523edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
523et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400 and 322102/321489 in the 11-limit. | 523et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 26214400/26198073, 78675968/78594219, 759375/758912, 496125/495616, [[6250/6237]], 42875/42768, [[19712/19683]], 1479016/1476225, 16808715/16777216, 3294225/3294172, 43923/43904, 102487/102400, and 322102/321489 in the 11-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 12: | Line 12: | ||
== Regular temperament properties == | == 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 | | 2.3 | ||
| {{ | | {{Monzo| 829 -523 }} | ||
| {{ | | {{Mapping| 523 829 }} | ||
| | | −0.0468 | ||
| 0.0468 | | 0.0468 | ||
| 2.04 | | 2.04 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| 1600000/1594323, {{monzo|-101 11 36}} | | 1600000/1594323, {{monzo| -101 11 36 }} | ||
| {{ | | {{Mapping| 523 829 1214 }} | ||
| +0.0901 | | +0.0901 | ||
| 0.1974 | | 0.1974 | ||
| Line 30: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 1600000/1594323, 341796875/339738624 | | 2401/2400, 1600000/1594323, 341796875/339738624 | ||
| {{ | | {{Mapping| 523 829 1214 1468 }} | ||
| +0.1180 | | +0.1180 | ||
| 0.1776 | | 0.1776 | ||
| Line 36: | Line 45: | ||
|- | |- | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 6250/6237 | | 2401/2400, 6250/6237, 19712/19683, 166375/165888 | ||
| {{ | | {{Mapping| 523 829 1214 1468 1809 }} | ||
| +0.1319 | | +0.1319 | ||
| 0.1613 | | 0.1613 | ||
| Line 43: | Line 52: | ||
|- | |- | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 2080/2079, | | 625/624, 2080/2079, 2401/2400, 19712/19683, 50193/50176 | ||
| {{ | | {{Mapping| 523 829 1214 1468 1809 1935 }} | ||
| +0.1440 | | +0.1440 | ||
| 0.1497 | | 0.1497 | ||
| 6.52 | | 6.52 | ||
|} | |||
=== Rank-2 temperaments === | === 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 | | 1 | ||
| Line 69: | Line 85: | ||
| 339.58 | | 339.58 | ||
| 243/200 | | 243/200 | ||
| [[Amity]] | | [[Amity]] (5-limit) | ||
|} | |||
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "(not) stuck" from ''hope in dark times'' (2024) | * "(not) stuck" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] | [https://francium223.bandcamp.com/track/not-stuck Bandcamp] | [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube] | ||
* "get their way." from ''with our kindness.'' (2026) – [https://francium223.bandcamp.com/track/get-their-way Bandcamp] | [https://www.youtube.com/watch?v=ZDA5Qf0tl98 YouTube] | |||
[[Category:Listen]] | [[Category:Listen]] | ||