523edo: Difference between revisions

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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]]

Revision as of 02:10, 16 November 2024

← 522edo 523edo 524edo →
Prime factorization 523 (prime)
Step size 2.29446 ¢ 
Fifth 306\523 (702.103 ¢)
Semitones (A1:m2) 50:39 (114.7 ¢ : 89.48 ¢)
Consistency limit 15
Distinct consistency limit 15

Template:EDO intro

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.

Prime harmonics

Approximation of prime harmonics in 523edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.15 -0.85 -0.57 -0.65 -0.76 +0.59 +0.77 +0.41 +0.63 -0.10
Relative (%) +0.0 +6.5 -36.8 -24.7 -28.3 -33.0 +25.7 +33.4 +17.7 +27.6 -4.5
Steps
(reduced) 		523
(0) 		829
(306) 		1214
(168) 		1468
(422) 		1809
(240) 		1935
(366) 		2138
(46) 		2222
(130) 		2366
(274) 		2541
(449) 		2591
(499)

Subsets and supersets

523edo is the 99th prime edo.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [829 -523⟩ | [⟨523 829]] | −0.0468 | 0.0468 | 2.04 |- | 2.3.5 | 1600000/1594323, [-101 11 36⟩ | [⟨523 829 1214]] | +0.0901 | 0.1974 | 8.60 |- | 2.3.5.7 | 2401/2400, 1600000/1594323, 341796875/339738624 | [⟨523 829 1214 1468]] | +0.1180 | 0.1776 | 7.74 |- | 2.3.5.7.11 | 6250/6237, 2401/2400, 19712/19683, 166375/165888 | [⟨523 829 1214 1468 1809]] | +0.1319 | 0.1613 | 7.03 |- | 2.3.5.7.11.13 | 2080/2079, 625/624, 4459/4455, 19712/19683, 50193/50176 | [⟨523 829 1214 1468 1809 1935]] | +0.1440 | 0.1497 | 6.52 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 37\523 | 84.89 | 21/20 | Amicable |- | 1 | 52\523 | 119.31 | 15/14 | Septidiasemi |- | 1 | 148\523 | 339.58 | 243/200 | Amity Template:Rank-2 end Template:Orf

Music

Francium
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