User:Francium/2239edo

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Revision as of 19:29, 28 July 2025 by Francium (talk | contribs) (Created page with "{{Infobox ET}} {{ED intro}} == Theory == 2239edo is consistent to the 7-limit, tempering out 4375/4374, 3955078125/3954653486 and {{monzo|67 -22 -9 -4}}. As an equal temperament, it supports olympic. === Odd harmonics === {{Harmonics in equal|2239}}")
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← 2238edo 2239edo 2240edo →
Prime factorization 2239 (prime)
Step size 0.535954 ¢ 
Fifth 1310\2239 (702.099 ¢)
Semitones (A1:m2) 214:167 (114.7 ¢ : 89.5 ¢)
Consistency limit 7
Distinct consistency limit 7

2239 equal divisions of the octave (abbreviated 2239edo or 2239ed2), also called 2239-tone equal temperament (2239tet) or 2239 equal temperament (2239et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2239 equal parts of about 0.536 ¢ each. Each step represents a frequency ratio of 21/2239, or the 2239th root of 2.

Theory

2239edo is consistent to the 7-limit, tempering out 4375/4374, 3955078125/3954653486 and [67 -22 -9 -4. As an equal temperament, it supports olympic.

Odd harmonics

Approximation of odd harmonics in 2239edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.144 +0.109 +0.178 -0.248 +0.178 -0.152 +0.253 +0.091 -0.059 -0.214 -0.137
Relative (%) +26.9 +20.3 +33.2 -46.2 +33.3 -28.5 +47.2 +17.1 -11.0 -39.9 -25.5
Steps
(reduced)
3549
(1310)
5199
(721)
6286
(1808)
7097
(380)
7746
(1029)
8285
(1568)
8748
(2031)
9152
(196)
9511
(555)
9834
(878)
10128
(1172)