User:MisterShafXen/6edo

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← 5edo 6edo 7edo →
Prime factorization 2 × 3 (highly composite)
Step size 200 ¢ 
Fifth 4\6 (800 ¢) (→ 2\3)
Semitones (A1:m2) 4:-2 (800 ¢ : -400 ¢)
Dual sharp fifth 4\6 (800 ¢) (→ 2\3)
Dual flat fifth 3\6 (600 ¢) (→ 1\2)
Dual major 2nd 1\6 (200 ¢)
(convergent)
Consistency limit 7
Distinct consistency limit 3

6 equal divisions of the octave (abbreviated 6edo or 6ed2), also called 6-tone equal temperament (6tet) or 6 equal temperament (6et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 6 equal parts of exactly 200 ¢ each. Each step represents a frequency ratio of 21/6, or the 6th root of 2.

Intervals

Steps Cents Approximate ratios Ups and downs notation
(Dual flat fifth 3\6)
Ups and downs notation
(Dual sharp fifth 4\6)
0 0 1/1 D, E, C D, F, B
1 200 8/7, 11/10, 12/11, 17/15 ^D, ^E, ^C, ^F♭, ^G♭, ^A♭, ^B♭ ^D, ^F, ^B, vE, vG
2 400 5/4, 13/10, 14/11, 16/13, 21/17 vD♯, vE♯, vC♯, vF, vG, vA, vB E, G
3 600 7/5, 10/7, 11/8, 16/11, 17/12, 19/13 F, G, A, B ^E, ^G, vA, vC
4 800 8/5, 11/7, 13/8, 17/11, 20/13 ^F, ^G, ^A, ^B, ^D♭ A, C
5 1000 7/4, 11/6, 20/11 vF♯, vG♯, vA♯, vB♯, vD ^A, ^C, vD
6 1200 2/1 D D

Harmonics

Approximation of prime harmonics in 6edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0 +98.0 +13.7 +31.2 +48.7 -40.5 +95.0 -97.5 -28.3 -29.6 +55.0
Relative (%) +0.0 +49.0 +6.8 +15.6 +24.3 -20.3 +47.5 -48.8 -14.1 -14.8 +27.5
Steps
(reduced)
6
(0)
10
(4)
14
(2)
17
(5)
21
(3)
22
(4)
25
(1)
25
(1)
27
(3)
29
(5)
30
(0)