503edo: Difference between revisions

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Line 26: Line 26:
| {{monzo|-797 503}}
| {{monzo|-797 503}}
| {{val|503 797}}
| {{val|503 797}}
| 0.1777
| +0.1777
| 0.1777
| 0.1777
| 7.45
| 7.45
Line 33: Line 33:
| {{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
Line 40: Line 40:
| 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
Line 47: Line 47:
| 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
Line 54: Line 54:
| 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
Line 61: Line 61:
| 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
Line 106: Line 106:
| [[Subneutral]]
| [[Subneutral]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


== Music ==
== Music ==
; [[Francium]]
; [[Francium]]
* "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]
* "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) &ndash; [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]


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

Revision as of 14:06, 16 January 2025

← 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

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
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

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
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

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Music

Francium
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