
+Vals: {{val list| 99e, 212, 311, 1145c, 1456cd }}
+Badness: 0.0489
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
+Mapping: [{{val| 1 3 6 5 14 17 }}, {{val| 0 -20 -52 -31 -149 -188 }}]
+POTE generator: ~21/20 = 84.8910
+Vals: {{val list| 99ef, 212, 311, 834, 1145c }}
+Badness: 0.0347
+=== Pseudoamical ===
+Subgroup: 2.3.5.7.11
+Comma list: 385/384, 1375/1372, 1600000/1594323
+Mapping: [{{val| 1 3 6 5 -1 }}, {{val| 0 -20 -52 -31 63 }}]
+POTE generator: ~21/20 = 84.9091
+Vals: {{val list| 99, 113, 212, 961ccdeee }}
+Badness: 0.0858
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 385/384, 1375/1372, 19773/19712
+Mapping: [{{val| 1 3 6 5 -1 2 }}, {{val| 0 -20 -52 -31 63 24 }}]
+POTE generator: ~21/20 = 84.9127
+Vals: {{val list| 99, 113, 212, 537cdeff, 749ccdeefff }}
+Badness: 0.0470
+=== Pseudoamorous ===
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 441/440, 980000/970299
+Mapping: [{{val| 1 3 6 5 7 }}, {{val| 0 -20 -52 -31 -50 }}]
+POTE generator: ~21/20 = 84.9164
+Vals: {{val list| 99e, 212e }}
+Badness: 0.0566
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 364/363, 441/440, 1875/1859
+Mapping: [{{val| 1 3 6 5 7 10 }}, {{val| 0 -20 -52 -31 -50 -89 }}]
+POTE generator: ~21/20 = 84.9164
+Vals: {{val list| 99ef, 113, 212ef }}
+Badness: 0.0428
+=== Floral ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 9801/9800, 14641/14580
+Mapping: [{{val| 2 6 12 10 13 }}, {{val| 0 -20 -52 -31 -43 }}]
+POTE generator: ~21/20 = 84.8788
+Vals: {{val list| 198, 212, 410 }}
+Badness: 0.0651
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580
+Mapping: [{{val| 2 6 12 10 13 19 }}, {{val| 0 -20 -52 -31 -43 -82 }}]
+POTE generator: ~21/20 = 84.8750
+Vals: {{val list| 198, 410 }}
+Badness: 0.0370
+=== Humorous ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 3025/3024, 1600000/1594323
+Mapping: [{{val| 1 3 6 5 3 }}, {{val| 0 -40 -104 -62 13 }}]
+POTE generator: ~4096/3993 = 42.4391
+Vals: {{val list| 85c, 113, 198, 311, 509, 820 }}
+Badness: 0.0582
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024
+Mapping: [{{val| 1 3 6 5 3 6 }}, {{val| 0 -40 -104 -62 13 -65 }}]
+POTE generator: ~40/39 = 42.4391
+Vals: {{val list| 85c, 113, 198, 311, 509, 820f }}
+Badness: 0.0283
 == Septidiasemi ==