431edo: Difference between revisions
+music |
m Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|" Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
431edo is the 83rd [[prime edo]]. | 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 | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 34: | Line 38: | ||
| 32805/32768, {{monzo| 7 63 -46 }} | | 32805/32768, {{monzo| 7 63 -46 }} | ||
| {{mapping| 431 683 1001 }} | | {{mapping| 431 683 1001 }} | ||
| | | −0.0230 | ||
| 0.2082 | | 0.2082 | ||
| 7.48 | | 7.48 | ||
| Line 41: | Line 45: | ||
| 2401/2400, 32805/32768, {{monzo| 3 16 -11 -1 }} | | 2401/2400, 32805/32768, {{monzo| 3 16 -11 -1 }} | ||
| {{mapping| 431 683 1001 1210 }} | | {{mapping| 431 683 1001 1210 }} | ||
| | | −0.0299 | ||
| 0.1803 | | 0.1803 | ||
| 6.48 | | 6.48 | ||
| Line 48: | Line 52: | ||
| 2401/2400, 5632/5625, 8019/8000, 43923/43904 | | 2401/2400, 5632/5625, 8019/8000, 43923/43904 | ||
| {{mapping| 431 683 1001 1210 1491 }} | | {{mapping| 431 683 1001 1210 1491 }} | ||
| | | −0.0215 | ||
| 0.1621 | | 0.1621 | ||
| 5.82 | | 5.82 | ||
| Line 55: | Line 59: | ||
| 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655 | | 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655 | ||
| {{mapping| 431 683 1001 1210 1491 1595 }} | | {{mapping| 431 683 1001 1210 1491 1595 }} | ||
| | | −0.0318 | ||
| 0.1498 | | 0.1498 | ||
| 5.38 | | 5.38 | ||
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=== 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 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 85: | Line 90: | ||
| 498.55 | | 498.55 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 93: | Line 98: | ||
| [[Ostara]] | | [[Ostara]] | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[Francium]] | ; [[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] | * "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:Listen]] | |||