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Septiennealimmal clan: Difference between revisions

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Move the description of no-five septiennealimmal here from the septimmal ennealimma article
+tunings
Line 21: Line 21:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~2592/2401 = 133.333, ~3/2 = 701.965
* [[CTE]]: ~2592/2401 = 133.333, ~3/2 = 702.0044
: [[error map]]: {{val| 0.0000 +0.0494 -0.1549 }}
* [[POTE]]: ~2592/2401 = 133.333, ~3/2 = 701.9649
: error map: {{val| 0.0000 +0.0099 -0.1944 }}


{{Optimal ET sequence|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, …, 8397dd, 8703dd }}
{{Optimal ET sequence|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, …, 8397dd, 8703dd }}
Line 37: Line 40:


Optimal tunings:  
Optimal tunings:  
* POTE: ~121/112 = 133.333, ~99/98 = 17.626
* CTE: ~121/112 = 133.333, 343/198 = 951.0143 (~99/98 = 17.6810)
* POTE: ~121/112 = 133.333, 343/198 = 950.9591 (~99/98 = 17.6258)


{{Optimal ET sequence|legend=0| 54, 63, 72, 135, 342, 477, 1089, 1566 }}
{{Optimal ET sequence|legend=0| 54, 63, 72, 135, 342, 477, 1089, 1566 }}
Line 68: Line 72:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~27/25 = 133.3333, ~5/3 = 884.3317 (~36/35 = 49.0016)
: [[error map]]: {{val| 0.0000 +0.0416 +0.0146 -0.1626 }}
* [[POTE]]: ~27/25 = 133.3333, ~5/3 = 884.3129 (~36/35 = 49.0205)
* [[POTE]]: ~27/25 = 133.3333, ~5/3 = 884.3129 (~36/35 = 49.0205)
: error map: {{val| 0.0000 +0.0040 -0.0418 -0.2002 }}


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 89: Line 96:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.4385 (~36/35 = 48.8948)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4679 (~36/35 = 48.8654)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4679 (~36/35 = 48.8654)


Line 103: Line 111:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.4285 (~36/35 = 48.9048)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4304 (~36/35 = 48.9030)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4304 (~36/35 = 48.9030)


Line 117: Line 126:


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4304 (~36/35 = 48.9030)
* CTE: ~27/25 = 133.3333, ~5/3 = 884.4110 (~36/35 = 48.9223)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4234 (~36/35 = 48.9099)


{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
Line 129: Line 139:


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4304 (~36/35 = 48.9030)
* CTE: ~27/25 = 133.3333, ~5/3 = 884.4139 (~36/35 = 48.9194)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4270 (~36/35 = 48.9063)


{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
Line 142: Line 153:
Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.4560 (~36/35 = 48.8773)
* CTE: ~27/25 = 133.3333, ~5/3 = 884.4560 (~36/35 = 48.8773)
* CWE: ~27/25 = 133.3333, ~5/3 = 884.4745 (~36/35 = 48.8588)


{{Optimal ET sequence|legend=0| 99ef, 171ef, 270, 639, 909, 1179, 2088bce }}
{{Optimal ET sequence|legend=0| 99ef, 171ef, 270, 639, 909, 1179, 2088bce }}
Line 157: Line 169:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.4113 (~36/35 = 48.9220)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4089 (~36/35 = 48.9244)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.4089 (~36/35 = 48.9244)


Line 171: Line 184:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.4055 (~36/35 = 48.9278)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.3997 (~36/35 = 48.9336)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.3997 (~36/35 = 48.9336)


{{Optimal ET sequence|legend=0| 99, 171, 270, 711, 981, 1692e, 2673e }}
{{Optimal ET sequence|legend=0| 99, 171, 270, 711, 981, 1692e }}


Badness (Smith): 0.016607
Badness (Smith): 0.016607
Line 185: Line 199:


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/25 = 133.3333, ~5/3 = 884.3997 (~36/35 = 48.9336)
* CTE: ~27/25 = 133.3333, ~5/3 = 884.3867 (~36/35 = 48.9466)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.3808 (~36/35 = 48.9525)


{{Optimal ET sequence|legend=0| 99, 171, 270 }}
{{Optimal ET sequence|legend=0| 99, 171, 270 }}
Line 197: Line 212:


