9ed4

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← 7ed49ed411ed4 →
Prime factorization 32
Step size 266.667¢ 
Octave 5\9ed4 (1333.33¢)
Twelfth 7\9ed4 (1866.67¢)
(semiconvergent)
Consistency limit 1
Distinct consistency limit 1

9 equal divisions of the 4th harmonic (abbreviated 9ed4) is a nonoctave tuning system that divides the interval of 4/1 into 9 equal parts of about 267 ¢ each. Each step represents a frequency ratio of 41/9, or the 9th root of 4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 266.667 7/6, 13/11
2 533.333 18/13
3 800 11/7, 21/13
4 1066.667 11/6, 13/7, 17/9, 20/11
5 1333.333 13/6
6 1600 18/7
7 1866.667 3/1
8 2133.333 7/2, 17/5
9 2400

Harmonics

Approximation of harmonics in 9ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +133 -35 +0 -120 +98 +98 +133 -71 +14 +115 -35
Relative (%) +50.0 -13.2 +0.0 -44.9 +36.8 +36.7 +50.0 -26.5 +5.1 +43.3 -13.2
Steps
(reduced)
5
(5)
7
(7)
9
(0)
10
(1)
12
(3)
13
(4)
14
(5)
14
(5)
15
(6)
16
(7)
16
(7)
Approximation of harmonics in 9ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +93 -35 +112 +0 -105 +63 -31 -120 +63 -18 -95
Relative (%) +34.8 -13.3 +41.9 +0.0 -39.4 +23.5 -11.6 -44.9 +23.5 -6.7 -35.6
Steps
(reduced)
17
(8)
17
(8)
18
(0)
18
(0)
18
(0)
19
(1)
19
(1)
19
(1)
20
(2)
20
(2)
20
(2)