415edo

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Revision as of 04:11, 16 June 2023 by FloraC (talk | contribs) (Cleanup; +prime error table; +subsets and supersets)
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← 414edo 415edo 416edo →
Prime factorization 5 × 83
Step size 2.89157 ¢ 
Fifth 243\415 (702.651 ¢)
Semitones (A1:m2) 41:30 (118.6 ¢ : 86.75 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

If harmonic 5 is used, 415edo tends very sharp. In the 5-limit the equal temperament tempers out the parakleisma, [8 14 -13; in the 7-limit 3136/3125 and 4375/4374, so that it supports the parakleismic temperament and provides the optimal patent val.

Odd harmonics

Approximation of odd harmonics in 415edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.70 +1.16 -0.15 +1.39 +0.97 +0.92 -1.04 -0.86 +0.32 +0.54 -0.80
Relative (%) +24.1 +40.0 -5.2 +48.1 +33.6 +31.8 -36.0 -29.7 +11.0 +18.8 -27.8
Steps
(reduced)
658
(243)
964
(134)
1165
(335)
1316
(71)
1436
(191)
1536
(291)
1621
(376)
1696
(36)
1763
(103)
1823
(163)
1877
(217)

Subsets and supersets

415edo has subset edos 5 and 83.