38ed11/5

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38ed11/5

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Prime factorization	2 × 19
Step size	35.9212¢
Octave	33\38ed11/5 (1185.4¢)
Twelfth	53\38ed11/5 (1903.82¢)
Consistency limit	3
Distinct consistency limit	3

38 equal divisions of 11/5 (abbreviated 38ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 38 equal parts of about 35.9 ¢ each. Each step represents a frequency ratio of (11/5)^1/38, or the 38th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	35.921
2	71.842	23/22, 27/26
3	107.763
4	143.685
5	179.606	10/9, 21/19
6	215.527	17/15, 26/23
7	251.448	15/13, 22/19
8	287.369	13/11
9	323.29	23/19
10	359.212	21/17, 27/22
11	395.133	29/23
12	431.054	9/7, 23/18
13	466.975	17/13
14	502.896
15	538.817	15/11, 26/19
16	574.739
17	610.66	10/7, 27/19
18	646.581	29/20
19	682.502
20	718.423
21	754.344	17/11
22	790.266
23	826.187	21/13, 29/18
24	862.108	23/14
25	898.029
26	933.95
27	969.871
28	1005.793
29	1041.714
30	1077.635	13/7
31	1113.556	19/10, 21/11
32	1149.477
33	1185.398
34	1221.32
35	1257.241	29/14
36	1293.162	19/9
37	1329.083
38	1365.004	11/5

Harmonics

Approximation of harmonics in 38ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-14.6	+1.9	+6.7	+15.5	-12.7	+7.8	-7.9	+3.7	+0.9	+15.5	+8.6
	Relative (%)	-40.6	+5.2	+18.7	+43.3	-35.5	+21.6	-21.9	+10.4	+2.6	+43.3	+23.9
Steps (reduced)		33 (33)	53 (15)	67 (29)	78 (2)	86 (10)	94 (18)	100 (24)	106 (30)	111 (35)	116 (2)	120 (6)

Approximation of harmonics in 38ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+13.7	-6.8	+17.4	+13.4	+16.2	-10.9	+3.3	-13.7	+9.6	+0.9	-4.2
	Relative (%)	+38.1	-19.0	+48.4	+37.4	+45.2	-30.3	+9.2	-38.0	+26.8	+2.6	-11.6
Steps (reduced)		124 (10)	127 (13)	131 (17)	134 (20)	137 (23)	139 (25)	142 (28)	144 (30)	147 (33)	149 (35)	151 (37)