17ed11/5

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17ed11/5

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Prime factorization	17 (prime)
Step size	80.2944¢
Octave	15\17ed11/5 (1204.42¢) (semiconvergent)
Twelfth	24\17ed11/5 (1927.06¢)
Consistency limit	8
Distinct consistency limit	4

17 equal divisions of 11/5 (abbreviated 17ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 17 equal parts of about 80.3 ¢ each. Each step represents a frequency ratio of (11/5)^1/17, or the 17th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	80.294	21/20, 22/21, 23/22, 24/23
2	160.589	11/10, 12/11, 23/21
3	240.883	8/7, 23/20
4	321.177	6/5, 17/14
5	401.472	5/4, 14/11
6	481.766	4/3, 17/13, 21/16
7	562.061	11/8
8	642.355	16/11, 19/13, 23/16
9	722.649	23/15
10	802.944	8/5
11	883.238	5/3
12	963.532	7/4
13	1043.827	11/6, 20/11
14	1124.121	21/11, 23/12
15	1204.415	2/1
16	1284.71	21/10, 23/11
17	1365.004	11/5, 20/9, 24/11

Harmonics

Approximation of harmonics in 17ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.4	+25.1	+8.8	+24.0	+29.5	+3.5	+13.2	-30.1	+28.4	+24.0	+33.9
	Relative (%)	+5.5	+31.3	+11.0	+29.9	+36.8	+4.4	+16.5	-37.5	+35.4	+29.9	+42.3
Steps (reduced)		15 (15)	24 (7)	30 (13)	35 (1)	39 (5)	42 (8)	45 (11)	47 (13)	50 (16)	52 (1)	54 (3)

Approximation of harmonics in 17ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-24.3	+8.0	-31.2	+17.7	-7.0	-25.7	-39.0	+32.8	+28.6	+28.4	+31.7
	Relative (%)	-30.3	+9.9	-38.9	+22.0	-8.7	-32.0	-48.5	+40.9	+35.7	+35.4	+39.5
Steps (reduced)		55 (4)	57 (6)	58 (7)	60 (9)	61 (10)	62 (11)	63 (12)	65 (14)	66 (15)	67 (16)	68 (0)