Amity family: Difference between revisions

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BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
Re-added POTE tunings
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
m Made consistent with the formatting of other temperament pages
Line 14: Line 14:
: mapping generators: ~2, ~243/200
: mapping generators: ~2, ~243/200


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~243/200 = 339.537
[[Optimal tuning]]s:
 
* [[CTE]]: ~2 = 1\1, ~243/200 = 339.537
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.519
* [[POTE]]: ~2 = 1\1, ~243/200 = 339.519


{{Optimal ET sequence|legend=1| 7, 32c, 39, 46, 53, 152, 205, 258, 1085, 1343, 1601, 1859b, 2117bc }}
{{Optimal ET sequence|legend=1| 7, 32c, 39, 46, 53, 152, 205, 258, 1085, 1343, 1601, 1859b, 2117bc }}
Line 44: Line 44:
{{Multival|legend=1| 5 13 -17 9 -41 -76 }}
{{Multival|legend=1| 5 13 -17 9 -41 -76 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~128/105 = 339.446
Optimal tunings:
 
* CTE: ~2 = 1\1, ~128/105 = 339.446
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~128/105 = 339.432
* POTE: ~2 = 1\1, ~128/105 = 339.432


{{Optimal ET sequence|legend=1| 7, 32cd, 39, 46, 53, 99, 152, 251, 905bcdd }}
{{Optimal ET sequence|legend=1| 7, 32cd, 39, 46, 53, 99, 152, 251, 905bcdd }}
Line 59: Line 59:
Mapping: {{mapping| 1 3 6 -2 21 | 0 -5 -13 17 -62 }}
Mapping: {{mapping| 1 3 6 -2 21 | 0 -5 -13 17 -62 }}


Optimal tuning (CTE): ~2 = 1\1, ~128/105 = 339.485
Optimal tunings:
 
* CTE: ~2 = 1\1, ~128/105 = 339.485
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.464
* POTE: ~2 = 1\1, ~128/105 = 339.464


Optimal ET sequence: {{Optimal ET sequence| 46e, 53, 99e, 152, 357d, 509dd, 661dd }}
Optimal ET sequence: {{Optimal ET sequence| 46e, 53, 99e, 152, 357d, 509dd, 661dd }}
Line 74: Line 74:
Mapping: {{mapping| 1 3 6 -2 21 17 | 0 -5 -13 17 -62 -47 }}
Mapping: {{mapping| 1 3 6 -2 21 17 | 0 -5 -13 17 -62 -47 }}


Optimal tuning (CTE): ~2 = 1\1, ~128/105 = 339.508
Optimal tunings:
 
* CTE: ~2 = 1\1, ~128/105 = 339.508
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.481
* POTE: ~2 = 1\1, ~128/105 = 339.481


Optimal ET sequence: {{Optimal ET sequence| 46ef, 53, 99ef, 152f, 205 }}
Optimal ET sequence: {{Optimal ET sequence| 46ef, 53, 99ef, 152f, 205 }}
Line 115: Line 115:
Mapping: {{mapping| 1 3 6 -2 6 | 0 -5 -13 17 -9 }}
Mapping: {{mapping| 1 3 6 -2 6 | 0 -5 -13 17 -9 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 339.390
Optimal tunings:
 
* CTE: ~2 = 1\1, ~11/9 = 339.390
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.390
* POTE: ~2 = 1\1, ~11/9 = 339.390


Optimal ET sequence: {{Optimal ET sequence| 7, 25cdde, 32cd, 39, 46, 53, 99 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 25cdde, 32cd, 39, 46, 53, 99 }}
Line 130: Line 130:
Mapping: {{mapping| 1 3 6 -2 6 2 | 0 -5 -13 17 -9 6 }}
Mapping: {{mapping| 1 3 6 -2 6 2 | 0 -5 -13 17 -9 6 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 339.411
Optimal tunings:
 
* CTE: ~2 = 1\1, ~11/9 = 339.411
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.419
* POTE: ~2 = 1\1, ~11/9 = 339.419


Optimal ET sequence: {{Optimal ET sequence| 7, 25cddef, 32cd, 39, 46, 53, 99 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 25cddef, 32cd, 39, 46, 53, 99 }}
Line 145: Line 145:
Mapping: {{mapping| 1 3 6 -2 6 2 -1 | 0 -5 -13 17 -9 6 18 }}
Mapping: {{mapping| 1 3 6 -2 6 2 -1 | 0 -5 -13 17 -9 6 18 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 339.366
Optimal tunings:
 
* CTE: ~2 = 1\1, ~11/9 = 339.366
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.366
* POTE: ~2 = 1\1, ~11/9 = 339.366


Optimal ET sequence: {{Optimal ET sequence| 7, 25cddefgg, 32cdg, 39, 46, 99 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 25cddefgg, 32cdg, 39, 46, 99 }}
Line 160: Line 160:
Mapping: {{mapping| 1 3 6 -2 6 2 -1 0 | 0 -5 -13 17 -9 6 18 15 }}
Mapping: {{mapping| 1 3 6 -2 6 2 -1 0 | 0 -5 -13 17 -9 6 18 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 339.415
Optimal tunings:
 
* CTE: ~2 = 1\1, ~11/9 = 339.415
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.407
* POTE: ~2 = 1\1, ~11/9 = 339.407


Optimal ET sequence: {{Optimal ET sequence| 7, 25cddefgghh, 32cdgh, 39h, 46, 53, 99h }}
Optimal ET sequence: {{Optimal ET sequence| 7, 25cddefgghh, 32cdgh, 39h, 46, 53, 99h }}
Line 177: Line 177:
Mapping: {{mapping| 1 3 6 -2 -7 | 0 -5 -13 17 37 }}
Mapping: {{mapping| 1 3 6 -2 -7 | 0 -5 -13 17 37 }}


Optimal tuning (CTE): ~2 = 1\1, ~128/105 = 339.314
Optimal tunings:
 
* CTE: ~2 = 1\1, ~128/105 = 339.314
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.340
* POTE: ~2 = 1\1, ~128/105 = 339.340


Optimal ET sequence: {{Optimal ET sequence| 46, 99e, 145 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 99e, 145 }}
Line 192: Line 192:
Mapping: {{mapping| 1 3 6 -2 -7 -11 | 0 -5 -13 17 37 52 }}
Mapping: {{mapping| 1 3 6 -2 -7 -11 | 0 -5 -13 17 37 52 }}


Optimal tuning (CTE): ~2 = 1\1, ~128/105 = 339.277
Optimal tunings:
 
* CTE: ~2 = 1\1, ~128/105 = 339.277
Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.313
* POTE: ~2 = 1\1, ~128/105 = 339.313


Optimal ET sequence: {{Optimal ET sequence| 46, 99ef, 145, 191c, 336cef, 527bccef }}
Optimal ET sequence: {{Optimal ET sequence| 46, 99ef, 145, 191c, 336cef, 527bccef }}
Line 207: Line 207:
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 | 0 -5 -13 17 37 52 18 }}
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 | 0 -5 -13 17 37 52 18 }}


Optimal tuning (CTE): ~2 = 1\1, ~17/14 = 339.272
Optimal tunings:
 
* CTE: ~2 = 1\1, ~17/14 = 339.272
Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.313
* POTE: ~2 = 1\1, ~17/14 = 339.313


Optimal ET sequence: {{Optimal ET sequence| 46, 99ef, 145, 191c }}
Optimal ET sequence: {{Optimal ET sequence| 46, 99ef, 145, 191c }}
Line 222: Line 222:
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 -13 | 0 -5 -13 17 37 52 18 61 }}
Mapping: {{mapping| 1 3 6 -2 -7 -11 -1 -13 | 0 -5 -13 17 37 52 18 61 }}


Optimal tuning (CTE): ~2 = 1\1, ~17/14 = 339.282
Optimal tunings:
 
* CTE: ~2 = 1\1, ~17/14 = 339.282
Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.325
* POTE: ~2 = 1\1, ~17/14 = 339.325


Optimal ET sequence: {{Optimal ET sequence| 46, 99ef, 145, 191c, 336cefg }}
Optimal ET sequence: {{Optimal ET sequence| 46, 99ef, 145, 191c, 336cefg }}
Line 239: Line 239:
: mapping generators: ~99/70, ~64/55
: mapping generators: ~99/70, ~64/55


