Xenharmonic Wiki

431edo: Difference between revisions

← Older edit
VisualWikitext
Commas
m Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"
Tags: Mobile edit Mobile web edit
 
(17 intermediate revisions by 8 users not shown)
Line 1: Line 1:
{{Infobox ET
{{Infobox ET}}
| Prime factorization = 431 (prime)
{{ED intro}}
| Step size = 2.78422¢
| Fifth = 252\431 (701.62¢)
| Semitones = 40:33 (111.37¢ : 91.88¢)
| Consistency = 15
}}
The '''431 equal divisions of the octave''' ('''431edo'''), or the '''431(-tone) equal temperament''' ('''431tet''', '''431et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 431 parts of about 2.78 [[cent]]s each.


== Theory ==
== Theory ==
431edo is [[consistent]] to the [[15-odd-limit]], tempering out the [[schisma]] in the 5-limit; [[2401/2400]] in the 7-limit; [[5632/5625]] and [[8019/8000]] in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit. It [[support]]s the [[sesquiquartififths]] temperament.
431edo is [[consistent]] to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[schisma]] in the 5-limit; [[2401/2400]] in the 7-limit; [[5632/5625]] and [[8019/8000]] in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit. It [[support]]s the [[sesquiquartififths]] temperament.


431edo is the 83rd [[prime edo]].  
It allows [[essentially tempered chord]]s of [[squbemic chords]] and [[sinbadmic chords]] in the [[13-odd-limit]].  


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|431}}
{{Harmonics in equal|431}}
=== Subsets and supersets ===
431edo is the 83rd [[prime edo]].
== Intervals ==
{{Main|Table of 431edo intervals}}


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning error
|-
|-
Line 29: Line 30:
| 2.3
| 2.3
| {{monzo| -683 431 }}
| {{monzo| -683 431 }}
| [{{val| 431 683 }}]
| {{mapping| 431 683 }}
| +0.1044
| +0.1044
| 0.1044
| 0.1044
Line 36: Line 37:
| 2.3.5
| 2.3.5
| 32805/32768, {{monzo| 7 63 -46 }}
| 32805/32768, {{monzo| 7 63 -46 }}
| [{{val| 431 683 1001 }}]
| {{mapping| 431 683 1001 }}
| -0.0230
| −0.0230
| 0.2082
| 0.2082
| 7.48
| 7.48
Line 43: Line 44:
| 2.3.5.7
| 2.3.5.7
| 2401/2400, 32805/32768, {{monzo| 3 16 -11 -1 }}
| 2401/2400, 32805/32768, {{monzo| 3 16 -11 -1 }}
| [{{val| 431 683 1001 1210 }}]
| {{mapping| 431 683 1001 1210 }}
| -0.0299
| −0.0299
| 0.1803
| 0.1803
| 6.48
| 6.48
Line 50: Line 51:
| 2.3.5.7.11
| 2.3.5.7.11
| 2401/2400, 5632/5625, 8019/8000, 43923/43904
| 2401/2400, 5632/5625, 8019/8000, 43923/43904
| [{{val| 431 683 1001 1210 1491 }}]
| {{mapping| 431 683 1001 1210 1491 }}
| -0.0215
| −0.0215
| 0.1621
| 0.1621
| 5.82
| 5.82
Line 57: Line 58:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655
| 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655
| [{{val| 431 683 1001 1210 1491 1595 }}]
| {{mapping| 431 683 1001 1210 1491 1595 }}
| -0.0318
| −0.0318
| 0.1498
| 0.1498
| 5.38
| 5.38
Line 65: Line 66:
=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Periods<br>per octave
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
Line 79: Line 81:
|-
|-
| 1
| 1
| 172\431
| 176\431
| 490.02
| 65/49
| [[Surmarvelpyth]]
|-
| 1
| 179\431
| 498.55
| 498.55
| 4/3
| 4/3
| [[Helmholtz]]
| [[Helmholtz (temperament)|Helmholtz]]
|-
| 1
| 190\431
| 529.00
| 19/14
| [[Ostara]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Music ==
; [[Francium]]
* "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] | [https://francium223.bandcamp.com/track/take-advantage Bandcamp] | [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]
* "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] | [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] | [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]
* "I Will Get You." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1FkxDVzNv6SuSfB5vc8T5y Spotify] | [https://francium223.bandcamp.com/track/i-will-get-you Bandcamp] | [https://www.youtube.com/watch?v=_jioqFrcwz8 YouTube] – in Nordenmarkic, 431edo tuning


[[Category:Equal divisions of the octave]]
[[Category:Listen]]
[[Category:Prime EDOs]]
Retrieved from "https://en.xen.wiki/w/431edo"