31ed11/5

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31ed11/5

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Prime factorization	31 (prime)
Step size	44.0324¢
Octave	27\31ed11/5 (1188.87¢)
Twelfth	43\31ed11/5 (1893.39¢)
Consistency limit	3
Distinct consistency limit	3

31 equal divisions of 11/5 (abbreviated 31ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 31 equal parts of about 44 ¢ each. Each step represents a frequency ratio of (11/5)^1/31, or the 31st root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	44.032
2	88.065
3	132.097	14/13, 27/25
4	176.13	10/9, 21/19
5	220.162	17/15, 25/22, 26/23
6	264.194
7	308.227	6/5
8	352.259	11/9, 27/22
9	396.292
10	440.324	22/17
11	484.356
12	528.389	15/11, 19/14, 23/17, 27/20
13	572.421	25/18
14	616.454
15	660.486	19/13, 22/15, 25/17
16	704.518	3/2
17	748.551	17/11, 23/15
18	792.583	27/17
19	836.615	21/13
20	880.648	5/3
21	924.68	17/10
22	968.713
23	1012.745	9/5
24	1056.777	11/6
25	1100.81	17/9
26	1144.842
27	1188.875
28	1232.907
29	1276.939	23/11, 25/12
30	1320.972
31	1365.004	11/5

Harmonics

Approximation of harmonics in 31ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.1	-8.6	+21.8	-12.3	-19.7	+21.7	+10.7	-17.1	+20.6	-12.3	+13.2
	Relative (%)	-25.3	-19.4	+49.5	-27.9	-44.7	+49.2	+24.2	-38.9	+46.9	-27.9	+30.0
Steps (reduced)		27 (27)	43 (12)	55 (24)	63 (1)	70 (8)	77 (15)	82 (20)	86 (24)	91 (29)	94 (1)	98 (5)

Approximation of harmonics in 31ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.7	+10.5	-20.8	-0.5	-17.4	+15.8	+10.2	+9.5	+13.1	+20.6	-12.3
	Relative (%)	+15.3	+23.9	-47.3	-1.1	-39.4	+35.8	+23.3	+21.6	+29.8	+46.9	-27.9
Steps (reduced)		101 (8)	104 (11)	106 (13)	109 (16)	111 (18)	114 (21)	116 (23)	118 (25)	120 (27)	122 (29)	123 (30)