18ed11/5

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18ed11/5

19ed11/5 →

Prime factorization	2 × 32
Step size	75.8336¢
Octave	16\18ed11/5 (1213.34¢) (→8\9ed11/5)
Twelfth	25\18ed11/5 (1895.84¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	2

18 equal divisions of 11/5 (abbreviated 18ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 18 equal parts of about 75.8 ¢ each. Each step represents a frequency ratio of (11/5)^1/18, or the 18th root of 11/5.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	75.834	19/18, 23/22, 24/23
2	151.667	11/10, 12/11, 13/12
3	227.501	17/15, 23/20
4	303.334	6/5, 13/11
5	379.168	5/4
6	455.001	13/10, 17/13, 22/17
7	530.835	15/11, 19/14, 23/17
8	606.669	17/12, 24/17
9	682.502
10	758.336	14/9, 17/11, 20/13
11	834.169	13/8
12	910.003	17/10, 22/13
13	985.836	23/13
14	1061.67	11/6, 24/13
15	1137.504	23/12
16	1213.337	2/1
17	1289.171	17/8, 19/9, 23/11
18	1365.004	11/5, 24/11

Harmonics

Approximation of harmonics in 18ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+13.3	-6.1	+26.7	+19.5	+7.2	-32.1	-35.8	-12.2	+32.9	+19.5	+20.6
	Relative (%)	+17.6	-8.1	+35.2	+25.8	+9.5	-42.4	-47.2	-16.1	+43.3	+25.8	+27.1
Steps (reduced)		16 (16)	25 (7)	32 (14)	37 (1)	41 (5)	44 (8)	47 (11)	50 (14)	53 (17)	55 (1)	57 (3)

Approximation of harmonics in 18ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+33.7	-18.8	+13.4	-22.5	+24.2	+1.1	-16.7	-29.6	+37.6	+32.9	+31.7
	Relative (%)	+44.4	-24.8	+17.7	-29.7	+31.9	+1.5	-22.0	-39.1	+49.5	+43.3	+41.9
Steps (reduced)		59 (5)	60 (6)	62 (8)	63 (9)	65 (11)	66 (12)	67 (13)	68 (14)	70 (16)	71 (17)	72 (0)