16ed7/4

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16ed7/4

17ed7/4 →

Prime factorization	24
Step size	60.5516¢
Octave	20\16ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth	31\16ed7/4 (1877.1¢) (semiconvergent)
Consistency limit	2
Distinct consistency limit	2

16 equal divisions of 7/4 (abbreviated 16ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 16 equal parts of about 60.6 ¢ each. Each step represents a frequency ratio of (7/4)^1/16, or the 16th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	60.552	23/22, 24/23
2	121.103	13/12
3	181.655	11/10, 19/17, 21/19
4	242.206	8/7, 15/13, 23/20
5	302.758	6/5
6	363.31	21/17
7	423.861	14/11, 19/15, 24/19
8	484.413	17/13
9	544.965	11/8, 18/13
10	605.516	10/7, 17/12, 24/17
11	666.068	16/11, 19/13
12	726.619
13	787.171	11/7, 19/12
14	847.723	21/13, 23/14
15	908.274	17/10
16	968.826	7/4

Harmonics

Approximation of harmonics in 16ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.0	-24.9	+22.1	-0.9	-13.8	+22.1	-27.5	+10.8	+10.1	+26.7	-2.8
	Relative (%)	+18.2	-41.0	+36.4	-1.6	-22.8	+36.4	-45.3	+17.9	+16.7	+44.2	-4.6
Steps (reduced)		20 (4)	31 (15)	40 (8)	46 (14)	51 (3)	56 (8)	59 (11)	63 (15)	66 (2)	69 (5)	71 (7)

Approximation of harmonics in 16ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-20.3	-27.5	-25.8	-16.4	-0.3	+21.9	-11.2	+21.1	-2.8	-22.8	+21.4
	Relative (%)	-33.5	-45.3	-42.6	-27.1	-0.5	+36.1	-18.5	+34.9	-4.6	-37.6	+35.3
Steps (reduced)		73 (9)	75 (11)	77 (13)	79 (15)	81 (1)	83 (3)	84 (4)	86 (6)	87 (7)	88 (8)	90 (10)