6edt

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← 5edt 6edt 7edt →
Prime factorization 2 × 3
Step size 316.993 ¢ 
Octave 4\6edt (1267.97 ¢) (→ 2\3edt)
Consistency limit 7
Distinct consistency limit 2
Special properties

6 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 6edt or 6ed3), is a nonoctave tuning system that divides the interval of 3/1 into 6 equal parts of about 317 ¢ each. Each step represents a frequency ratio of 31/6, or the 6th root of 3.

Theory

Since 6edt contains one interval of 2edt and two intervals of 3edt, it introduces 2 new notes unseen in previous edts. These new notes happen to approximate 6/5 and 5/2 very well, the former being only 1.351 cents sharp. 6edt is therefore the smallest edt other than 5edt to accurately approximate 5-limit harmony, as well as some elements from the 13-limit inherited from 3edt. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54...

Harmonics

Approximation of harmonics in 6edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Error Absolute (¢) +68 +0 +136 +67 +68 +118 -113 +0 +135 -30 +136 -3 -131 +67 -45 -150
Relative (%) +21.4 +0.0 +42.9 +21.0 +21.4 +37.3 -35.7 +0.0 +42.5 -9.6 +42.9 -0.8 -41.3 +21.0 -14.2 -47.3
Steps
(reduced)
4
(4)
6
(0)
8
(2)
9
(3)
10
(4)
11
(5)
11
(5)
12
(0)
13
(1)
13
(1)
14
(2)
14
(2)
14
(2)
15
(3)
15
(3)
15
(3)

Intervals

Steps Cents Hekts Approximate ratios
0 0 0 1/1
1 317 216.7 6/5, 7/6, 11/9, 13/11
2 634 433.3 7/5, 10/7, 13/9, 19/13
3 951 650 7/4, 12/7, 19/11
4 1268 866.7 15/7, 19/9, 21/10
5 1585 1083.3 5/2, 18/7
6 1902 1300 3/1