30ed11/5

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 29ed11/5

30ed11/5

31ed11/5 →

Prime factorization	2 × 3 × 5
Step size	45.5001¢
Octave	26\30ed11/5 (1183¢) (→13\15ed11/5)
Twelfth	42\30ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit	2
Distinct consistency limit	2

30 equal divisions of 11/5 (abbreviated 30ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 30 equal parts of about 45.5 ¢ each. Each step represents a frequency ratio of (11/5)^1/30, or the 30th root of 11/5.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	45.5
2	91	18/17, 19/18
3	136.5	25/23
4	182.001	21/19
5	227.501	25/22
6	273.001	7/6
7	318.501	6/5
8	364.001	21/17, 26/21
9	409.501	14/11, 19/15
10	455.001	17/13
11	500.502
12	546.002	15/11, 26/19
13	591.502	7/5
14	637.002	13/9
15	682.502
16	728.002	26/17
17	773.502	11/7
18	819.003
19	864.503	23/14
20	910.003
21	955.503	19/11, 26/15
22	1001.003	25/14
23	1046.503	11/6
24	1092.003	17/9
25	1137.504
26	1183.004
27	1228.504
28	1274.004	23/11, 25/12, 27/13
29	1319.504	15/7
30	1365.004	11/5

Harmonics

Approximation of harmonics in 30ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-17.0	+9.1	+11.5	-10.8	-7.9	-1.8	-5.5	+18.1	+17.7	-10.8	+20.6
	Relative (%)	-37.4	+19.9	+25.3	-23.7	-17.5	-4.0	-12.1	+39.8	+38.9	-23.7	+45.2
Steps (reduced)		26 (26)	42 (12)	53 (23)	61 (1)	68 (8)	74 (14)	79 (19)	84 (24)	88 (28)	91 (1)	95 (5)

Approximation of harmonics in 30ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+18.5	-18.8	-1.8	-22.5	+9.1	+1.1	-1.5	+0.7	+7.2	+17.7	-13.8
	Relative (%)	+40.6	-41.3	-3.9	-49.4	+19.9	+2.4	-3.3	+1.5	+15.9	+38.9	-30.2
Steps (reduced)		98 (8)	100 (10)	103 (13)	105 (15)	108 (18)	110 (20)	112 (22)	114 (24)	116 (26)	118 (28)	119 (29)