2897edo

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← 2896edo2897edo2898edo →
Prime factorization 2897 (prime)
Step size 0.414222¢
Fifth 1695\2897 (702.106¢)
Semitones (A1:m2) 277:216 (114.7¢ : 89.47¢)
Dual sharp fifth 1695\2897 (702.106¢)
Dual flat fifth 1694\2897 (701.691¢)
Dual major 2nd 492\2897 (203.797¢)
Consistency limit 7
Distinct consistency limit 7

2897 equal divisions of the octave (abbreviated 2897edo), or 2897-tone equal temperament (2897tet), 2897 equal temperament (2897et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2897 equal parts of about 0.414 ¢ each. Each step of 2897edo represents a frequency ratio of 21/2897, or the 2897th root of 2.

Theory

Although 2897edo is a dual-fifth system which only has a consistency limit of 7, one of its multiples, 31867edo, is not only a denominator in the series of convergents for log23, but is also consistent to the 21-odd-limit.

Prime harmonics

Approximation of odd harmonics in 2897edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.151 +0.155 +0.038 -0.113 +0.011 -0.072 -0.109 -0.157 -0.102 +0.189 +0.100
relative (%) +36 +37 +9 -27 +3 -17 -26 -38 -25 +46 +24
Steps
(reduced)
4592
(1695)
6727
(933)
8133
(2339)
9183
(492)
10022
(1331)
10720
(2029)
11318
(2627)
11841
(253)
12306
(718)
12725
(1137)
13105
(1517)