Xenharmonic Wiki

436edo: Difference between revisions

VisualWikitext
Created page with "That's a double of 218edo!!!"
 
m Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"
Tags: Mobile edit Mobile web edit
 
(25 intermediate revisions by 11 users not shown)
Line 1: Line 1:
That's a double of [[218edo]]!!!
{{Infobox ET}}
{{ED intro}}
 
== Theory ==
436edo is [[consistent]] to the [[23-odd-limit]]. The [[patent val]] of 436edo has a distinct flat tendency, in the sense that if the [[octave]] is pure, [[harmonic]]s from 3 to 37 are all flat.
 
It [[tempering out|tempers out]] [[32805/32768]] and {{monzo| 1 -68 46 }} in the 5-limit; [[390625/388962]], 420175/419904, and [[2100875/2097152]] in the 7-limit; 1375/1372, [[6250/6237]], [[41503/41472]], and 322102/321489 in the 11-limit; [[625/624]], [[1716/1715]], [[2080/2079]], [[10648/10647]], and 15379/15360 in the 13-limit; [[715/714]], [[1089/1088]], [[1225/1224]], [[1275/1274]], [[2025/2023]], and 11271/11264 in the 17-limit; 1331/1330, [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 4394/4389, and 4875/4864 in the 19-limit; 875/874, 897/896, 1105/1104, 1863/1862, 2024/2023, 2185/2184, 2300/2299, and 2530/2527 in the 23-limit. It [[support]]s and gives a good tuning to [[quadrant]]. It also supports [[tsaharuk]], but [[171edo]] is better suited for that purpose.
 
436edo is accurate for some intervals including [[3/2]], [[7/4]], [[11/10]], [[13/10]], [[18/17]], and [[19/18]], so it is especially suitable for the 2.3.7.11/5.13/5.17.19 [[subgroup]].
 
=== Prime harmonics ===
{{Harmonics in equal|436}}
 
=== Subsets and supersets ===
Since 436 factors into {{factorization|436}}, 436edo has subset edos {{EDOs| 2, 4, 109, and 218 }}.
 
[[1308edo]], which divides its edostep into three, is a [[zeta gap edo]] and is consistent in the 21-odd-limit.
 
== 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| -691 436 }}
| {{mapping| 436 691 }}
| +0.0379
| 0.0379
| 1.38
|-
| 2.3.5
| 32805/32768, {{monzo| 1 -68 46 }}
| {{mapping| 436 691 1012 }}
| +0.1678
| 0.1863
| 6.77
|-
| 2.3.5.7
| 32805/32768, 390625/388962, 420175/419904
| {{mapping| 436 691 1012 1224 }}
| +0.1275
| 0.1758
| 6.39
|-
| 2.3.5.7.11
| 1375/1372, 6250/6237, 32805/32768, 41503/41472
| {{mapping| 436 691 1012 1224 1508 }}
| +0.1517
| 0.1645
| 5.98
|-
| 2.3.5.7.11.13
| 625/624, 1375/1372, 2080/2079, 10648/10647, 15379/15360
| {{mapping| 436 691 1012 1224 1508 1613 }}
| +0.1749
| 0.1589
| 5.77
|-
| 2.3.5.7.11.13.17
| 625/624, 715/714, 1089/1088, 1225/1224, 2431/2430, 10648/10647
| {{mapping| 436 691 1012 1224 1508 1613 1782 }}
| +0.1628
| 0.1501
| 5.45
|-
| 2.3.5.7.11.13.17.19
| 625/624, 715/714, 1089/1088, 1225/1224, 1331/1330, 1445/1444, 1729/1728
| {{mapping| 436 691 1012 1224 1508 1613 1782 1852 }}
| +0.1503
| 0.1443
| 5.24
|}
 
=== 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
| 51\436
| 140.37
| 243/224
| [[Tsaharuk]]
|-
| 1
| 181\436
| 498.17
| 4/3
| [[Helmholtz (temperament)|Helmholtz]]
|-
| 4
| 181\436<br>(37\436)
| 498.17<br>(101.83)
| 4/3<br>(35/33)
| [[Quadrant]]
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
Retrieved from "https://en.xen.wiki/w/436edo"