Xenharmonic Wiki

Septiennealimmal clan: Difference between revisions

← Older editNewer edit →
VisualWikitext
Overthink (talk | contribs)
autopatrolled
2,676 edits
→Ennealimnic: + distinguish (very similar name; just letter "m" and "n" difference)
m Units & misc. cleanup. + category
Line 18: Line 18:


{{Mapping|legend=2| 9 0 11 | 0 1 1 }}
{{Mapping|legend=2| 9 0 11 | 0 1 1 }}
 
: mapping generators: ~2592/2401, ~3
: sval mapping generators: ~2592/2401, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2592/2401 = 133.3333, ~3/2 = 702.0044
* [[CTE]]: ~2592/2401 = 133.3333{{c}}, ~3/2 = 702.0044{{c}}
: [[error map]]: {{val| 0.0000 +0.0494 -0.1549 }}
: [[error map]]: {{val| 0.0000 +0.0494 -0.1549 }}
* [[POTE]]: ~2592/2401 = 133.3333, ~3/2 = 701.9649
* [[POTE]]: ~2592/2401 = 133.3333{{c}}, ~3/2 = 701.9649{{c}}
: error map: {{val| 0.0000 +0.0099 -0.1944 }}
: error map: {{val| 0.0000 +0.0099 -0.1944 }}


Line 40: Line 39:
{{Mapping|legend=2| 9 0 11 19 | 0 1 1 1 }}
{{Mapping|legend=2| 9 0 11 19 | 0 1 1 1 }}


[[Optimal tuning]] ([[CTE]]): ~13/12 = 133.333, ~3/2 = 702.638
[[Optimal tuning]] ([[CTE]]): ~13/12 = 133.333{{c}}, ~3/2 = 702.638{{c}}


{{Optimal ET sequence|legend=1| 27, 36, 99, 135f, 171f }}
{{Optimal ET sequence|legend=1| 27, 36, 99, 135f, 171f }}
Line 58: Line 57:


Optimal tunings:  
Optimal tunings:  
* CTE: ~121/112 = 133.3333, 343/198 = 951.0143 (~99/98 = 17.6810)
* CTE: ~121/112 = 133.3333{{c}}, 343/198 = 951.0143{{c}} (~99/98 = 17.6810{{c}})
* POTE: ~121/112 = 133.3333, 343/198 = 950.9591 (~99/98 = 17.6258)
* POTE: ~121/112 = 133.3333{{c}}, 343/198 = 950.9591{{c}} (~99/98 = 17.6258{{c}})


{{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 84: Line 83:


{{Mapping|legend=1| 9 1 1 12 | 0 2 3 2 }}
{{Mapping|legend=1| 9 1 1 12 | 0 2 3 2 }}
: mapping generators: ~27/25, ~5/3
: mapping generators: ~27/25, ~5/3


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


Line 112: Line 110:


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


{{Optimal ET sequence|legend=0| 99e, 171e, 270, 909, 1179, 1449c, 1719c }}
{{Optimal ET sequence|legend=0| 99e, 171e, 270, 909, 1179, 1449c, 1719c }}
Line 127: Line 125:


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


{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
Line 142: Line 140:


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


{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
Line 155: Line 153:


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


{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
{{Optimal ET sequence|legend=0| 99e, 171e, 270 }}
Line 168: Line 166:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.4560 (~36/35 = 48.8773)
* CTE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.4560{{c}} (~36/35 = 48.8773{{c}})
* CWE: ~27/25 = 133.3333, ~5/3 = 884.4745 (~36/35 = 48.8588)
* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.4745{{c}} (~36/35 = 48.8588{{c}})


{{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 185: Line 183:


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


{{Optimal ET sequence|legend=0| 99, 171, 270, 711, 981, 1251, 2232e }}
{{Optimal ET sequence|legend=0| 99, 171, 270, 711, 981, 1251, 2232e }}
Line 200: Line 198:


