487edo: Difference between revisions
Expansion |
+RTT table and rank-2 temperaments |
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| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
487et tempers out {{monzo| 24 -21 4 }} ([[vulture comma]]) and {{monzo| 55 -1 -23 }} in the 5-limit, | 487et tempers out {{monzo| 24 -21 4 }} ([[vulture comma]]) and {{monzo| 55 -1 -23 }} in the 5-limit, 4375/4374 ([[ragisma]]), 235298/234375 ([[triwellisma]]), and 33554432/33480783 ([[garischisma]]) in the 7-limit, [[5632/5625]], [[12005/11979]], [[19712/19683]], [[41503/41472]] in the 11-limit, [[676/675]], [[1001/1000]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. It supports [[semidimfourth]], [[seniority]], and [[vulture]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 10: | Line 10: | ||
=== Miscellaneous properties === | === Miscellaneous properties === | ||
487edo is the 93rd [[prime edo]]. | 487edo is the 93rd [[prime edo]]. | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list|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| 772 -487 }} | |||
| [{{val| 487 772 }}] | |||
| -0.0958 | |||
| 0.0958 | |||
| 3.89 | |||
|- | |||
| 2.3.5 | |||
| {{monzo| 24 -21 4 }}, {{monzo| 55 -1 -23 }} | |||
| [{{val| 487 772 1131 }}] | |||
| -0.1421 | |||
| 0.1020 | |||
| 4.14 | |||
|- | |||
| 2.3.5.7 | |||
| 4375/4374, 235298/234375, 33554432/33480783 | |||
| [{{val| 487 772 1131 1367 }}] | |||
| -0.0667 | |||
| 0.1577 | |||
| 6.40 | |||
|- | |||
| 2.3.5.7.11 | |||
| 4375/4374, 5632/5625, 12005/11979, 41503/41472 | |||
| [{{val| 487 772 1131 1367 1685 }}] | |||
| -0.0899 | |||
| 0.1485 | |||
| 6.03 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979 | |||
| [{{val| 487 772 1131 1367 1685 1802 }}] | |||
| -0.0623 | |||
| 0.1490 | |||
| 6.05 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(Reduced) | |||
! Cents<br>(Reduced) | |||
! Associated<br>Ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 131\487 | |||
| 322.79 | |||
| 3087/2560 | |||
| [[Seniority]] | |||
|- | |||
| 1 | |||
| 182\487 | |||
| 448.46 | |||
| 35/27 | |||
| [[Semidimfourth]] | |||
|- | |||
| 1 | |||
| 193\487 | |||
| 475.56 | |||
| 320/243 | |||
| [[Vulture]] | |||
|- | |||
| 1 | |||
| 202\487 | |||
| 497.74 | |||
| 4/3 | |||
| [[Gary]] | |||
|- | |||
| 1 | |||
| 227\487 | |||
| 559.34 | |||
| 864/625 | |||
| [[Tritriple]] (5-limit) | |||
|} | |||
== Scales == | == Scales == | ||