Optimal tuning (CTE): ~99/70 = 1\2, ~64/55 = 260.566
Optimal tunings:
 
* CTE: ~99/70 = 1\2, ~64/55 = 260.566
Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.561
* POTE: ~99/70 = 1\2, ~64/55 = 260.561


Optimal ET sequence: {{Optimal ET sequence| 14cde, 32cde, 46, 106, 152, 350 }}
Optimal ET sequence: {{Optimal ET sequence| 14cde, 32cde, 46, 106, 152, 350 }}
Line 254: Line 254:
Mapping: {{mapping| 2 1 -1 13 13 20 | 0 5 13 -17 -14 -29 }}
Mapping: {{mapping| 2 1 -1 13 13 20 | 0 5 13 -17 -14 -29 }}


Optimal tuning (CTE): ~99/70 = 1\2, ~64/55 = 260.607
Optimal tunings:
 
* CTE: ~99/70 = 1\2, ~64/55 = 260.607
Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.583
* POTE: ~99/70 = 1\2, ~64/55 = 260.583


Optimal ET sequence: {{Optimal ET sequence| 46, 106f, 152f, 198 }}
Optimal ET sequence: {{Optimal ET sequence| 46, 106f, 152f, 198 }}
Line 271: Line 271:
{{Multival|legend=1| 5 13 29 9 32 31 }}
{{Multival|legend=1| 5 13 29 9 32 31 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~243/200 = 339.154
Optimal tunings:
 
* CTE: ~2 = 1\1, ~243/200 = 339.154
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 338.993
* POTE: ~2 = 1\1, ~243/200 = 338.993


{{Optimal ET sequence|legend=1| 7d, 25cddd, 32cdd, 39d, 46 }}
{{Optimal ET sequence|legend=1| 7d, 25cddd, 32cdd, 39d, 46 }}
Line 286: Line 286:
Mapping: {{mapping| 1 3 6 11 6 | 0 -5 -13 -29 -9 }}
Mapping: {{mapping| 1 3 6 11 6 | 0 -5 -13 -29 -9 }}


Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 339.136
Optimal tunings:
 
* CTE: ~2 = 1\1, ~11/9 = 339.136
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.047
* POTE: ~2 = 1\1, ~11/9 = 339.047


Optimal ET sequence: {{Optimal ET sequence| 7d, 25cddde, 32cdd, 39d, 46 }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 25cddde, 32cdd, 39d, 46 }}
Line 305: Line 305:
{{Multival|legend=1| 5 13 36 9 43 47 }}
{{Multival|legend=1| 5 13 36 9 43 47 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~243/200 = 339.711
Optimal tunings:
 
* CTE: ~2 = 1\1, ~243/200 = 339.711
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.763
* POTE: ~2 = 1\1, ~243/200 = 339.763


{{Optimal ET sequence|legend=1| 7d, 32cdddd, 39ddd, 46d, 53, 166, 219c, 272c }}
{{Optimal ET sequence|legend=1| 7d, 32cdddd, 39ddd, 46d, 53, 166, 219c, 272c }}
Line 320: Line 320:
Mapping: {{mapping| 1 3 6 13 -9 | 0 -5 -13 -36 44 }}
Mapping: {{mapping| 1 3 6 13 -9 | 0 -5 -13 -36 44 }}


Optimal tuning (CTE): ~2 = 1\1, ~243/200 = 339.751
Optimal tunings:
 
* CTE: ~2 = 1\1, ~243/200 = 339.751
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.763
* POTE: ~2 = 1\1, ~243/200 = 339.763


Optimal ET sequence: {{Optimal ET sequence| 53, 113, 166, 551ccee }}
Optimal ET sequence: {{Optimal ET sequence| 53, 113, 166, 551ccee }}
Line 335: Line 335:
Mapping: {{mapping| 1 3 6 13 -9 2 | 0 -5 -13 -36 44 6 }}
Mapping: {{mapping| 1 3 6 13 -9 2 | 0 -5 -13 -36 44 6 }}


Optimal tuning (CTE): ~2 = 1\1, ~39/32 = 339.754
Optimal tunings:
 
* CTE: ~2 = 1\1, ~39/32 = 339.754
Optimal tuning (POTE): ~2 = 1\1, ~39/32 = 339.764
* POTE: ~2 = 1\1, ~39/32 = 339.764


Optimal ET sequence: {{Optimal ET sequence| 53, 113, 166 }}
Optimal ET sequence: {{Optimal ET sequence| 53, 113, 166 }}
Line 350: Line 350:
Mapping: [{{val| 1 3 6 13 6 }}, {{val| 0 -5 -13 -36 -9 }}]
Mapping: [{{val| 1 3 6 13 6 }}, {{val| 0 -5 -13 -36 -9 }}]


Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 339.680
Optimal tunings:
 
* CTE: ~2 = 1\1, ~11/9 = 339.680
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.814
* POTE: ~2 = 1\1, ~11/9 = 339.814


Optimal ET sequence: {{Optimal ET sequence| 7d, 32cdddd, 39ddd, 46d, 53 }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 32cdddd, 39ddd, 46d, 53 }}
Line 365: Line 365:
Mapping: [{{val| 1 3 6 13 6 2 }}, {{val| 0 -5 -13 -36 -9 6 }}]
Mapping: [{{val| 1 3 6 13 6 2 }}, {{val| 0 -5 -13 -36 -9 6 }}]


Optimal tuning (CTE): ~2 = 1\1, ~11/9 = 339.685
Optimal tunings:
 
* CTE: ~2 = 1\1, ~11/9 = 339.685
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.784
* POTE: ~2 = 1\1, ~11/9 = 339.784


Optimal ET sequence: {{Optimal ET sequence| 7d, 32cdddd, 39ddd, 46d, 53 }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 32cdddd, 39ddd, 46d, 53 }}
Line 382: Line 382:
{{Mapping|legend=1| 1 3 6 -17 | 0 -5 -13 70 }}
{{Mapping|legend=1| 1 3 6 -17 | 0 -5 -13 70 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~243/200 = 339.554
Optimal tunings:
 
* CTE: ~2 = 1\1, ~243/200 = 339.554
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~243/200 = 339.553
* POTE: ~2 = 1\1, ~243/200 = 339.553


{{Optimal ET sequence|legend=1| 53, 205d, 258, 311, 675, 986 }}
{{Optimal ET sequence|legend=1| 53, 205d, 258, 311, 675, 986 }}
Line 397: Line 397:
Mapping: {{mapping| 1 3 6 -17 36 | 0 -5 -13 70 -115 }}
Mapping: {{mapping| 1 3 6 -17 36 | 0 -5 -13 70 -115 }}


Optimal tuning (CTE): ~2 = 1\1, ~243/200 = 339.554
Optimal tunings:
 
* CTE: ~2 = 1\1, ~243/200 = 339.554
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
* POTE: ~2 = 1\1, ~243/200 = 339.554


Optimal ET sequence: {{Optimal ET sequence| 53, 205de, 258, 311, 675, 986 }}
Optimal ET sequence: {{Optimal ET sequence| 53, 205de, 258, 311, 675, 986 }}
Line 412: Line 412:
Mapping: {{mapping| 1 3 6 -17 36 17 | 0 -5 -13 70 -115 -47 }}
Mapping: {{mapping| 1 3 6 -17 36 17 | 0 -5 -13 70 -115 -47 }}


Optimal tuning (CTE): ~2 = 1\1, ~243/200 = 339.554
Optimal tunings:
 
* CTE: ~2 = 1\1, ~243/200 = 339.554
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554
* POTE: ~2 = 1\1, ~243/200 = 339.554


Optimal ET sequence: {{Optimal ET sequence| 53, 205de, 258, 311, 675, 986, 1661cf }}
Optimal ET sequence: {{Optimal ET sequence| 53, 205de, 258, 311, 675, 986, 1661cf }}
Line 427: Line 427:
Mapping: {{mapping| 1 3 6 -17 36 17 -31 | 0 -5 -13 70 -115 -47 124 }}
Mapping: {{mapping| 1 3 6 -17 36 17 -31 | 0 -5 -13 70 -115 -47 124 }}


Optimal tuning (CTE): ~2 = 1\1, ~243/200 = 339.555
Optimal tunings:
 
