# 6edf

 ← 5edf 6edf 7edf →
Prime factorization 2 × 3
Step size 116.993¢
Octave 10\6edf (1169.93¢) (→5\3edf)
Twelfth 16\6edf (1871.88¢) (→8\3edf)
Consistency limit 2
Distinct consistency limit 2
Special properties

6 equal divisions of the perfect fifth (abbreviated 6edf or 6ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 6 equal parts of about 117 ¢ each. Each step represents a frequency ratio of (3/2)1/6, or the 6th root of 3/2. It corresponds to 10.2571 edo.

## Theory

6edf is related to the miracle temperament, which tempers out 225/224 and 1029/1024 in the 7-limit.

### Harmonics

Approximation of harmonics in 6edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -30.1 -30.1 +56.8 +21.5 +56.8 +24.0 +26.8 +56.8 -8.6 -56.6 +26.8
Relative (%) -25.7 -25.7 +48.6 +18.4 +48.6 +20.5 +22.9 +48.6 -7.3 -48.4 +22.9
Steps
(reduced)
10
(4)
16
(4)
21
(3)
24
(0)
27
(3)
29
(5)
31
(1)
33
(3)
34
(4)
35
(5)
37
(1)

## Intervals

# Cents Approximate Ratios Neptunian
Notation
0 0 1/1 C
1 117 16/15, 15/14 C#
2 234 8/7 Db
3 351 11/9, 27/22 D
4 468 21/16 E
5 585 7/5, 45/32 F
6 702 3/2 C
7 819 8/5, 21/13 C#
8 936 12/7, 55/32 Db
9 1053 11/6 D
10 1170 49/25, 160/81, 2/1 E
11 1287 F
12 1404 9/4 C
13 1521 C#
14 1638 Db
15 1755 D
16 1872 E
17 1988 F
18 2106 27/8 C
19 2223 C#
20 2340 Db
21 2457 D
22 2574 E
23 2691 F
24 2808 81/16 C

Carlo Serafini
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