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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 ===
{{Harmonics in equal|523}}
{{Harmonics in equal|523}}


===Subsets and supersets===
=== Subsets and supersets ===
523edo is the 99th [[prime edo]].  
523edo is the 99th [[prime edo]].  


==Regular temperament properties==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|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}}
| {{monzo|829 -523}}
|{{mapping|523 829}}
| {{mapping|523 829}}
| -0.0468
| &minus;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}}
| {{mapping|523 829 1214}}
| +0.0901
| +0.0901
| 0.1974
| 0.1974
| 8.60
| 8.60
|-
|-
|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}}
| {{mapping|523 829 1214 1468}}
| +0.1180
| +0.1180
| 0.1776
| 0.1776
| 7.74
| 7.74
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|6250/6237, 2401/2400, 19712/19683, 166375/165888
| 6250/6237, 2401/2400, 19712/19683, 166375/165888
|{{mapping|523 829 1214 1468 1809}}
| {{mapping|523 829 1214 1468 1809}}
| +0.1319
| +0.1319
| 0.1613
| 0.1613
| 7.03
| 7.03
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|2080/2079, 625/624, 4459/4455, 19712/19683, 50193/50176
| 2080/2079, 625/624, 4459/4455, 19712/19683, 50193/50176
|{{mapping|523 829 1214 1468 1809 1935}}
| {{mapping|523 829 1214 1468 1809 1935}}
| +0.1440
| +0.1440
| 0.1497
| 0.1497
| 6.52
| 6.52
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
|1
| 1
|37\523
| 37\523
|84.89
| 84.89
|21/20
| 21/20
|[[Amicable]]
| [[Amicable]]
|-
|-
|1
| 1
|52\523
| 52\523
|119.31
| 119.31
|15/14
| 15/14
|[[Septidiasemi]]
| [[Septidiasemi]]
|-
|-
|1
| 1
|148\523
| 148\523
|339.58
| 339.58
|243/200
| 243/200
|[[Amity]]
| [[Amity]]
|}
{{rank-2 end}}
 
{{orf}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct


== Music ==
== Music ==
; [[Francium]]
; [[Francium]]
* "(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]
* "(not) stuck" from ''hope in dark times'' (2024) &ndash; [https://open.spotify.com/track/1mgtvDuMtk980D6wDp9RH4 Spotify] | [https://francium223.bandcamp.com/track/not-stuck Bandcamp] | [https://www.youtube.com/watch?v=ZmPQHWLVCfQ YouTube]


[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/523edo"