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/25 = 133.3333, ~5/3 = 884.3997 (~36/35 = 48.9336)
* CTE: ~27/25 = 133.3333, ~5/3 = 884.3960 (~36/35 = 48.9373)
* POTE: ~27/25 = 133.3333, ~5/3 = 884.3985 (~36/35 = 48.9348)


{{Optimal ET sequence|legend=0| 99, 171, 270 }}
{{Optimal ET sequence|legend=0| 99, 171, 270 }}
Line 210: Line 226:
Mapping: {{mapping| 9 1 1 12 -2 | 0 2 3 2 5 }}
Mapping: {{mapping| 9 1 1 12 -2 | 0 2 3 2 5 }}


Optimal tuning (POTE): ~27/25 = 1\9, ~5/3 = 883.9386 (~36/35 = 49.3948)
Optimal tunings:
* CTE: ~27/25 = 133.3333, ~5/3 = 884.0697 (~36/35 = 49.2636)
* POTE: ~27/25 = 133.3333, ~5/3 = 883.9386 (~36/35 = 49.3948)


Tuning ranges:  
Tuning ranges:  
Line 230: Line 248:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.0603 (~36/35 = 49.2730)
* POTE: ~27/25 = 133.3333, ~5/3 = 883.9920 (~36/35 = 49.3414)
* POTE: ~27/25 = 133.3333, ~5/3 = 883.9920 (~36/35 = 49.3414)


Line 248: Line 267:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.0742 (~36/35 = 49.2591)
* POTE: ~27/25 = 133.3333, ~5/3 = 883.9981 (~36/35 = 49.3353)
* POTE: ~27/25 = 133.3333, ~5/3 = 883.9981 (~36/35 = 49.3353)


Line 264: Line 284:


Mapping: {{mapping| 9 1 1 12 -2 -33 -3 78  | 0 2 3 2 5 10 6 -6 }}
Mapping: {{mapping| 9 1 1 12 -2 -33 -3 78  | 0 2 3 2 5 10 6 -6 }}
Optimal tunings:
* CTE: ~27/25 = 133.3333, ~5/3 = 884.0366 (~36/35 = 49.2967)
* CWE: ~27/25 = 133.3333, ~5/3 = 883.9630 (~36/35 = 49.3703)


{{Optimal ET sequence|legend=0| 72, 171, 243 }}
{{Optimal ET sequence|legend=0| 72, 171, 243 }}
Line 275: Line 299:


Optimal tunings:  
Optimal tunings:  
* CTE: ~13/12 = 133.3333, ~5/3 = 884.2055 (~36/35 = 49.1278)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.6257 (~36/35 = 49.7076)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.6257 (~36/35 = 49.7076)


Line 289: Line 314:


Optimal tunings:  
Optimal tunings:  
* CTE: ~13/12 = 133.3333, ~5/3 = 884.1935 (~36/35 = 49.1398)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.6257 (~36/35 = 49.7076)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.6257 (~36/35 = 49.7076)


Line 301: Line 327:


Optimal tunings:  
Optimal tunings:  
* CTE: ~13/12 = 133.3333, ~5/3 = 884.1388 (~36/35 = 49.1945)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.6257 (~36/35 = 49.7076)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.6257 (~36/35 = 49.7076)


Line 313: Line 340:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.0925 (~36/35 = 49.2408)
* POTE: ~27/25 = 133.3333, ~5/3 = 883.8298 (~36/35 = 49.5036)
* POTE: ~27/25 = 133.3333, ~5/3 = 883.8298 (~36/35 = 49.5036)


Line 327: Line 355:


Optimal tunings:  
Optimal tunings:  
* CTE: ~13/12 = 133.3333, ~5/3 = 884.2648 (~36/35 = 49.0685)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.8476 (~36/35 = 49.4857)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.8476 (~36/35 = 49.4857)


Line 341: Line 370:


Optimal tunings:  
Optimal tunings:  
* CTE: ~13/12 = 133.3333, ~5/3 = 884.1032 (~36/35 = 49.2301)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.8476 (~36/35 = 49.4857)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.8476 (~36/35 = 49.4857)


Line 353: Line 383:


Optimal tunings:  
Optimal tunings:  
* CTE: ~13/12 = 133.3333, ~5/3 = 884.0186 (~36/35 = 49.3147)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.8476 (~36/35 = 49.4857)
* POTE: ~13/12 = 133.3333, ~5/3 = 883.8476 (~36/35 = 49.4857)


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