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


{{Optimal ET sequence|legend=0| 99, 171, 270, 711, 981, 1692e }}
{{Optimal ET sequence|legend=0| 99, 171, 270, 711, 981, 1692e }}
Line 215: Line 213:


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


{{Optimal ET sequence|legend=0| 99, 171, 270 }}
{{Optimal ET sequence|legend=0| 99, 171, 270 }}
Line 228: Line 226:


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


{{Optimal ET sequence|legend=0| 99, 171, 270 }}
{{Optimal ET sequence|legend=0| 99, 171, 270 }}


=== Ennealimnic ===
=== Ennealimnic ===
{{Distinguish|Ennealimmic}}
{{Distinguish| Ennealimmic }}
 
Ennealimnic ({{nowrap| 72 & 171 }}) equates 11/9 with 27/22, 49/40, and 60/49 as a neutral third interval.
Ennealimnic ({{nowrap| 72 & 171 }}) equates 11/9 with 27/22, 49/40, and 60/49 as a neutral third interval.


Line 244: Line 243:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.0697 (~36/35 = 49.2636)
* CTE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.0697{{c}} (~36/35 = 49.2636{{c}})
* POTE: ~27/25 = 133.3333, ~5/3 = 883.9386 (~36/35 = 49.3948)
* POTE: ~27/25 = 133.3333{{c}}, ~5/3 = 883.9386{{c}} (~36/35 = 49.3948{{c}})


Tuning ranges:  
Tuning ranges:  
Line 265: Line 264:


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


Tuning ranges:  
Tuning ranges:  
Line 284: Line 283:


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


Tuning ranges:  
Tuning ranges:  
Line 303: Line 302:


Optimal tunings:  
Optimal tunings:  
* CTE: ~27/25 = 133.3333, ~5/3 = 884.0366 (~36/35 = 49.2967)
* CTE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.0366{{c}} (~36/35 = 49.2967{{c}})
* CWE: ~27/25 = 133.3333, ~5/3 = 883.9630 (~36/35 = 49.3703)
* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 883.9630{{c}} (~36/35 = 49.3703{{c}})


{{Optimal ET sequence|legend=0| 72, 171, 243 }}
{{Optimal ET sequence|legend=0| 72, 171, 243 }}
Line 316: Line 315:


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


{{Optimal ET sequence|legend=0| 27e, 45ef, 72 }}
{{Optimal ET sequence|legend=0| 27e, 45ef, 72 }}
Line 331: Line 330:


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


{{Optimal ET sequence|legend=0| 27eg, 45efg, 72 }}
{{Optimal ET sequence|legend=0| 27eg, 45efg, 72 }}
Line 344: Line 343:


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


{{Optimal ET sequence|legend=0| 27eg, 45efg, 72 }}
{{Optimal ET sequence|legend=0| 27eg, 45efg, 72 }}
Line 357: Line 356:


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


{{Optimal ET sequence|legend=0| 27, 45, 72, 171e, 243e, 315e }}
{{Optimal ET sequence|legend=0| 27, 45, 72, 171e, 243e, 315e }}
Line 372: Line 371:


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


{{Optimal ET sequence|legend=0| 27, 45f, 72, 171ef, 243eff }}
{{Optimal ET sequence|legend=0| 27, 45f, 72, 171ef, 243eff }}
Line 387: Line 386:


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


{{Optimal ET sequence|legend=0| 27, 45f, 72 }}
{{Optimal ET sequence|legend=0| 27, 45f, 72 }}
Line 400: Line 399:


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


{{Optimal ET sequence|legend=0| 27, 45f, 72 }}
{{Optimal ET sequence|legend=0| 27, 45f, 72 }}
Line 415: Line 414:


Mapping: {{mapping| 18 0 -1 22 48 | 0 2 3 2 1 }}
Mapping: {{mapping| 18 0 -1 22 48 | 0 2 3 2 1 }}
: mapping generators: ~80/77, ~400/231
: mapping generators: ~80/77, ~400/231


