157edo: Difference between revisions
+intro and prime harmonics table |
+RTT table |
||
| Line 8: | Line 8: | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Primes in edo|157}} | {{Primes in edo|157}} | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" | Subgroup | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| 249 -157 }} | |||
| [{{val| 157 249 }}] | |||
| -0.388 | |||
| 0.388 | |||
| 5.08 | |||
|- | |||
| 2.3.5 | |||
| 78732/78125, {{val| 37 -16 -5 }} | |||
| [{{val| 157 249 365 }}] | |||
| -0.760 | |||
| 0.614 | |||
| 8.04 | |||
|- | |||
| 2.3.5.7 | |||
| 2401/2400, 5120/5103, 78732/78125 | |||
| [{{val| 157 249 365 441 }}] | |||
| -0.737 | |||
| 0.533 | |||
| 6.98 | |||
|- | |||
| 2.3.5.7.11 | |||
| 176/175, 1331/1323, 2401/2400, 5120/5103 | |||
| [{{val| 157 249 365 441 543 }}] | |||
| -0.532 | |||
| 0.629 | |||
| 8.24 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 176/175, 351/350, 847/845, 1331/1323, 2197/2187 | |||
| [{{val| 157 249 365 441 543 581 }}] | |||
| -0.454 | |||
| 0.600 | |||
| 7.86 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 176/175, 256/255, 351/350, 442/441, 715/714, 2197/2187 | |||
| [{{val| 157 249 365 441 543 581 642 }}] | |||
| -0.461 | |||
| 0.556 | |||
| 7.28 | |||
|- | |||
| 2.3.5.7.11.13.17.19 | |||
| 176/175, 256/255, 286/285, 351/350, 361/360, 442/441, 476/475 | |||
| [{{val| 157 249 365 441 543 581 642 667 }}] | |||
| -0.420 | |||
| 0.531 | |||
| 6.95 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all right-3 left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per octave | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperament | |||
|- | |||
| 1 | |||
| 46\157 | |||
| 351.59 | |||
| 49/40 | |||
| [[Hemififths]] | |||
|- | |||
| 1 | |||
| 56\157 | |||
| 428.03 | |||
| 2800/2187 | |||
| [[Osiris]] | |||
|- | |||
| 1 | |||
| 58\157 | |||
| 443.31 | |||
| 49/40 | |||
| [[Sensipent]] | |||
|- | |||
| 1 | |||
| 64\157 | |||
| 489.17 | |||
| 250/189 | |||
| [[Catafourth]] | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||