373edo: Difference between revisions
Cleanup; +prime error table |
+RTT table and rank-2 temperaments |
||
| Line 1: | Line 1: | ||
'''373edo''' is the [[EDO|equal division of the octave]] into 373 parts of 3.21716 [[cent]]s each. | '''373edo''' is the [[EDO|equal division of the octave]] into 373 parts of 3.21716 [[cent]]s each. | ||
== Theory == | |||
373edo is consistent to the [[15-odd-limit]], tempering out 1224440064/1220703125 ([[parakleisma]]) and {{monzo| -51 19 9 }}; (untritonic comma) in the 5-limit; [[2401/2400]], 65625/65536, and 43046721/42875000 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, and 496125/495616 in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4225/4224]], and [[10648/10647]] in the 13-limit. It supports the [[Breedsmic temperaments #Hemitert|hemitert temperament]]. | |||
373edo is the 74th [[prime edo]]. | 373edo is the 74th [[prime edo]]. | ||
| Line 5: | Line 8: | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Primes in edo|373}} | {{Primes in edo|373}} | ||
== 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| -591 373 }} | |||
| [{{val| 373 591 }}] | |||
| +0.1939 | |||
| 0.1939 | |||
| 6.03 | |||
|- | |||
| 2.3.5 | |||
| {{monzo| 8 14 -13 }}, {{monzo| -51 19 9 }} | |||
| [{{val| 373 591 866 }}] | |||
| +0.1658 | |||
| 0.1632 | |||
| 5.07 | |||
|- | |||
| 2.3.5.7 | |||
| 2401/2400, 65625/65536, 43046721/42875000 | |||
| [{{val| 373 591 866 1047 }}] | |||
| +0.1654 | |||
| 0.1413 | |||
| 4.39 | |||
|- | |||
| 2.3.5.7.11 | |||
| 2401/2400, 3025/3024, 8019/8000, 65625/65536 | |||
| [{{val| 373 591 866 1047 1290 }}] | |||
| +0.2008 | |||
| 0.1449 | |||
| 4.50 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224 | |||
| [{{val| 373 591 866 1047 1290 1380 }}] | |||
| +0.2056 | |||
| 0.1327 | |||
| 4.12 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per octave | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 12\373 | |||
| 38.61 | |||
| 45/44 | |||
| [[Hemitert]] | |||
|- | |||
| 1 | |||
| 24\373 | |||
| 77.21 | |||
| 256/245 | |||
| [[Tertiaseptal]] | |||
|- | |||
| 1 | |||
| 98\373 | |||
| 315.28 | |||
| 6/5 | |||
| [[Parakleismic]] (5-limit) | |||
|- | |||
| 1 | |||
| 111\373 | |||
| 357.10 | |||
| 768/625 | |||
| [[Dodifo]] (5-limit) | |||
|- | |||
| 1 | |||
| 162\373 | |||
| 521.18 | |||
| 875/648 | |||
| [[Maviloid]] | |||
|- | |||
| 1 | |||
| 183\373 | |||
| 588.74 | |||
| 45/32 | |||
| [[Untriton]] (5-limit) | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||