17ed7/3

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17ed7/3

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Prime factorization	17 (prime)
Step size	86.2865¢
Octave	14\17ed7/3 (1208.01¢)
Twelfth	22\17ed7/3 (1898.3¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	3

17 equal divisions of 7/3 (abbreviated 17ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 17 equal parts of about 86.3 ¢ each. Each step represents a frequency ratio of (7/3)^1/17, or the 17th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	86.287	17/16, 18/17, 19/18, 20/19, 21/20, 22/21, 23/22, 24/23
2	172.573	10/9, 11/10, 21/19, 23/21
3	258.86	7/6, 15/13, 22/19, 23/20
4	345.146	11/9, 17/14, 23/19
5	431.433	9/7, 14/11, 22/17, 23/18
6	517.719	15/11, 19/14, 23/17
7	604.006	10/7, 17/12, 24/17
8	690.292	3/2
9	776.579	11/7, 14/9, 19/12
10	862.865	18/11, 23/14
11	949.152	12/7, 19/11
12	1035.438	9/5, 11/6, 20/11
13	1121.725	19/10, 21/11, 23/12
14	1208.011	2/1
15	1294.298	17/8, 19/9, 21/10, 23/11
16	1380.584	11/5, 20/9
17	1466.871	7/3

Harmonics

Approximation of harmonics in 17ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.0	-3.7	+16.0	-25.1	+4.4	-3.7	+24.0	-7.3	-17.1	-9.6	+12.4
	Relative (%)	+9.3	-4.2	+18.6	-29.1	+5.1	-4.2	+27.9	-8.5	-19.9	-11.1	+14.3
Steps (reduced)		14 (14)	22 (5)	28 (11)	32 (15)	36 (2)	39 (5)	42 (8)	44 (10)	46 (12)	48 (14)	50 (16)

Approximation of harmonics in 17ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-39.9	+4.4	-28.8	+32.0	+13.4	+0.7	-6.6	-9.1	-7.3	-1.6	+7.8
	Relative (%)	-46.3	+5.1	-33.4	+37.1	+15.5	+0.8	-7.7	-10.6	-8.5	-1.8	+9.0
Steps (reduced)		51 (0)	53 (2)	54 (3)	56 (5)	57 (6)	58 (7)	59 (8)	60 (9)	61 (10)	62 (11)	63 (12)