* CTE: ~2 = 1\1, ~243/200 = 339.555
Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.555
* POTE: ~2 = 1\1, ~243/200 = 339.555


Optimal ET sequence: {{Optimal ET sequence| 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf }}
Optimal ET sequence: {{Optimal ET sequence| 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf }}
Line 442: Line 442:
Mapping: {{mapping| 1 3 6 -17 36 17 -31 15 | 0 -5 -13 70 -115 -47 124 -38 }}
Mapping: {{mapping| 1 3 6 -17 36 17 -31 15 | 0 -5 -13 70 -115 -47 124 -38 }}


Optimal tuning (CTE): ~2 = 1\1, ~208/171 = 339.555
Optimal tunings:
 
* CTE: ~2 = 1\1, ~208/171 = 339.555
Optimal tuning (POTE): ~2 = 1\1, ~208/171 = 339.555
* POTE: ~2 = 1\1, ~208/171 = 339.555


Optimal ET sequence: {{Optimal ET sequence| 53, 205deg, 258g, 311, 675, 986, 1661cfh }}
Optimal ET sequence: {{Optimal ET sequence| 53, 205deg, 258g, 311, 675, 986, 1661cfh }}
Line 463: Line 463:
{{Multival|legend=1| 10 26 12 18 -9 -45 }}
{{Multival|legend=1| 10 26 12 18 -9 -45 }}


[[Optimal tuning]] ([[CTE]]): ~343/240 = 1\2, ~7/6 = 260.563
Optimal tunings:
 
* CTE: ~343/240 = 1\2, ~7/6 = 260.563
[[Optimal tuning]] ([[POTE]]): ~343/240 = 1\2, ~7/6 = 260.402
* POTE: ~343/240 = 1\2, ~7/6 = 260.402


{{Optimal ET sequence|legend=1| 14c, 32c, 46, 106d, 152d }}
{{Optimal ET sequence|legend=1| 14c, 32c, 46, 106d, 152d }}
Line 478: Line 478:
Mapping: {{mapping| 2 1 -1 3 3 | 0 5 13 6 9 }}
Mapping: {{mapping| 2 1 -1 3 3 | 0 5 13 6 9 }}


Optimal tuning (CTE): ~99/70 = 1\2, ~7/6 = 260.653
Optimal tunings:
 
* CTE: ~99/70 = 1\2, ~7/6 = 260.653
Optimal tuning (POTE): ~99/70 = 1\2, ~7/6 = 260.393
* POTE: ~99/70 = 1\2, ~7/6 = 260.393


Optimal ET sequence: {{Optimal ET sequence| 14c, 32c, 46, 152de, 198, 244dee }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 32c, 46, 152de, 198, 244dee }}
Line 493: Line 493:
Mapping: {{mapping| 2 1 -1 3 3 0 | 0 5 13 6 9 17 }}
Mapping: {{mapping| 2 1 -1 3 3 0 | 0 5 13 6 9 17 }}


Optimal tuning (CTE): ~55/39 = 1\2, ~7/6 = 260.811
Optimal tunings:
 
* CTE: ~55/39 = 1\2, ~7/6 = 260.811
Optimal tuning (POTE): ~55/39 = 1\2, ~7/6 = 260.618
* POTE: ~55/39 = 1\2, ~7/6 = 260.618


Optimal ET sequence: {{Optimal ET sequence| 14cf, 32cf, 46 }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 32cf, 46 }}
Line 514: Line 514:
{{Multival|legend=1| 10 26 19 18 2 -29 }}
{{Multival|legend=1| 10 26 19 18 2 -29 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~9/7 = 430.168
Optimal tunings:
 
* CTE: ~2 = 1\1, ~9/7 = 430.168
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 430.219
* POTE: ~2 = 1\1, ~9/7 = 430.219


{{Optimal ET sequence|legend=1| 14c, 39d, 53 }}
{{Optimal ET sequence|legend=1| 14c, 39d, 53 }}
Line 529: Line 529:
Mapping: {{mapping| 1 8 19 15 15 | 0 -10 -26 -19 -18 }}
Mapping: {{mapping| 1 8 19 15 15 | 0 -10 -26 -19 -18 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 430.220
Optimal tunings:
 
* CTE: ~2 = 1\1, ~9/7 = 430.220
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.192
* POTE: ~2 = 1\1, ~9/7 = 430.192


Optimal ET sequence: {{Optimal ET sequence| 14c, 39d, 53 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 39d, 53 }}
Line 544: Line 544:
Mapping: {{mapping| 1 8 19 15 15 30 | 0 -10 -26 -19 -18 -41 }}
Mapping: {{mapping| 1 8 19 15 15 30 | 0 -10 -26 -19 -18 -41 }}


Optimal tuning (CTE): ~2 = 1\1, ~9/7 = 430.233
Optimal tunings:
 
* CTE: ~2 = 1\1, ~9/7 = 430.233
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.216
* POTE: ~2 = 1\1, ~9/7 = 430.216


Optimal ET sequence: {{Optimal ET sequence| 14cf, 39df, 53 }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 39df, 53 }}
Line 565: Line 565:
{{Multival|legend=1| 15 39 -5 27 -50 -121 }}
{{Multival|legend=1| 15 39 -5 27 -50 -121 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~189/160 = 286.816
Optimal tunings:
 
* CTE: ~2 = 1\1, ~189/160 = 286.816
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~189/160 = 286.787
* POTE: ~2 = 1\1, ~189/160 = 286.787


{{Optimal ET sequence|legend=1| 46, 113, 159, 205d, 364d }}
{{Optimal ET sequence|legend=1| 46, 113, 159, 205d, 364d }}
Line 580: Line 580:
Mapping: {{mapping| 1 13 32 -1 -11 | 0 -15 -39 5 19 }}
Mapping: {{mapping| 1 13 32 -1 -11 | 0 -15 -39 5 19 }}


Optimal tuning (CTE): ~2 = 1\1, ~33/28 = 286.813
Optimal tunings:
 
* CTE: ~2 = 1\1, ~33/28 = 286.813
Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 286.797
* POTE: ~2 = 1\1, ~33/28 = 286.797


Optimal ET sequence: {{Optimal ET sequence| 46, 113, 159, 205d, 364d }}
Optimal ET sequence: {{Optimal ET sequence| 46, 113, 159, 205d, 364d }}
Line 595: Line 595:
Mapping: {{mapping| 1 13 32 -1 -11 -10 | 0 -15 -39 5 19 18 }}
Mapping: {{mapping| 1 13 32 -1 -11 -10 | 0 -15 -39 5 19 18 }}


Optimal tuning (CTE): ~2 = 1\1, ~13/11 = 286.803
Optimal tunings:
 
* CTE: ~2 = 1\1, ~13/11 = 286.803
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.789
* POTE: ~2 = 1\1, ~13/11 = 286.789


Optimal ET sequence: {{Optimal ET sequence| 46, 113, 159, 364df, 523ddff }}
Optimal ET sequence: {{Optimal ET sequence| 46, 113, 159, 364df, 523ddff }}
Line 610: Line 610:
Mapping: {{mapping| 1 13 32 -1 -11 -10 -2 | 0 -15 -39 5 19 18 8 }}
Mapping: {{mapping| 1 13 32 -1 -11 -10 -2 | 0 -15 -39 5 19 18 8 }}


Optimal tuning (CTE): ~2 = 1\1, ~13/11 = 286.804
Optimal tunings:
 
* CTE: ~2 = 1\1, ~13/11 = 286.804
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.795
* POTE: ~2 = 1\1, ~13/11 = 286.795


Optimal ET sequence: {{Optimal ET sequence| 46, 113, 159, 364df, 523ddff }}
Optimal ET sequence: {{Optimal ET sequence| 46, 113, 159, 364df, 523ddff }}
Line 629: Line 629:
{{Multival|legend=1| 15 39 101 27 118 125 }}
{{Multival|legend=1| 15 39 101 27 118 125 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~168/125 = 513.180
Optimal tunings:
 
* CTE: ~2 = 1\1, ~168/125 = 513.180
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~168/125 = 513.178
* POTE: ~2 = 1\1, ~168/125 = 513.178


