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{{EDO intro|487}}
{{Infobox ET}}
{{ED intro}}


== Theory ==
== Theory ==
487edo is [[consistency|distinctly consistent]] to the [[13-odd-limit]]. As an equal temperament, it [[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 ===
{{Harmonics in equal|487}}
{{Harmonics in equal|487}}
=== Subsets and supersets ===
487edo is the 93rd [[prime edo]].
== 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| 772 -487 }}
| {{mapping| 487 772 }}
| −0.0958
| 0.0958
| 3.89
|-
| 2.3.5
| {{monzo| 24 -21 4 }}, {{monzo| 55 -1 -23 }}
| {{mapping| 487 772 1131 }}
| −0.1421
| 0.1020
| 4.14
|-
| 2.3.5.7
| 4375/4374, 235298/234375, 33554432/33480783
| {{mapping| 487 772 1131 1367 }}
| −0.0667
| 0.1577
| 6.40
|-
| 2.3.5.7.11
| 4375/4374, 5632/5625, 12005/11979, 41503/41472
| {{mapping| 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
| {{mapping| 487 772 1131 1367 1685 1802 }}
| −0.0623
| 0.1490
| 6.05
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
|-
| 1
| 131\487
| 322.79
| 3087/2560
| [[Seniority]]
|-
| 1
| 157\487
| 386.86
| 5/4
| [[Counterwürschmidt]]
|-
| 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)
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


== Scales ==
== Scales ==
Line 9: Line 112:
* [[Silver17]]
* [[Silver17]]


[[Category:487edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave]]
[[Category:Silver]]
[[Category:Silver]]
Retrieved from "https://en.xen.wiki/w/487edo"