Optimal tunings:  
Optimal tunings:  
* POTE: ~80/77 = 66.6667, ~400/231 = 950.9553
* POTE: ~80/77 = 66.6667{{c}}, ~400/231 = 950.9553{{c}}


Tuning ranges:  
Tuning ranges:  
Line 437: Line 435:


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/26 = 66.6667, ~26/15 = 951.0837
* POTE: ~27/26 = 66.6667{{c}}, ~26/15 = 951.0837{{c}}


Tuning ranges:  
Tuning ranges:  
Line 457: Line 455:


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/26 = 66.6667, ~26/15 = 951.0837
* POTE: ~27/26 = 66.6667{{c}}, ~26/15 = 951.0837{{c}}


{{Optimal ET sequence|legend=0| 72, 198g, 270 }}
{{Optimal ET sequence|legend=0| 72, 198g, 270 }}
Line 469: Line 467:


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/26 = 66.6667, ~26/15 = 951.0837
* POTE: ~27/26 = 66.6667{{c}}, ~26/15 = 951.0837{{c}}


{{Optimal ET sequence|legend=1| 72, 198g, 270 }}
{{Optimal ET sequence|legend=1| 72, 198g, 270 }}
Line 483: Line 481:


Optimal tunings:  
Optimal tunings:  
* POTE: ~80/77 = 66.6667, ~1053/800 = 475.4727
* POTE: ~80/77 = 66.6667{{c}}, ~1053/800 = 475.4727{{c}}


{{Optimal ET sequence|legend=0| 126, 144, 270, 684, 954 }}
{{Optimal ET sequence|legend=0| 126, 144, 270, 684, 954 }}
Line 495: Line 493:


Mapping: {{mapping| 18 0 -1 22 48 88 -119 | 0 4 6 4 2 -3 27 }}
Mapping: {{mapping| 18 0 -1 22 48 88 -119 | 0 4 6 4 2 -3 27 }}
: mapping generators: ~80/77, ~1053/800


Optimal tunings:  
Optimal tunings:  
* POTE: ~80/77 = 66.6667, ~1053/800 = 475.4727
* POTE: ~80/77 = 66.6667{{c}}, ~1053/800 = 475.4727{{c}}


{{Optimal ET sequence|legend=0| 270, 684, 954 }}
{{Optimal ET sequence|legend=0| 270, 684, 954 }}
Line 511: Line 507:


Mapping: {{mapping| 18 0 -1 22 48 88 -119 -2 | 0 4 6 4 2 -3 27 11 }}
Mapping: {{mapping| 18 0 -1 22 48 88 -119 -2 | 0 4 6 4 2 -3 27 11 }}
: mapping generators: ~80/77, ~1053/800


Optimal tunings:  
Optimal tunings:  
* POTE: ~80/77 = 66.6667, ~1053/800 = 475.4727
* POTE: ~80/77 = 66.6667{{c}}, ~1053/800 = 475.4727{{c}}


{{Optimal ET sequence|legend=0| 270, 684h, 954h, 1224 }}
{{Optimal ET sequence|legend=0| 270, 684h, 954h, 1224 }}
Line 529: Line 523:


Mapping: {{mapping| 9 3 4 14 18 | 0 6 9 6 7 }}
Mapping: {{mapping| 9 3 4 14 18 | 0 6 9 6 7 }}
: mapping generators: ~27/25, ~140/121
: mapping generators: ~27/25, ~140/121


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/25 = 133.3333, ~140/121 = 250.3367
* POTE: ~27/25 = 133.3333{{c}}, ~140/121 = 250.3367{{c}}


{{Optimal ET sequence|legend=0| 72, 369, 441 }}
{{Optimal ET sequence|legend=0| 72, 369, 441 }}
Line 547: Line 540:


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/25 = 133.3333, ~140/121 = 250.3375
* POTE: ~27/25 = 133.3333{{c}}, ~140/121 = 250.3375{{c}}


{{Optimal ET sequence|legend=0| 72, 297ef, 369f, 441 }}
{{Optimal ET sequence|legend=0| 72, 297ef, 369f, 441 }}
Line 559: Line 552:


