369edo: Difference between revisions
Expansion |
+RTT table and rank-2 temperaments |
||
| Line 8: | Line 8: | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Primes in edo|369}} | {{Primes in edo|369}} | ||
== 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]] (%) | |||
|- | |||
| 2.3.5 | |||
| {{monzo| 32 -7 -9 }}, {{monzo| 1 -27 18 }} | |||
| [{{val| 369 585 857 }}] | |||
| -0.1991 | |||
| 0.1409 | |||
| 4.33 | |||
|- | |||
| 2.3.5.7 | |||
| 2401/2400, 4375/4374, {{monzo| 32 -7 -9 }} | |||
| [{{val| 369 585 857 1036 }}] | |||
| -0.1743 | |||
| 0.1294 | |||
| 3.98 | |||
|- | |||
| 2.3.5.7.11 | |||
| 2401/2400, 4000/3993, 4375/4374, 5632/5625 | |||
| [{{val| 369 585 857 1036 1277 }}] | |||
| -0.2277 | |||
| 0.1576 | |||
| 4.85 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 1575/1573, 2080/2079, 2200/2197, 2401/2400, 3584/3575 | |||
| [{{val| 369 585 857 1036 1277 1366 }}] (369f) | |||
| -0.2685 | |||
| 0.1703 | |||
| 5.24 | |||
|} | |||
=== 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 | |||
| 17\369 | |||
| 339.56 | |||
| 33/32 | |||
| [[Escapade]] | |||
|- | |||
| 1 | |||
| 172\369 | |||
| 559.35 | |||
| 864/625 | |||
| [[Tritriple]] (5-limit) | |||
|- | |||
| 9 | |||
| 77\369<br>(5\369) | |||
| 250.41<br>(16.26) | |||
| 140/121<br>(100/99) | |||
| [[Semiennealimmal]] | |||
|- | |||
| 9 | |||
| 97\369<br>(15\369) | |||
| 315.45<br>(48.78) | |||
| 6/5<br>(36/35) | |||
| [[Ennealimmal]] | |||
|- | |||
| 9 | |||
| 68\369<br>(14\369) | |||
| 221.14<br>(45.53) | |||
| 25/22<br>(77/75) | |||
| [[Quadraennealimmal]] | |||
|- | |||
| 41 | |||
| 55\369<br>(1\369) | |||
| 178.86<br>(3.25) | |||
| 567/512<br>(352/351) | |||
| [[Hemicounterpyth]] | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Semiporwellismic]] | [[Category:Semiporwellismic]] | ||