3776edo

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← 3775edo3776edo3777edo →
Prime factorization 26 × 59
Step size 0.317797¢
Fifth 2209\3776 (702.013¢)
Semitones (A1:m2) 359:283 (114.1¢ : 89.94¢)
Consistency limit 13
Distinct consistency limit 13

3776 equal divisions of the octave (3776edo), or 3776-tone equal temperament (3776tet), 3776 equal temperament (3776et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 3776 equal parts of about 0.318 ¢ each.

Theory

3776edo is a tuning for the oganesson temperament in the 17-limit, which sets 1/118th of the octave to an interval that represents 169/168~170/169 tempered together.

It tempers out the quartisma in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament.

While it does tune both 13th and 17th prime harmonic resonably, it is no longer consistent in the 15-odd-limit.

Odd harmonics

Approximation of odd harmonics in 3776edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.058 +0.127 +0.136 +0.115 +0.059 +0.044 -0.133 -0.083 -0.055 -0.124 +0.010
relative (%) +18 +40 +43 +36 +19 +14 -42 -26 -17 -39 +3
Steps
(reduced)
5985
(2209)
8768
(1216)
10601
(3049)
11970
(642)
13063
(1735)
13973
(2645)
14752
(3424)
15434
(330)
16040
(936)
16585
(1481)
17081
(1977)

Regular temperament properties

Rank-2 temperaments

Periods
per 8ve
Generator
(reduced)
Cents
(reduced)
Associated
ratio
Temperaments
118 1781\3776
(21\3776)
565.995
(6.67)
165/119
(?)
Oganesson