Mapping: {{mapping| 9 1 1 12 -7 | 0 8 12 8 23 }}
Mapping: {{mapping| 9 1 1 12 -7 | 0 8 12 8 23 }}
: mapping generators: ~27/25, ~25/22
: mapping generators: ~27/25, ~25/22


Optimal tunings:  
Optimal tunings:  
* POTE: ~27/25 = 133.3333, ~25/22 = 221.0717
* POTE: ~27/25 = 133.3333{{c}}, ~25/22 = 221.0717{{c}}


{{Optimal ET sequence|legend=0| 342, 1053, 1395, 1737, 4869dd, 6606cdd }}
{{Optimal ET sequence|legend=0| 342, 1053, 1395, 1737, 4869dd, 6606cdd }}
Line 575: Line 567:


Mapping: {{mapping| 27 1 0 34 177 | 0 2 3 2 -4 }}
Mapping: {{mapping| 27 1 0 34 177 | 0 2 3 2 -4 }}
: mapping generators: ~2744/2673, ~2352/1375
: mapping generators: ~2744/2673, ~2352/1375


Optimal tunings:  
Optimal tunings:  
* POTE: ~2744/2673 = 44.4444, ~2352/1375 = 928.8000
* POTE: ~2744/2673 = 44.4444{{c}}, ~2352/1375 = 928.8000{{c}}


{{Optimal ET sequence|legend=0| 27, 243, 270, 783, 1053, 1323 }}
{{Optimal ET sequence|legend=0| 27, 243, 270, 783, 1053, 1323 }}
Line 595: Line 586:


Mapping: {{mapping| 45 1 -1 56 226 | 0 2 3 2 -2 }}
Mapping: {{mapping| 45 1 -1 56 226 | 0 2 3 2 -2 }}
: mapping generators: ~3072/3025, ~55/32
: mapping generators: ~3072/3025, ~55/32


Optimal tunings:  
Optimal tunings:  
* CTE: ~3072/3025 = 26.6667, ~55/32 = 937.6658 (~385/384 = 4.3325)
* CTE: ~3072/3025 = 26.6667{{c}}, ~55/32 = 937.6658{{c}} (~385/384 = 4.3325{{c}})
* CWE: ~3072/3025 = 26.6667, ~55/32 = 937.6630 (~385/384 = 4.3397)
* CWE: ~3072/3025 = 26.6667{{c}}, ~55/32 = 937.6630{{c}} (~385/384 = 4.3397{{c}})


{{Optimal ET sequence|legend=0| 45, 225c, 270, 1125, 1395, 1665, 5265d }}
{{Optimal ET sequence|legend=0| 45, 225c, 270, 1125, 1395, 1665, 5265d }}
Line 614: Line 604:


Optimal tunings:  
Optimal tunings:  
* CTE: ~66/65 = 26.6667, ~55/32 = 937.6569 (~385/384 = 4.3236)
* CTE: ~66/65 = 26.6667{{c}}, ~55/32 = 937.6569{{c}} (~385/384 = 4.3236{{c}})
* CWE: ~66/65 = 26.6667, ~55/32 = 937.6515 (~385/384 = 4.3182)
* CWE: ~66/65 = 26.6667{{c}}, ~55/32 = 937.6515{{c}} (~385/384 = 4.3182{{c}})


{{Optimal ET sequence|legend=0| 45, 270, 855, 1125, 1395, 1665, 3060d, 4725df }}
{{Optimal ET sequence|legend=0| 45, 270, 855, 1125, 1395, 1665, 3060d, 4725df }}
Line 631: Line 621:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~126/125 = 12.121, ~11/8 = 552.756
* [[POTE]]: ~126/125 = 12.121{{c}}, ~11/8 = 552.756{{c}}


{{Optimal ET sequence|legend=1| 99e, 198, 297e, 495ce }}
{{Optimal ET sequence|legend=1| 99e, 198, 297e, 495ce }}
Line 645: Line 635:


