20203edo: Difference between revisions

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{{Infobox ET|Consistency=45|Distinct consistency=45}}
{{Infobox ET|Consistency=45|Distinct consistency=45}}
'''20203edo''' is the [[EDO|equal division of the octave]] into 20203 parts of 0.05939712 [[cent]]s each. It is a very strong high limit edo, with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until 128125. It is also distinctly consistent through the [[45-odd-limit|45-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.
{{EDO intro|20203}}
==Theory==
2023edo is a very strong high limit edo, with a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until 128125. It is also distinctly consistent through the [[45-odd-limit|45-limit]], and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.
===Prime harmonics===
{{harmonics in equal|20203}}


[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->

Revision as of 21:36, 4 January 2023

← 20202edo 20203edo 20204edo →
Prime factorization 89 × 227
Step size 0.0593971 ¢ 
Fifth 11818\20203 (701.955 ¢)
Semitones (A1:m2) 1914:1519 (113.7 ¢ : 90.22 ¢)
Consistency limit 45
Distinct consistency limit 45

Template:EDO intro

Theory

2023edo is a very strong high limit edo, with a lower 19-limit relative error than any edo until 128125. It is also distinctly consistent through the 45-limit, and has a lower relative error than any smaller distinctly consistent 41-limit patent val except 17461. It tempers out 47151/47150, 52326/52325, 69875/69874, 81796/81795, 111112/111111, 127281/127280, 156520/156519, 315495/315491, 395200/395199, 728365/728364, 1324323/1324300, 1518804/1518803, and 3845961/3845920 in the 43-limit.

Prime harmonics

Approximation of prime harmonics in 20203edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 +0.0002 +0.0051 +0.0005 +0.0061 +0.0010 -0.0007 +0.0072 +0.0284 +0.0125 +0.0221
Relative (%) +0.0 +0.3 +8.7 +0.9 +10.3 +1.6 -1.2 +12.0 +47.8 +21.0 +37.2
Steps
(reduced) 		20203
(0) 		32021
(11818) 		46910
(6504) 		56717
(16311) 		69891
(9282) 		74760
(14151) 		82579
(1767) 		85821
(5009) 		91390
(10578) 		98146
(17334) 		100090
(19278)
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