487edo: Difference between revisions
+counterwuerschmidt |
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
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| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
487edo is [[consistency|distinctly consistent]] to the [[13-odd-limit]]. The equal temperament [[tempering out|tempers out]] {{monzo| 24 -21 4 }} ([[vulture comma]]) and {{monzo| 55 -1 -23 }} (counterwürschmidt comma) 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 24: | Line 24: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 772 -487 }} | | {{monzo| 772 -487 }} | ||
| | | {{mapping| 487 772 }} | ||
| -0.0958 | | -0.0958 | ||
| 0.0958 | | 0.0958 | ||
| Line 31: | Line 31: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 24 -21 4 }}, {{monzo| 55 -1 -23 }} | | {{monzo| 24 -21 4 }}, {{monzo| 55 -1 -23 }} | ||
| | | {{mapping| 487 772 1131 }} | ||
| -0.1421 | | -0.1421 | ||
| 0.1020 | | 0.1020 | ||
| Line 38: | Line 38: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, 235298/234375, 33554432/33480783 | | 4375/4374, 235298/234375, 33554432/33480783 | ||
| | | {{mapping| 487 772 1131 1367 }} | ||
| -0.0667 | | -0.0667 | ||
| 0.1577 | | 0.1577 | ||
| Line 45: | Line 45: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 4375/4374, 5632/5625, 12005/11979, 41503/41472 | | 4375/4374, 5632/5625, 12005/11979, 41503/41472 | ||
| | | {{mapping| 487 772 1131 1367 1685 }} | ||
| -0.0899 | | -0.0899 | ||
| 0.1485 | | 0.1485 | ||
| Line 52: | Line 52: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979 | | 676/675, 1001/1000, 4096/4095, 4375/4374, 12005/11979 | ||
| | | {{mapping| 487 772 1131 1367 1685 1802 }} | ||
| -0.0623 | | -0.0623 | ||
| 0.1490 | | 0.1490 | ||
| Line 62: | Line 62: | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 103: | Line 103: | ||
| [[Tritriple]] (5-limit) | | [[Tritriple]] (5-limit) | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Scales == | == Scales == | ||
| Line 109: | Line 110: | ||
* [[Silver17]] | * [[Silver17]] | ||
[[Category:Silver]] | [[Category:Silver]] | ||