2901edo

 ← 2900edo 2901edo 2902edo →
Prime factorization 3 × 967
Step size 0.41365¢
Fifth 1697\2901 (701.965¢)
Semitones (A1:m2) 275:218 (113.8¢ : 90.18¢)
Consistency limit 17
Distinct consistency limit 17

2901 equal divisions of the octave (abbreviated 2901edo or 2901ed2), also called 2901-tone equal temperament (2901tet) or 2901 equal temperament (2901et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2901 equal parts of about 0.414 ¢ each. Each step represents a frequency ratio of 21/2901, or the 2901st root of 2.

Theory

2901edo is consistent in the 17-odd-limit and is otherwise an excellent 31-limit system, with only the pair {19/17, 34/19} being mapped inconsistently in the 31-odd-limit. It provides a good tuning for the jacobin temperament in the 13-limit, the rank-5 temperament tempering out 6656/6655. Alongside jacobin, it tunes the tridecimal quartismic temperament, which also tempers out 123201/123200. It also tunes the monzismic temperament.

Prime harmonics

Approximation of prime harmonics in 2901edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.010 +0.036 -0.057 +0.078 +0.010 +0.112 -0.098 +0.061 -0.001 -0.051
Relative (%) +0.0 +2.4 +8.7 -13.7 +18.9 +2.4 +27.0 -23.8 +14.7 -0.3 -12.3
Steps
(reduced)
2901
(0)
4598
(1697)
6736
(934)
8144
(2342)
10036
(1333)
10735
(2032)
11858
(254)
12323
(719)
13123
(1519)
14093
(2489)
14372
(2768)

Subsets and supersets

Since 2901 factors into 3 × 967, 2901edo contains 3edo and 967edo as subsets.

Eliora