5ed4

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← 3ed45ed47ed4 →
Prime factorization 5 (prime)
Step size 480¢ 
Octave 3\5ed4 (1440¢)
Twelfth 4\5ed4 (1920¢)
(convergent)
Consistency limit 1
Distinct consistency limit 1

5 equal divisions of the 4th harmonic (abbreviated 5ed4) is a nonoctave tuning system that divides the interval of 4/1 into 5 equal parts of exactly 480 ¢ each. Each step represents a frequency ratio of 41/5, or the 5th root of 4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 480 9/7, 14/11, 15/11, 17/13, 19/14, 19/15
2 960 9/5, 19/11
3 1440 7/3
4 1920 3/1
5 2400

Harmonics

Approximation of harmonics in 5ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +240 +18 +0 +94 -222 -9 +240 +36 -146 +169 +18
Relative (%) +50.0 +3.8 +0.0 +19.5 -46.2 -1.8 +50.0 +7.5 -30.5 +35.1 +3.8
Steps
(reduced)
3
(3)
4
(4)
5
(0)
6
(1)
6
(1)
7
(2)
8
(3)
8
(3)
8
(3)
9
(4)
9
(4)
Approximation of harmonics in 5ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -121 +231 +112 +0 -105 -204 +182 +94 +9 -71 -148
Relative (%) -25.1 +48.2 +23.3 +0.0 -21.9 -42.5 +38.0 +19.5 +1.9 -14.9 -30.9
Steps
(reduced)
9
(4)
10
(0)
10
(0)
10
(0)
10
(0)
10
(0)
11
(1)
11
(1)
11
(1)
11
(1)
11
(1)