{{Optimal ET sequence|legend=1| 7d, …, 145d, 152, 311, 774, 1085 }}
{{Optimal ET sequence|legend=1| 7d, …, 145d, 152, 311, 774, 1085 }}
Line 644: Line 644:
Mapping: {{mapping| 1 8 19 46 18 | 0 -15 -39 -101 -34 }}
Mapping: {{mapping| 1 8 19 46 18 | 0 -15 -39 -101 -34 }}


Optimal tuning (CTE): ~2 = 1\1, ~121/90 = 513.181
Optimal tunings:
 
* CTE: ~2 = 1\1, ~121/90 = 513.181
Optimal tuning (POTE): ~2 = 1\1, ~121/90 = 513.177
* POTE: ~2 = 1\1, ~121/90 = 513.177


Optimal ET sequence: {{Optimal ET sequence| 7d, …, 145d, 152, 311, 774, 1085e, 1396e }}
Optimal ET sequence: {{Optimal ET sequence| 7d, …, 145d, 152, 311, 774, 1085e, 1396e }}
Line 659: Line 659:
Mapping: {{mapping| 1 8 19 46 18 64 | 0 -15 -39 -101 -34 -141 }}
Mapping: {{mapping| 1 8 19 46 18 64 | 0 -15 -39 -101 -34 -141 }}


Optimal tuning (CTE): ~2 = 1\1, ~35/26 = 513.184
Optimal tunings:
 
* CTE: ~2 = 1\1, ~35/26 = 513.184
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.182
* POTE: ~2 = 1\1, ~35/26 = 513.182


Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311 }}
Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311 }}
Line 674: Line 674:
Mapping: {{mapping| 1 8 19 46 18 64 -22 | 0 -15 -39 -101 -34 -141 61 }}
Mapping: {{mapping| 1 8 19 46 18 64 -22 | 0 -15 -39 -101 -34 -141 61 }}


Optimal tuning (CTE): ~2 = 1\1, ~35/26 = 513.185
Optimal tunings:
 
* CTE: ~2 = 1\1, ~35/26 = 513.185
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
* POTE: ~2 = 1\1, ~35/26 = 513.186


Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311, 1714cdeg, 2025cdefgg, 2336bccdefgg }}
Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311, 1714cdeg, 2025cdefgg, 2336bccdefgg }}
Line 689: Line 689:
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 | 0 -15 -39 -101 -34 -141 61 -114 }}
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 | 0 -15 -39 -101 -34 -141 61 -114 }}


Optimal tuning (CTE): ~2 = 1\1, ~35/26 = 513.184
Optimal tunings:
 
* CTE: ~2 = 1\1, ~35/26 = 513.184
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
* POTE: ~2 = 1\1, ~35/26 = 513.185


Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311 }}
Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311 }}
Line 704: Line 704:
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 | 0 -15 -39 -101 -34 -141 61 -114 -104 }}
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 | 0 -15 -39 -101 -34 -141 61 -114 -104 }}


Optimal tuning (CTE): ~2 = 1\1, ~35/26 = 513.184
Optimal tunings:
 
* CTE: ~2 = 1\1, ~35/26 = 513.184
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185
* POTE: ~2 = 1\1, ~35/26 = 513.185


Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311, 1714cdeghi, 2025cdefgghhi, 2336bccdefgghhi }}
Optimal ET sequence: {{Optimal ET sequence| 152f, 159, 311, 1714cdeghi, 2025cdefgghhi, 2336bccdefgghhi }}
Line 719: Line 719:
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 72 | 0 -15 -39 -101 -34 -141 61 -114 -104 -157 }}
Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 72 | 0 -15 -39 -101 -34 -141 61 -114 -104 -157 }}


Optimal tuning (CTE): ~2 = 1\1, ~35/26 = 513.185
Optimal tunings:
 
* CTE: ~2 = 1\1, ~35/26 = 513.185
Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186
* POTE: ~2 = 1\1, ~35/26 = 513.186


Optimal ET sequence: {{Optimal ET sequence| 152fj, 159, 311, 1403cdgh, 1714cdeghi, 2025cdefgghhij, 2336bccdefgghhij }}
Optimal ET sequence: {{Optimal ET sequence| 152fj, 159, 311, 1403cdgh, 1714cdeghi, 2025cdefgghhij, 2336bccdefgghhij }}
Line 740: Line 740:
{{Multival|legend=1| 20 52 31 36 -7 -74 }}
{{Multival|legend=1| 20 52 31 36 -7 -74 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~21/20 = 84.8831
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 84.8831
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 84.880
* POTE: ~2 = 1\1, ~21/20 = 84.880


{{Optimal ET sequence|legend=1| 14c, …, 85c, 99, 212, 311, 721, 1032, 1753b }}
{{Optimal ET sequence|legend=1| 14c, …, 85c, 99, 212, 311, 721, 1032, 1753b }}
Line 755: Line 755:
Mapping: {{mapping| 1 3 6 5 -8 | 0 -20 -52 -31 162 }}
Mapping: {{mapping| 1 3 6 5 -8 | 0 -20 -52 -31 162 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 84.8843
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 84.8843
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8843
* POTE: ~2 = 1\1, ~21/20 = 84.8843


Optimal ET sequence: {{Optimal ET sequence| 99, 212e, 311, 721, 1032, 1343, 2375bc }}
Optimal ET sequence: {{Optimal ET sequence| 99, 212e, 311, 721, 1032, 1343, 2375bc }}
Line 770: Line 770:
Mapping: {{mapping| 1 3 6 5 -8 -5 | 0 -20 -52 -31 162 123 }}
Mapping: {{mapping| 1 3 6 5 -8 -5 | 0 -20 -52 -31 162 123 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 84.8837
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 84.8837
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8838
* POTE: ~2 = 1\1, ~21/20 = 84.8838


Optimal ET sequence: {{Optimal ET sequence| 99, 212ef, 311, 721, 1032 }}
Optimal ET sequence: {{Optimal ET sequence| 99, 212ef, 311, 721, 1032 }}
Line 785: Line 785:
Mapping: {{mapping| 1 3 6 5 14 | 0 -20 -52 -31 -149 }}
Mapping: {{mapping| 1 3 6 5 14 | 0 -20 -52 -31 -149 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 84.8883
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 84.8883
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8896
* POTE: ~2 = 1\1, ~21/20 = 84.8896


Optimal ET sequence: {{Optimal ET sequence| 99e, 212, 311, 2389bccd, 2700bccde, 3011bccde, 3322bccdde }}
Optimal ET sequence: {{Optimal ET sequence| 99e, 212, 311, 2389bccd, 2700bccde, 3011bccde, 3322bccdde }}
Line 800: Line 800:
Mapping: {{mapping| 1 3 6 5 14 17 | 0 -20 -52 -31 -149 -188 }}
Mapping: {{mapping| 1 3 6 5 14 17 | 0 -20 -52 -31 -149 -188 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 84.8895
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 84.8895
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8910
* POTE: ~2 = 1\1, ~21/20 = 84.8910


Optimal ET sequence: {{Optimal ET sequence| 99ef, 212, 311, 1145c, 1456cd, 1767cd }}
Optimal ET sequence: {{Optimal ET sequence| 99ef, 212, 311, 1145c, 1456cd, 1767cd }}
Line 815: Line 815:
Mapping: {{mapping| 1 3 6 5 -1 | 0 -20 -52 -31 63 }}
Mapping: {{mapping| 1 3 6 5 -1 | 0 -20 -52 -31 63 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 84.9005
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 84.9005
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9091
* POTE: ~2 = 1\1, ~21/20 = 84.9091


Optimal ET sequence: {{Optimal ET sequence| 14ce, …, 85cee, 99, 212 }}
Optimal ET sequence: {{Optimal ET sequence| 14ce, …, 85cee, 99, 212 }}
Line 830: Line 830:
Mapping: {{mapping| 1 3 6 5 -1 2 | 0 -20 -52 -31 63 24 }}
Mapping: {{mapping| 1 3 6 5 -1 2 | 0 -20 -52 -31 63 24 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 84.9049
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 84.9049
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9127
* POTE: ~2 = 1\1, ~21/20 = 84.9127


Optimal ET sequence: {{Optimal ET sequence| 14ce, …, 85ceef, 99, 113, 212 }}
Optimal ET sequence: {{Optimal ET sequence| 14ce, …, 85ceef, 99, 113, 212 }}
Line 845: Line 845:
Mapping: {{mapping| 1 3 6 5 7 | 0 -20 -52 -31 -50 }}
Mapping: {{mapping| 1 3 6 5 7 | 0 -20 -52 -31 -50 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 84.9022
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 84.9022
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8917
* POTE: ~2 = 1\1, ~21/20 = 84.8917


