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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|503}}
{{ED intro}}


== Theory ==
== Theory ==
503et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 100663296/100656875, 10333575/10307264, 46656/46585, 166698/166375, 759375/758912, 496125/495616, 226492416/226474325, 2359296/2358125, 172032/171875, 369140625/369098752, 4302592/4296875, 24057/24010, [[8019/8000]], 16808715/16777216, 766656/765625, 391314/390625, 3294225/3294172, 43923/43904 and 102487/102400 in the 11-limit.
503et tempers out [[2401/2400]] in the 7-limit; 56723625/56689952, 100663296/100656875, 10333575/10307264, 46656/46585, 166698/166375, 759375/758912, 496125/495616, 226492416/226474325, 2359296/2358125, 172032/171875, 369140625/369098752, 4302592/4296875, 24057/24010, [[8019/8000]], 16808715/16777216, 766656/765625, 391314/390625, 3294225/3294172, 43923/43904 and 102487/102400 in the 11-limit.


===Prime harmonics===
=== Prime harmonics ===
{{Harmonics in equal|503}}
{{Harmonics in equal|503}}


===Subsets and supersets===
=== Subsets and supersets ===
503edo is the 96th [[prime edo]].  
503edo is the 96th [[prime edo]].  


== 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" |[[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
! rowspan="2" | [[Subgroup]]
|{{monzo|-797 503}}
! rowspan="2" | [[Comma list]]
|{{val|503 797}}
! rowspan="2" | [[Mapping]]
| 0.1777
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo|-797 503}}
| {{val|503 797}}
| +0.1777
| 0.1777
| 0.1777
| 7.45
| 7.45
|-
|-
|2.3.5
| 2.3.5
|{{monzo|38 -2 -15}}, {{monzo|-5 31 -19}}
| {{monzo| 38 -2 -15 }}, {{monzo| -5 31 -19 }}
|{{val|503 797 1168}}
| {{val| 503 797 1168}}
| 0.0944
| +0.0944
| 0.1869
| 0.1869
| 7.83
| 7.83
|-
|-
|2.3.5.7
| 2.3.5.7
|2401/2400, 1959552/1953125, 26873856/26796875
| 2401/2400, 1959552/1953125, 26873856/26796875
|{{val|503 797 1168 1412}}
| {{val| 503 797 1168 1412 }}
| 0.0920
| +0.0920
| 0.1619
| 0.1619
| 6.79
| 6.79
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|2401/2400, 8019/8000, 24057/24010, 43923/43904
| 2401/2400, 8019/8000, 24057/24010, 43923/43904
|{{val|503 797 1168 1412 1740}}
| {{val| 503 797 1168 1412 1740 }}
| 0.0866
| +0.0866
| 0.1452
| 0.1452
| 6.09
| 6.09
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|729/728, 1001/1000, 1716/1715, 4225/4224, 6656/6655
| 729/728, 1001/1000, 1716/1715, 4225/4224, 6656/6655
|{{val|503 797 1168 1412 1740 1861}}
| {{val| 503 797 1168 1412 1740 1861 }}
| 0.1066
| +0.1066
| 0.1400
| 0.1400
| 5.87
| 5.87
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|729/728, 936/935, 1001/1000, 1716/1715, 2401/2400, 2601/2600
| 729/728, 936/935, 1001/1000, 1716/1715, 2401/2400, 2601/2600
|{{val|503 797 1168 1412 1740 1861 2056}}
| {{val| 503 797 1168 1412 1740 1861 2056 }}
| 0.0909
| +0.0909
| 0.1352
| 0.1352
| 5.67
| 5.67
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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>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|11\503
| 11\503
|26.24
| 26.24
|1594323/1562500
| 1594323/1562500
|[[Sfourth]] (5-limit)
| [[Sfourth]] (5-limit)
|-
|-
|1
| 1
|50\503
| 50\503
|119.28
| 119.28
|15/14
| 15/14
|[[Septidiasemi]]
| [[Septidiasemi]]
|-
|-
|1
| 1
|81\503
| 81\503
|193.24
| 193.24
|262144/234375
| 262144/234375
|[[Luna]]
| [[Luna]]
|-
|-
|1
| 1
|127\503
| 127\503
|302.98
| 302.98
|25/21
| 25/21
|[[Quinmite]]
| [[Quinmite]]
|-
|-
|1
| 1
|146\503
| 146\503
|348.31
| 348.31
|57344/46875
| 57344/46875
|[[Subneutral]]
| [[Subneutral]]
|}
|}
 
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
<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 ==
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* "optimism" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/3NSsgELzO7yYspH6khOWsf Spotify] | [https://francium223.bandcamp.com/track/optimism Bandcamp] | [https://www.youtube.com/watch?v=HMSmRAepIzQ YouTube]
* "optimism" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/3NSsgELzO7yYspH6khOWsf Spotify] | [https://francium223.bandcamp.com/track/optimism Bandcamp] | [https://www.youtube.com/watch?v=HMSmRAepIzQ YouTube]
* "YOU'RE BORING!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/7lgeaWyYccByXxvISoPX4m Spotify] | [https://francium223.bandcamp.com/track/youre-boring Bandcamp] | [https://www.youtube.com/watch?v=GLhxsupHAug YouTube]
* "YOU'RE BORING!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/7lgeaWyYccByXxvISoPX4m Spotify] | [https://francium223.bandcamp.com/track/youre-boring Bandcamp] | [https://www.youtube.com/watch?v=GLhxsupHAug YouTube]
* "Entrap Fools" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/2DKihbJg3uFXu7zerVCZvl Spotify] | [https://francium223.bandcamp.com/track/entrap-fools Bandcamp] | [https://www.youtube.com/watch?v=emTkkxzYdZw YouTube]


[[Category:Listen]]
[[Category:Listen]]
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