Optimal tunings:  
Optimal tunings:  
* POTE: ~144/143 = 12.121, ~11/8 = 552.024
* POTE: ~144/143 = 12.121{{c}}, ~11/8 = 552.024{{c}}


{{Optimal ET sequence|legend=0| 99ef, 198 }}
{{Optimal ET sequence|legend=0| 99ef, 198 }}
Line 661: Line 651:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~225/224 = 7.018, ~11/8 = 550.954
* [[POTE]]: ~225/224 = 7.018{{c}}, ~11/8 = 550.954{{c}}


{{Optimal ET sequence|legend=1| 171, 342 }}
{{Optimal ET sequence|legend=1| 171, 342 }}
Line 675: Line 665:


Optimal tunings:  
Optimal tunings:  
* POTE: ~225/224 = 7.018, ~11/8 = 551.322
* POTE: ~225/224 = 7.018{{c}}, ~11/8 = 551.322{{c}}


{{Optimal ET sequence|legend=0| 171, 342, 855ff, 1197fff }}
{{Optimal ET sequence|legend=0| 171, 342, 855ff, 1197fff }}
Line 689: Line 679:


Optimal tunings:  
Optimal tunings:  
* POTE: ~225/224 = 7.018, ~11/8 = 551.365
* POTE: ~225/224 = 7.018{{c}}, ~11/8 = 551.365{{c}}


{{Optimal ET sequence|legend=0| 171, 342, 855ff, 1197fff }}
{{Optimal ET sequence|legend=0| 171, 342, 855ff, 1197fff }}
Line 703: Line 693:


Optimal tunings:  
Optimal tunings:  
* POTE: ~225/224 = 7.018, ~11/8 = 551.625
* POTE: ~225/224 = 7.018{{c}}, ~11/8 = 551.625{{c}}


{{Optimal ET sequence|legend=1| 171, 342f, 513, 855f }}
{{Optimal ET sequence|legend=1| 171, 342f, 513, 855f }}
Line 717: Line 707:


Optimal tunings:  
Optimal tunings:  
* POTE: ~225/224 = 7.018, ~11/8 = 551.756
* POTE: ~225/224 = 7.018{{c}}, ~11/8 = 551.756{{c}}


{{Optimal ET sequence|legend=0| 171, 342f, 513, 855f }}
{{Optimal ET sequence|legend=0| 171, 342f, 513, 855f }}
Line 733: Line 723:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[POTE]]: ~32805/32768 = 2.7211, ~11/8 = 551.3584
* [[POTE]]: ~32805/32768 = 2.7211{{c}}, ~11/8 = 551.3584{{c}}


{{Optimal ET sequence|legend=1| 441, 882, 1323, 2205, 3528 }}
{{Optimal ET sequence|legend=1| 441, 882, 1323, 2205, 3528 }}
Line 747: Line 737:


Optimal tunings:  
Optimal tunings:  
* POTE: ~729/728 = 2.7211, ~11/8 = 551.4043
* POTE: ~729/728 = 2.7211{{c}}, ~11/8 = 551.4043{{c}}


{{Optimal ET sequence|legend=0| 441, 882, 1323, 3528f, 4851ff, 6174dff }}
{{Optimal ET sequence|legend=0| 441, 882, 1323, 3528f, 4851ff, 6174dff }}
Line 761: Line 751:


Optimal tunings:  
Optimal tunings:  
* POTE: ~729/728 = 2.7211, ~11/8 = 551.3688
* POTE: ~729/728 = 2.7211{{c}}, ~11/8 = 551.3688{{c}}


{{Optimal ET sequence|legend=0| 441, 882, 1323, 2205f, 3528f }}
{{Optimal ET sequence|legend=0| 441, 882, 1323, 2205f, 3528f }}
Line 767: Line 757:
Badness (Smith): 0.029334
Badness (Smith): 0.029334


[[Category:Septiennealimmal clan| ]] <!-- main article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Septiennealimmal_clan"