Optimal ET sequence: {{Optimal ET sequence| 14c, …, 85ce, 99e, 113, 212e }}
Optimal ET sequence: {{Optimal ET sequence| 14c, …, 85ce, 99e, 113, 212e }}
Line 860: Line 860:
Mapping: {{mapping| 1 3 6 5 7 10 | 0 -20 -52 -31 -50 -89 }}
Mapping: {{mapping| 1 3 6 5 7 10 | 0 -20 -52 -31 -50 -89 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 84.9153
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 84.9153
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9164
* POTE: ~2 = 1\1, ~21/20 = 84.9164


Optimal ET sequence: {{Optimal ET sequence| 14cf, …, 85ceff, 99ef, 113, 212ef, 325ce, 537cdeef }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, …, 85ceff, 99ef, 113, 212ef, 325ce, 537cdeef }}
Line 875: Line 875:
Mapping: {{mapping| 2 6 12 10 13 | 0 -20 -52 -31 -43 }}
Mapping: {{mapping| 2 6 12 10 13 | 0 -20 -52 -31 -43 }}


Optimal tuning (CTE): ~99/70 = 1\2, ~21/20 = 84.8781
Optimal tunings:
 
* CTE: ~99/70 = 1\2, ~21/20 = 84.8781
Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8788
* POTE: ~99/70 = 1\2, ~21/20 = 84.8788


Optimal ET sequence: {{Optimal ET sequence| 14c, …, 170bccde, 184c, 198, 212, 410 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, …, 170bccde, 184c, 198, 212, 410 }}
Line 890: Line 890:
Mapping: {{mapping| 2 6 12 10 13 19 | 0 -20 -52 -31 -43 -82 }}
Mapping: {{mapping| 2 6 12 10 13 19 | 0 -20 -52 -31 -43 -82 }}


Optimal tuning (CTE): ~99/70 = 1\2, ~21/20 = 84.8759
Optimal tunings:
 
* CTE: ~99/70 = 1\2, ~21/20 = 84.8759
Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8750
* POTE: ~99/70 = 1\2, ~21/20 = 84.8750


Optimal ET sequence: {{Optimal ET sequence| 14c, …, 184cff, 198, 410 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, …, 184cff, 198, 410 }}
Line 905: Line 905:
Mapping: {{mapping| 1 3 6 5 3 | 0 -40 -104 -62 13 }}
Mapping: {{mapping| 1 3 6 5 3 | 0 -40 -104 -62 13 }}


Optimal tuning (CTE): ~2 = 1\1, ~4096/3993 = 42.4414
Optimal tunings:
 
* CTE: ~2 = 1\1, ~4096/3993 = 42.4414
Optimal tuning (POTE): ~2 = 1\1, ~4096/3993 = 42.4391
* POTE: ~2 = 1\1, ~4096/3993 = 42.4391


Optimal ET sequence: {{Optimal ET sequence| 85c, 113, 198, 311, 1131, 1442, 1753be }}
Optimal ET sequence: {{Optimal ET sequence| 85c, 113, 198, 311, 1131, 1442, 1753be }}
Line 920: Line 920:
Mapping: {{mapping| 1 3 6 5 3 6 | 0 -40 -104 -62 13 -65 }}
Mapping: {{mapping| 1 3 6 5 3 6 | 0 -40 -104 -62 13 -65 }}


Optimal tuning (CTE): ~2 = 1\1, ~40/39 = 42.4425
Optimal tunings:
 
* CTE: ~2 = 1\1, ~40/39 = 42.4425
Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 42.4391
* POTE: ~2 = 1\1, ~40/39 = 42.4391


Optimal ET sequence: {{Optimal ET sequence| 85c, 113, 198, 311, 1753beff, 2064beff, 2375bceff }}
Optimal ET sequence: {{Optimal ET sequence| 85c, 113, 198, 311, 1753beff, 2064beff, 2375bceff }}
Line 937: Line 937:
{{Mapping|legend=1| 1 13 32 -15 | 0 -25 -65 39 }}
{{Mapping|legend=1| 1 13 32 -15 | 0 -25 -65 39 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~48/35 = 547.909
[[Optimal tuning]] (CTE): ~2 = 1\1, ~48/35 = 547.909


{{Optimal ET sequence|legend=1| 46, 219c, 265, 311 }}
{{Optimal ET sequence|legend=1| 46, 219c, 265, 311 }}
Line 980: Line 980:
{{Multival|legend=1| 25 65 67 45 36 -27 }}
{{Multival|legend=1| 25 65 67 45 36 -27 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~11907/10000 = 307.915
Optimal tunings:
 
* CTE: ~2 = 1\1, ~11907/10000 = 307.915
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11907/10000 = 307.941
* POTE: ~2 = 1\1, ~11907/10000 = 307.941


{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 265, 417, 1516ccdd, 1933ccdd }}
{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 265, 417, 1516ccdd, 1933ccdd }}
Line 995: Line 995:
Mapping: {{mapping| 1 8 19 20 5 | 0 -25 -65 -67 -6 }}
Mapping: {{mapping| 1 8 19 20 5 | 0 -25 -65 -67 -6 }}


Optimal tuning (CTE): ~2 = 1\1, ~3200/2673 = 307.915
Optimal tunings:
 
* CTE: ~2 = 1\1, ~3200/2673 = 307.915
Optimal tuning (POTE): ~2 = 1\1, ~3200/2673 = 307.906
* POTE: ~2 = 1\1, ~3200/2673 = 307.906


Optimal ET sequence: {{Optimal ET sequence| 39d, 74cd, 113, 152, 265, 417, 1099cdee }}
Optimal ET sequence: {{Optimal ET sequence| 39d, 74cd, 113, 152, 265, 417, 1099cdee }}
Line 1,010: Line 1,010:
Mapping: {{mapping| 1 8 19 20 5 25 | 0 -25 -65 -67 -6 -83 }}
Mapping: {{mapping| 1 8 19 20 5 25 | 0 -25 -65 -67 -6 -83 }}


Optimal tuning (CTE): ~2 = 1\1, ~143/120 = 307.922
Optimal tunings:
 
* CTE: ~2 = 1\1, ~143/120 = 307.922
Optimal tuning (POTE): ~2 = 1\1, ~143/120 = 307.913
* POTE: ~2 = 1\1, ~143/120 = 307.913


Optimal ET sequence: {{Optimal ET sequence| 39df, 74cdf, 113, 152f, 265 }}
Optimal ET sequence: {{Optimal ET sequence| 39df, 74cdf, 113, 152f, 265 }}

Revision as of 22:26, 19 March 2024

The amity family tempers out the 5-limit amity comma, 1600000/1594323. The generator for the amity temperament is the acute minor third, which means the 6/5 just minor third raised by an 81/80 comma to 243/200, and from this it derives its name. If you are looking for a different kind of neutral third this could be the temperament for you.

Amity

Main article: Amity

In the 5-limit amity is a genuine microtemperament, with 58\205 being a possible tuning. Another good choice is (64/5)1/13, which gives a pure classical major third. Mos scales of 11, 18, 25, 32, 39, 46 or 53 notes are available.

Subgroup: 2.3.5

Comma list: 1600000/1594323

Mapping: [⟨1 3 6], ⟨0 -5 -13]]

mapping generators: ~2, ~243/200

Optimal tunings:

  • CTE: ~2 = 1\1, ~243/200 = 339.537
  • POTE: ~2 = 1\1, ~243/200 = 339.519

Optimal ET sequence: 7, 32c, 39, 46, 53, 152, 205, 258, 1085, 1343, 1601, 1859b, 2117bc

Badness: 0.021960

Overview to extensions

The second comma to extend the 5-limit amity include 4375/4374 for septimal amity, 225/224 for houborizic, 65625/65536 for paramity, 126/125 for accord, 245/243 for bamity, 2430/2401 for hamity, 1029/1024 for gamity, 10976/10935 for chromat, 703125/702464 for trinity, 2401/2400 for amicable, 2100875/2097152 for calamity, 420175/419904 for witcher, and 16875/16807 for familia.

