695edo

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Revision as of 12:37, 2 November 2023 by FloraC (talk | contribs) (Rework on theory; +subsets and supersets)
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← 694edo 695edo 696edo →
Prime factorization 5 × 139
Step size 1.72662 ¢ 
Fifth 407\695 (702.734 ¢)
Semitones (A1:m2) 69:50 (119.1 ¢ : 86.33 ¢)
Dual sharp fifth 407\695 (702.734 ¢)
Dual flat fifth 406\695 (701.007 ¢)
Dual major 2nd 118\695 (203.741 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

695edo is only consistent to the 5-odd-limit and the error of harmonic 3 is quite large. The equal temperament is most notable for tempering out 10976/10935, providing the optimal patent val for the hemimage temperament. It also tempers out the escapade comma, [32 -7 -9 in the 5-limit; and [27 0 -8 -3 and [-9 5 -8 7 in the 7-limit.

Odd harmonics

Approximation of odd harmonics in 695edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.779 +0.449 -0.193 -0.169 -0.527 +0.336 -0.499 +0.368 -0.535 +0.586 +0.215
Relative (%) +45.1 +26.0 -11.2 -9.8 -30.5 +19.4 -28.9 +21.3 -31.0 +33.9 +12.4
Steps
(reduced)
1102
(407)
1614
(224)
1951
(561)
2203
(118)
2404
(319)
2572
(487)
2715
(630)
2841
(61)
2952
(172)
3053
(273)
3144
(364)

Subsets and supersets

Since 695 factors into 5 × 139, 695edo contains 5edo and 139edo as subsets.