17ed7/4

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17ed7/4

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Prime factorization	17 (prime)
Step size	56.9898¢
Octave	21\17ed7/4 (1196.78¢) (semiconvergent)
Twelfth	33\17ed7/4 (1880.66¢) (semiconvergent)
Consistency limit	5
Distinct consistency limit	3

17 equal divisions of 7/4 (abbreviated 17ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 17 equal parts of about 57 ¢ each. Each step represents a frequency ratio of (7/4)^1/17, or the 17th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	56.99	24/23
2	113.98	14/13, 15/14, 16/15, 17/16
3	170.969	11/10, 21/19, 23/21
4	227.959	8/7, 17/15, 23/20
5	284.949	7/6, 13/11, 19/16, 20/17
6	341.939	16/13, 17/14, 23/19
7	398.928	5/4, 14/11, 19/15, 24/19
8	455.918	13/10, 17/13, 21/16, 22/17
9	512.908	4/3, 19/14, 23/17
10	569.898	7/5, 11/8
11	626.887	10/7, 23/16
12	683.877	3/2
13	740.867	17/11, 20/13, 23/15
14	797.857	8/5, 11/7, 19/12
15	854.846	13/8, 23/14
16	911.836	17/10, 22/13
17	968.826	7/4, 23/13

Harmonics

Approximation of harmonics in 17ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-3.2	-21.3	-6.4	+6.2	-24.5	-6.4	-9.6	+14.4	+3.0	+8.9	-27.7
	Relative (%)	-5.6	-37.4	-11.3	+10.9	-43.0	-11.3	-16.9	+25.3	+5.2	+15.7	-48.6
Steps (reduced)		21 (4)	33 (16)	42 (8)	49 (15)	54 (3)	59 (8)	63 (12)	67 (16)	70 (2)	73 (5)	75 (7)

Approximation of harmonics in 17ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.7	-9.6	-15.1	-12.9	-3.8	+11.2	-25.4	-0.2	-27.7	+5.7	-14.2
	Relative (%)	+8.2	-16.9	-26.5	-22.6	-6.7	+19.6	-44.6	-0.4	-48.6	+10.0	-25.0
Steps (reduced)		78 (10)	80 (12)	82 (14)	84 (16)	86 (1)	88 (3)	89 (4)	91 (6)	92 (7)	94 (9)	95 (10)