Temperaments discussed elsewhere include:

The rest are considered below.

Septimal amity

Main article: Amity

Septimal amity can be described as the 46 & 53 temperament, which tempers out 4375/4374 and 5120/5103 in the 7-limit. 99edo is a good tuning, with generator 28\99.

Subgroup: 2.3.5.7

Comma list: 4375/4374, 5120/5103

Mapping: [⟨1 3 6 -2], ⟨0 -5 -13 17]]

Wedgie: ⟨⟨ 5 13 -17 9 -41 -76 ]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~128/105 = 339.446
  • POTE: ~2 = 1\1, ~128/105 = 339.432

Optimal ET sequence: 7, 32cd, 39, 46, 53, 99, 152, 251, 905bcdd

Badness: 0.023649

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4375/4374, 5120/5103

Mapping: [⟨1 3 6 -2 21], ⟨0 -5 -13 17 -62]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~128/105 = 339.485
  • POTE: ~2 = 1\1, ~128/105 = 339.464

Optimal ET sequence: 46e, 53, 99e, 152, 357d, 509dd, 661dd

Badness: 0.031506

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 625/624, 729/728

Mapping: [⟨1 3 6 -2 21 17], ⟨0 -5 -13 17 -62 -47]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~128/105 = 339.508
  • POTE: ~2 = 1\1, ~128/105 = 339.481

Optimal ET sequence: 46ef, 53, 99ef, 152f, 205

Badness: 0.028008

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 256/255, 352/351, 375/374, 540/539, 729/728

Mapping: [⟨1 3 6 -2 21 17 -1], ⟨0 -5 -13 17 -62 -47 18]]

Optimal tuning (CTE): ~2 = 1\1, ~17/14 = 339.496

Optimal ET sequence: 46ef, 53, 99ef, 152fg, 205gg

Badness: 0.026201

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 256/255, 324/323, 352/351, 375/374, 400/399, 456/455

Mapping: [⟨1 3 6 -2 21 17 -1 15], ⟨0 -5 -13 17 -62 -47 18 -38]]

Optimal tuning (CTE): ~2 = 1\1, ~17/14 = 339.501

Optimal ET sequence: 46efh, 53, 99ef, 152fg, 205gg

Badness: 0.018782

Hitchcock

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 2200/2187

Mapping: [⟨1 3 6 -2 6], ⟨0 -5 -13 17 -9]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~11/9 = 339.390
  • POTE: ~2 = 1\1, ~11/9 = 339.390

Optimal ET sequence: 7, 25cdde, 32cd, 39, 46, 53, 99

Badness: 0.035187

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 169/168, 176/175, 325/324

Mapping: [⟨1 3 6 -2 6 2], ⟨0 -5 -13 17 -9 6]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~11/9 = 339.411
  • POTE: ~2 = 1\1, ~11/9 = 339.419

Optimal ET sequence: 7, 25cddef, 32cd, 39, 46, 53, 99

Badness: 0.022448

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 121/120, 154/153, 169/168, 176/175, 273/272

Mapping: [⟨1 3 6 -2 6 2 -1], ⟨0 -5 -13 17 -9 6 18]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~11/9 = 339.366
  • POTE: ~2 = 1\1, ~11/9 = 339.366

Optimal ET sequence: 7, 25cddefgg, 32cdg, 39, 46, 99

Badness: 0.019395

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189

Mapping: [⟨1 3 6 -2 6 2 -1 0], ⟨0 -5 -13 17 -9 6 18 15]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~11/9 = 339.415
  • POTE: ~2 = 1\1, ~11/9 = 339.407

Optimal ET sequence: 7, 25cddefgghh, 32cdgh, 39h, 46, 53, 99h

Badness: 0.017513

Catamite

The catamite temperament (46 & 99ef) tempers out 441/440 (werckisma) and 896/891 (pentacircle) in the 11-limit; 196/195, 352/351 and 364/363 in the 13-limit. The word "catamite" itself is a term for male homosexual, but also a play on the words "cata-" (down) and "amity."

Subgroup: 2.3.5.7.11

Comma list: 441/440, 896/891, 4375/4374

Mapping: [⟨1 3 6 -2 -7], ⟨0 -5 -13 17 37]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~128/105 = 339.314
  • POTE: ~2 = 1\1, ~128/105 = 339.340

Optimal ET sequence: 46, 99e, 145

Badness: 0.040976

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 364/363, 4375/4374

Mapping: [⟨1 3 6 -2 -7 -11], ⟨0 -5 -13 17 37 52]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~128/105 = 339.277
  • POTE: ~2 = 1\1, ~128/105 = 339.313

Optimal ET sequence: 46, 99ef, 145, 191c, 336cef, 527bccef

Badness: 0.034215

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155

Mapping: [⟨1 3 6 -2 -7 -11 -1], ⟨0 -5 -13 17 37 52 18]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~17/14 = 339.272
  • POTE: ~2 = 1\1, ~17/14 = 339.313

Optimal ET sequence: 46, 99ef, 145, 191c

Badness: 0.021193

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475

Mapping: [⟨1 3 6 -2 -7 -11 -1 -13], ⟨0 -5 -13 17 37 52 18 61]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~17/14 = 339.282
  • POTE: ~2 = 1\1, ~17/14 = 339.325

Optimal ET sequence: 46, 99ef, 145, 191c, 336cefg

Badness: 0.018864

Hemiamity

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4375/4374, 5120/5103

Mapping: [⟨2 1 -1 13 13], ⟨0 5 13 -17 -14]]

mapping generators: ~99/70, ~64/55

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~64/55 = 260.566
  • POTE: ~99/70 = 1\2, ~64/55 = 260.561

Optimal ET sequence: 14cde, 32cde, 46, 106, 152, 350

Badness: 0.031307

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 847/845, 1716/1715, 3025/3024

Mapping: [⟨2 1 -1 13 13 20], ⟨0 5 13 -17 -14 -29]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~64/55 = 260.607
  • POTE: ~99/70 = 1\2, ~64/55 = 260.583

Optimal ET sequence: 46, 106f, 152f, 198

Badness: 0.025784

Accord

Subgroup: 2.3.5.7

Comma list: 126/125, 100352/98415

Mapping: [⟨1 3 6 11], ⟨0 -5 -13 -29]]

Wedgie: ⟨⟨ 5 13 29 9 32 31 ]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~243/200 = 339.154
  • POTE: ~2 = 1\1, ~243/200 = 338.993

Optimal ET sequence: 7d, 25cddd, 32cdd, 39d, 46

Badness: 0.095612

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 126/125, 896/891

Mapping: [⟨1 3 6 11 6], ⟨0 -5 -13 -29 -9]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~11/9 = 339.136
  • POTE: ~2 = 1\1, ~11/9 = 339.047

Optimal ET sequence: 7d, 25cddde, 32cdd, 39d, 46

Badness: 0.042468

Houborizic

The houborizic temperament (53 & 60) tempers out the marvel comma, 225/224. It is so named because it is closely related to the houboriz tuning (generator: 339.774971 cents).

Subgroup: 2.3.5.7

Comma list: 225/224, 1250000/1240029

Mapping: [⟨1 3 6 13], ⟨0 -5 -13 -36]]

Wedgie: ⟨⟨ 5 13 36 9 43 47 ]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~243/200 = 339.711
  • POTE: ~2 = 1\1, ~243/200 = 339.763

Optimal ET sequence: 7d, 32cdddd, 39ddd, 46d, 53, 166, 219c, 272c

Badness: 0.066638

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 1250000/1240029

Mapping: [⟨1 3 6 13 -9], ⟨0 -5 -13 -36 44]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~243/200 = 339.751
  • POTE: ~2 = 1\1, ~243/200 = 339.763

Optimal ET sequence: 53, 113, 166, 551ccee

Badness: 0.067891

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 325/324, 385/384, 2200/2197

Mapping: [⟨1 3 6 13 -9 2], ⟨0 -5 -13 -36 44 6]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~39/32 = 339.754
  • POTE: ~2 = 1\1, ~39/32 = 339.764

Optimal ET sequence: 53, 113, 166

Badness: 0.032996

Houbor

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 2200/2187

Mapping: [⟨1 3 6 13 6], ⟨0 -5 -13 -36 -9]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~11/9 = 339.680
  • POTE: ~2 = 1\1, ~11/9 = 339.814

Optimal ET sequence: 7d, 32cdddd, 39ddd, 46d, 53

Badness: 0.045232

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 225/224, 275/273, 325/324

Mapping: [⟨1 3 6 13 6 2], ⟨0 -5 -13 -36 -9 6]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~11/9 = 339.685
  • POTE: ~2 = 1\1, ~11/9 = 339.784

Optimal ET sequence: 7d, 32cdddd, 39ddd, 46d, 53

Badness: 0.031331

Paramity

The paramity temperament (53 & 311) tempers out the horwell comma (65625/65536) and garischisma (33554432/33480783).

