503edo: Difference between revisions

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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"
{{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|-797 503}}
| {{monzo|-797 503}}
|{{val|503 797}}
| {{val|503 797}}
| 0.1777
| 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
Line 66: Line 58:


=== 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
|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]]
|}
{{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]]
* "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) &ndash; [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) &ndash; [https://open.spotify.com/track/7lgeaWyYccByXxvISoPX4m Spotify] | [https://francium223.bandcamp.com/track/youre-boring Bandcamp] | [https://www.youtube.com/watch?v=GLhxsupHAug YouTube]


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

Revision as of 03:49, 16 November 2024

← 502edo 503edo 504edo →
Prime factorization 503 (prime)
Step size 2.38569 ¢ 
Fifth 294\503 (701.392 ¢)
Semitones (A1:m2) 46:39 (109.7 ¢ : 93.04 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

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.

Prime harmonics

Approximation of prime harmonics in 503edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.56 +0.17 -0.24 -0.22 -0.77 +0.01 +0.70 -0.84 +1.04 +0.09
Relative (%) +0.0 -23.6 +7.0 -10.0 -9.4 -32.1 +0.6 +29.2 -35.2 +43.6 +3.9
Steps
(reduced) 		503
(0) 		797
(294) 		1168
(162) 		1412
(406) 		1740
(231) 		1861
(352) 		2056
(44) 		2137
(125) 		2275
(263) 		2444
(432) 		2492
(480)

Subsets and supersets

503edo is the 96th prime edo.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [-797 503⟩ | ⟨503 797] | 0.1777 | 0.1777 | 7.45 |- | 2.3.5 | [38 -2 -15⟩, [-5 31 -19⟩ | ⟨503 797 1168] | 0.0944 | 0.1869 | 7.83 |- | 2.3.5.7 | 2401/2400, 1959552/1953125, 26873856/26796875 | ⟨503 797 1168 1412] | 0.0920 | 0.1619 | 6.79 |- | 2.3.5.7.11 | 2401/2400, 8019/8000, 24057/24010, 43923/43904 | ⟨503 797 1168 1412 1740] | 0.0866 | 0.1452 | 6.09 |- | 2.3.5.7.11.13 | 729/728, 1001/1000, 1716/1715, 4225/4224, 6656/6655 | ⟨503 797 1168 1412 1740 1861] | 0.1066 | 0.1400 | 5.87 |- | 2.3.5.7.11.13.17 | 729/728, 936/935, 1001/1000, 1716/1715, 2401/2400, 2601/2600 | ⟨503 797 1168 1412 1740 1861 2056] | 0.0909 | 0.1352 | 5.67 |}

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 11\503 | 26.24 | 1594323/1562500 | Sfourth (5-limit) |- | 1 | 50\503 | 119.28 | 15/14 | Septidiasemi |- | 1 | 81\503 | 193.24 | 262144/234375 | Luna |- | 1 | 127\503 | 302.98 | 25/21 | Quinmite |- | 1 | 146\503 | 348.31 | 57344/46875 | Subneutral Template:Rank-2 end Template:Orf

Music

Francium
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