5ed7/4

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5ed7/4

6ed7/4 →

Prime factorization	5 (prime)
Step size	193.765¢
Octave	6\5ed7/4 (1162.59¢) (semiconvergent)
Twelfth	10\5ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit	3
Distinct consistency limit	2

5 equal divisions of 7/4 (abbreviated 5ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 5 equal parts of about 194 ¢ each. Each step represents a frequency ratio of (7/4)^1/5, or the 5th root of 7/4.

In a context with octaves, this scale is associated with didacus temperament, where one step is equated to 28/25 and two steps make 5/4, and its extension hemiwurschmidt, where sixteen steps stack to 6/1 and twenty-eight stack to 23/1, hence the extremely accurate 6th and great 23rd harmonics this tuning provides.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	193.8	7/6, 8/7, 11/10, 12/11, 13/12, 15/13, 15/14, 17/15, 19/17, 21/19
2	387.5	5/4, 6/5, 14/11, 17/14, 19/15, 21/17
3	581.3	7/5, 10/7, 11/8, 13/9, 15/11, 16/11, 17/12, 18/13, 19/14
4	775.1	3/2, 8/5, 11/7, 17/11, 19/12, 21/13
5	968.8	7/4, 12/7, 17/10, 19/11, 20/11

Harmonics

Approximation of harmonics in 5ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-37.4	+35.7	-74.8	-73.6	-1.7	-74.8	+81.5	+71.4	+82.8	-82.2	-39.1
	Relative (%)	-19.3	+18.4	-38.6	-38.0	-0.9	-38.6	+42.1	+36.8	+42.7	-42.4	-20.2
Steps (reduced)		6 (1)	10 (0)	12 (2)	14 (4)	16 (1)	17 (2)	19 (4)	20 (0)	21 (1)	21 (1)	22 (2)

Approximation of harmonics in 5ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+16.1	+81.5	-37.9	+44.1	-60.8	+34.0	-59.6	+45.3	-39.1	+74.1	-2.8
	Relative (%)	+8.3	+42.1	-19.6	+22.8	-31.4	+17.5	-30.8	+23.4	-20.2	+38.2	-1.5
Steps (reduced)		23 (3)	24 (4)	24 (4)	25 (0)	25 (0)	26 (1)	26 (1)	27 (2)	27 (2)	28 (3)	28 (3)