Subgroup: 2.3.5.7

Comma list: 65625/65536, 1600000/1594323

Mapping: [⟨1 3 6 -17], ⟨0 -5 -13 70]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~243/200 = 339.554
  • POTE: ~2 = 1\1, ~243/200 = 339.553

Optimal ET sequence: 53, 205d, 258, 311, 675, 986

Badness: 0.113655

11-limit

Subgroup: 2.3.5.7.11

Comma list: 6250/6237, 19712/19683, 41503/41472

Mapping: [⟨1 3 6 -17 36], ⟨0 -5 -13 70 -115]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~243/200 = 339.554
  • POTE: ~2 = 1\1, ~243/200 = 339.554

Optimal ET sequence: 53, 205de, 258, 311, 675, 986

Badness: 0.064853

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683

Mapping: [⟨1 3 6 -17 36 17], ⟨0 -5 -13 70 -115 -47]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~243/200 = 339.554
  • POTE: ~2 = 1\1, ~243/200 = 339.554

Optimal ET sequence: 53, 205de, 258, 311, 675, 986, 1661cf

Badness: 0.030347

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430

Mapping: [⟨1 3 6 -17 36 17 -31], ⟨0 -5 -13 70 -115 -47 124]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~243/200 = 339.555
  • POTE: ~2 = 1\1, ~243/200 = 339.555

Optimal ET sequence: 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf

Badness: 0.024118

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197

Mapping: [⟨1 3 6 -17 36 17 -31 15], ⟨0 -5 -13 70 -115 -47 124 -38]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~208/171 = 339.555
  • POTE: ~2 = 1\1, ~208/171 = 339.555

Optimal ET sequence: 53, 205deg, 258g, 311, 675, 986, 1661cfh

Badness: 0.017420

Bamity

Bamity has a period of half octave and tempers out the sensamagic comma, 245/243. The name bamity is a contraction of bi- and amity.

Subgroup: 2.3.5.7

Comma list: 245/243, 64827/64000

Mapping: [⟨2 1 -1 3], ⟨0 5 13 6]]

mapping generators: ~343/240, ~7/6

Wedgie: ⟨⟨ 10 26 12 18 -9 -45 ]]

Optimal tunings:

  • CTE: ~343/240 = 1\2, ~7/6 = 260.563
  • POTE: ~343/240 = 1\2, ~7/6 = 260.402

Optimal ET sequence: 14c, 32c, 46, 106d, 152d

Badness: 0.083601

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 245/243, 441/440

Mapping: [⟨2 1 -1 3 3], ⟨0 5 13 6 9]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~7/6 = 260.653
  • POTE: ~99/70 = 1\2, ~7/6 = 260.393

Optimal ET sequence: 14c, 32c, 46, 152de, 198, 244dee

Badness: 0.035504

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 121/120, 245/243, 441/440

Mapping: [⟨2 1 -1 3 3 0], ⟨0 5 13 6 9 17]]

Optimal tunings:

  • CTE: ~55/39 = 1\2, ~7/6 = 260.811
  • POTE: ~55/39 = 1\2, ~7/6 = 260.618

Optimal ET sequence: 14cf, 32cf, 46

Badness: 0.030885

Hamity

Hamity has a generator of about 430 cents which represents 9/7. It is also generated by half of acute minor "tenth" (acute minor third of 243/200 plus an octave), and its name is a contraction of half and amity.

Subgroup: 2.3.5.7

Comma list: 2430/2401, 4000/3969

Mapping: [⟨1 8 19 15], ⟨0 -10 -26 -19]]

mapping generators: ~2, ~14/9

Wedgie: ⟨⟨ 10 26 19 18 2 -29 ]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~9/7 = 430.168
  • POTE: ~2 = 1\1, ~9/7 = 430.219

Optimal ET sequence: 14c, 39d, 53

Badness: 0.073956

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 121/120, 2200/2187

Mapping: [⟨1 8 19 15 15], ⟨0 -10 -26 -19 -18]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~9/7 = 430.220
  • POTE: ~2 = 1\1, ~9/7 = 430.192

Optimal ET sequence: 14c, 39d, 53

Badness: 0.042947

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 121/120, 275/273, 572/567

Mapping: [⟨1 8 19 15 15 30], ⟨0 -10 -26 -19 -18 -41]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~9/7 = 430.233
  • POTE: ~2 = 1\1, ~9/7 = 430.216

Optimal ET sequence: 14cf, 39df, 53

Badness: 0.029753

Gamity

The gamity temperament (46 & 113) tempers out the gamelisma, 1029/1024. It splits the interval of grave major sixth (~400/243, an octave minus acute minor third) in three.

Subgroup: 2.3.5.7

Comma list: 1029/1024, 1071875/1062882

Mapping: [⟨1 13 32 -1], ⟨0 -15 -39 5]]

mapping generators: ~2, ~320/189

Wedgie: ⟨⟨ 15 39 -5 27 -50 -121 ]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~189/160 = 286.816
  • POTE: ~2 = 1\1, ~189/160 = 286.787

Optimal ET sequence: 46, 113, 159, 205d, 364d

Badness: 0.125733

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 1071875/1062882

Mapping: [⟨1 13 32 -1 -11], ⟨0 -15 -39 5 19]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~33/28 = 286.813
  • POTE: ~2 = 1\1, ~33/28 = 286.797

Optimal ET sequence: 46, 113, 159, 205d, 364d

Badness: 0.051111

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 385/384, 10985/10976

Mapping: [⟨1 13 32 -1 -11 -10], ⟨0 -15 -39 5 19 18]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~13/11 = 286.803
  • POTE: ~2 = 1\1, ~13/11 = 286.789

Optimal ET sequence: 46, 113, 159, 364df, 523ddff

Badness: 0.030297

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757

Mapping: [⟨1 13 32 -1 -11 -10 -2], ⟨0 -15 -39 5 19 18 8]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~13/11 = 286.804
  • POTE: ~2 = 1\1, ~13/11 = 286.795

Optimal ET sequence: 46, 113, 159, 364df, 523ddff

Badness: 0.022036

Trinity

The trinity temperament (152 & 159) tempers out the meter, 703125/702464. It splits the acute minor tenth (~243/100, an octave plus acute minor third) in three. It was so named for the following reason – 133\311 (133 steps of 311edo) is a possible generator, which is placed around 3\7 (1.1¢ flat), three of which makes acute minor third of ~243/200 with octave reduction.

Subgroup: 2.3.5.7

Comma list: 703125/702464, 1600000/1594323

Mapping: [⟨1 8 19 46], ⟨0 -15 -39 -101]]

Wedgie: ⟨⟨ 15 39 101 27 118 125 ]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~168/125 = 513.180
  • POTE: ~2 = 1\1, ~168/125 = 513.178

Optimal ET sequence: 7d, …, 145d, 152, 311, 774, 1085

Badness: 0.119453

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4000/3993, 19712/19683

Mapping: [⟨1 8 19 46 18], ⟨0 -15 -39 -101 -34]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~121/90 = 513.181
  • POTE: ~2 = 1\1, ~121/90 = 513.177

Optimal ET sequence: 7d, …, 145d, 152, 311, 774, 1085e, 1396e

Badness: 0.031296

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689

Mapping: [⟨1 8 19 46 18 64], ⟨0 -15 -39 -101 -34 -141]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~35/26 = 513.184
  • POTE: ~2 = 1\1, ~35/26 = 513.182

Optimal ET sequence: 152f, 159, 311

Badness: 0.026418

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619

Mapping: [⟨1 8 19 46 18 64 -22], ⟨0 -15 -39 -101 -34 -141 61]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~35/26 = 513.185
  • POTE: ~2 = 1\1, ~35/26 = 513.186

