5edf

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5edf

6edf →

Prime factorization	5 (prime)
Step size	140.391¢
Octave	9\5edf (1263.52¢)
Twelfth	14\5edf (1965.47¢)
Consistency limit	2
Distinct consistency limit	2

5 equal divisions of the perfect fifth (abbreviated 5edf or 5ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 5 equal parts of about 140 ¢ each. Each step represents a frequency ratio of (3/2)^1/5, or the 5th root of 3/2. It corresponds to 8.5476 edo.

Theory

5edf is close to the bleu generator chain and every second step of 17edo. 4 steps of 5edf is a fraction of a cent away to the seventh harmonic (which is 112/81 instead of 7/4 since the equave is 3/2), which is an extremely accurate approximation for the size of this scale.

Harmonics

Approximation of harmonics in 5edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+63.5	+63.5	-13.4	+21.5	-13.4	+0.6	+50.2	-13.4	-55.4	+60.4	+50.2
	Relative (%)	+45.2	+45.2	-9.5	+15.3	-9.5	+0.4	+35.7	-9.5	-39.4	+43.0	+35.7
Steps (reduced)		9 (4)	14 (4)	17 (2)	20 (0)	22 (2)	24 (4)	26 (1)	27 (2)	28 (3)	30 (0)	31 (1)

Intervals

#	Cents	Approximate Ratios	Neptunian Notation
0	0.0	1/1	perfect unison	C
1	140.4	13/12, 49/45	augmented unison, minor second	C#, Db
2	280.8	75/64, 20/17, 13/11	major second, minor third	D, Eb
3	421.2	14/11, 23/18	major third, diminished fourth	E, Fb
4	561.6	11/8, 18/13, 25/18	perfect fourth	F
5	702.0	3/2	perfect fifth	C
6	842.3	21/13, 13/8, 18/11	augmented fifth, minor sixth	C#, Db
7	982.7	7/4, 30/17	major sixth, minor seventh	D, Eb
8	1123.1		major seventh, minor octave	E, Fb
9	1263.5		major octave	F
10	1403.9			C
11	1544.3			C#, Db
12	1684.7			D, Eb
13	1825.1			E
14	1965.5			F
15	2105.9			C
16	2246.3			C#, Db
17	2386.6			D