Optimal ET sequence: 152f, 159, 311, 1714cdeg, 2025cdefgg, 2336bccdefgg

Badness: 0.025588

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573

Mapping: [⟨1 8 19 46 18 64 -22 53], ⟨0 -15 -39 -101 -34 -141 61 -114]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~35/26 = 513.184
  • POTE: ~2 = 1\1, ~35/26 = 513.185

Optimal ET sequence: 152f, 159, 311

Badness: 0.018412

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104

Mapping: [⟨1 8 19 46 18 64 -22 53 49], ⟨0 -15 -39 -101 -34 -141 61 -114 -104]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~35/26 = 513.184
  • POTE: ~2 = 1\1, ~35/26 = 513.185

Optimal ET sequence: 152f, 159, 311, 1714cdeghi, 2025cdefgghhi, 2336bccdefgghhi

Badness: 0.014343

29-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044

Mapping: [⟨1 8 19 46 18 64 -22 53 49 72], ⟨0 -15 -39 -101 -34 -141 61 -114 -104 -157]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~35/26 = 513.185
  • POTE: ~2 = 1\1, ~35/26 = 513.186

Optimal ET sequence: 152fj, 159, 311, 1403cdgh, 1714cdeghi, 2025cdefgghhij, 2336bccdefgghhij

Badness: 0.012038

Amicable

The amicable temperament (99 & 311) 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

Comma list: 2401/2400, 1600000/1594323

Mapping: [⟨1 3 6 5], ⟨0 -20 -52 -31]]

Wedgie: ⟨⟨ 20 52 31 36 -7 -74 ]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~21/20 = 84.8831
  • POTE: ~2 = 1\1, ~21/20 = 84.880

Optimal ET sequence: 14c, …, 85c, 99, 212, 311, 721, 1032, 1753b

Badness: 0.045473

Amical

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 131072/130977, 1600000/1594323

Mapping: [⟨1 3 6 5 -8], ⟨0 -20 -52 -31 162]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~21/20 = 84.8843
  • POTE: ~2 = 1\1, ~21/20 = 84.8843

Optimal ET sequence: 99, 212e, 311, 721, 1032, 1343, 2375bc

Badness: 0.100668

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206

Mapping: [⟨1 3 6 5 -8 -5], ⟨0 -20 -52 -31 162 123]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~21/20 = 84.8837
  • POTE: ~2 = 1\1, ~21/20 = 84.8838

Optimal ET sequence: 99, 212ef, 311, 721, 1032

Badness: 0.049893

Amorous

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 6250/6237, 19712/19683

Mapping: [⟨1 3 6 5 14], ⟨0 -20 -52 -31 -149]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~21/20 = 84.8883
  • POTE: ~2 = 1\1, ~21/20 = 84.8896

Optimal ET sequence: 99e, 212, 311, 2389bccd, 2700bccde, 3011bccde, 3322bccdde

Badness: 0.048924

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647

Mapping: [⟨1 3 6 5 14 17], ⟨0 -20 -52 -31 -149 -188]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~21/20 = 84.8895
  • POTE: ~2 = 1\1, ~21/20 = 84.8910

Optimal ET sequence: 99ef, 212, 311, 1145c, 1456cd, 1767cd

Badness: 0.034681

Pseudoamical

Subgroup: 2.3.5.7.11

Comma list: 385/384, 1375/1372, 1600000/1594323

Mapping: [⟨1 3 6 5 -1], ⟨0 -20 -52 -31 63]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~21/20 = 84.9005
  • POTE: ~2 = 1\1, ~21/20 = 84.9091

Optimal ET sequence: 14ce, …, 85cee, 99, 212

Badness: 0.085837

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 385/384, 1375/1372, 19773/19712

Mapping: [⟨1 3 6 5 -1 2], ⟨0 -20 -52 -31 63 24]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~21/20 = 84.9049
  • POTE: ~2 = 1\1, ~21/20 = 84.9127

Optimal ET sequence: 14ce, …, 85ceef, 99, 113, 212

Badness: 0.047025

Pseudoamorous

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 980000/970299

Mapping: [⟨1 3 6 5 7], ⟨0 -20 -52 -31 -50]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~21/20 = 84.9022
  • POTE: ~2 = 1\1, ~21/20 = 84.8917

Optimal ET sequence: 14c, …, 85ce, 99e, 113, 212e

Badness: 0.056583

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 364/363, 441/440, 1875/1859

Mapping: [⟨1 3 6 5 7 10], ⟨0 -20 -52 -31 -50 -89]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~21/20 = 84.9153
  • POTE: ~2 = 1\1, ~21/20 = 84.9164

Optimal ET sequence: 14cf, …, 85ceff, 99ef, 113, 212ef, 325ce, 537cdeef

Badness: 0.042826

Floral

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 9801/9800, 14641/14580

Mapping: [⟨2 6 12 10 13], ⟨0 -20 -52 -31 -43]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~21/20 = 84.8781
  • POTE: ~99/70 = 1\2, ~21/20 = 84.8788

Optimal ET sequence: 14c, …, 170bccde, 184c, 198, 212, 410

Badness: 0.065110

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580

Mapping: [⟨2 6 12 10 13 19], ⟨0 -20 -52 -31 -43 -82]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~21/20 = 84.8759
  • POTE: ~99/70 = 1\2, ~21/20 = 84.8750

Optimal ET sequence: 14c, …, 184cff, 198, 410

Badness: 0.037013

Humorous

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024, 1600000/1594323

Mapping: [⟨1 3 6 5 3], ⟨0 -40 -104 -62 13]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~4096/3993 = 42.4414
  • POTE: ~2 = 1\1, ~4096/3993 = 42.4391

Optimal ET sequence: 85c, 113, 198, 311, 1131, 1442, 1753be

Badness: 0.058249

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024

Mapping: [⟨1 3 6 5 3 6], ⟨0 -40 -104 -62 13 -65]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~40/39 = 42.4425
  • POTE: ~2 = 1\1, ~40/39 = 42.4391

Optimal ET sequence: 85c, 113, 198, 311, 1753beff, 2064beff, 2375bceff

Badness: 0.028267

Calamity

The calamity temperament (46 & 311) tempers out the rainy comma, 2100875/2097152, splitting the interval of two octaves plus an acute minor third into five.

Subgroup: 2.3.5.7

Comma list: 1600000/1594323, 2100875/2097152

Mapping: [⟨1 13 32 -15], ⟨0 -25 -65 39]]

Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.909

Optimal ET sequence: 46, 219c, 265, 311

Badness: 0.198130

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 12005/11979, 131072/130977

Mapping: [⟨1 13 32 -15 -18], ⟨0 -25 -65 39 47]]

Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.908

Optimal ET sequence: 46, 219c, 265, 311, 979, 1290

Badness: 0.060408

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3025/3024, 4096/4095, 12005/11979

Mapping: [⟨1 13 32 -15 -18 -31], ⟨0 -25 -65 39 47 76]]

Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.907

Optimal ET sequence: 46, 265, 311, 668, 979, 1290

Badness: 0.033617

Familia

The familia temperament (113 & 152) tempers out the mirkwai comma, 16875/16807. It splits the interval of acute minor tenth (~243/100) in five.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 1600000/1594323

Mapping: [⟨1 8 19 20], ⟨0 -25 -65 -67]]

Wedgie: ⟨⟨ 25 65 67 45 36 -27 ]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~11907/10000 = 307.915
  • POTE: ~2 = 1\1, ~11907/10000 = 307.941

Optimal ET sequence: 39d, 74cd, 113, 152, 265, 417, 1516ccdd, 1933ccdd

Badness: 0.144551

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 1600000/1594323

Mapping: [⟨1 8 19 20 5], ⟨0 -25 -65 -67 -6]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~3200/2673 = 307.915
  • POTE: ~2 = 1\1, ~3200/2673 = 307.906

Optimal ET sequence: 39d, 74cd, 113, 152, 265, 417, 1099cdee

Badness: 0.051740

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1375/1372, 2205/2197

Mapping: [⟨1 8 19 20 5 25], ⟨0 -25 -65 -67 -6 -83]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~143/120 = 307.922
  • POTE: ~2 = 1\1, ~143/120 = 307.913

Optimal ET sequence: 39df, 74cdf, 113, 152f, 265

Badness: 0.038473

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