33edf

33 equal divisions of the perfect fifth (abbreviated 33edf or 33ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 33 equal parts of about 21.3 ¢ each. Each step represents a frequency ratio of (3/2)^1/33, or the 33rd root of 3/2.

← 32edf

33edf

34edf →

Prime factorization	3 × 11
Step size	21.2714 ¢
Octave	56\33edf (1191.2 ¢)
Twelfth	89\33edf (1893.15 ¢)
Consistency limit	3
Distinct consistency limit	3

33edf corresponds to 56.4139edo, similar to every fifth step of 282edo. It is related to the regular temperament which tempers out [-131 131 -33⟩ in the 5-limit, which is supported by 113-, 282-, 395-, 677-, 959-, 1072-, 1467-, and 1749edo.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	21.3
2	42.5
3	63.8	26/25, 28/27
4	85.1	21/20, 22/21, 23/22
5	106.4
6	127.6	15/14
7	148.9	25/23
8	170.2	11/10
9	191.4	19/17
10	212.7	9/8, 26/23
11	234
12	255.3
13	276.5
14	297.8	13/11
15	319.1
16	340.3
17	361.6
18	382.9
19	404.2
20	425.4
21	446.7
22	468	17/13, 25/19
23	489.2	4/3
24	510.5
25	531.8	15/11
26	553.1
27	574.3	7/5
28	595.6
29	616.9	10/7
30	638.1
31	659.4	19/13, 22/15, 25/17
32	680.7
33	702	3/2

Harmonics

Approximation of harmonics in 33edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-8.80	-8.80	+3.66	+0.23	+3.66	-7.95	-5.14	+3.66	-8.57	-3.40	-5.14
	Relative (%)	-41.4	-41.4	+17.2	+1.1	+17.2	-37.4	-24.2	+17.2	-40.3	-16.0	-24.2
Steps (reduced)		56 (23)	89 (23)	113 (14)	131 (32)	146 (14)	158 (26)	169 (4)	179 (14)	187 (22)	195 (30)	202 (4)

Approximation of harmonics in 33edf (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.19	+4.52	-8.57	+7.33	+8.73	-5.14	+7.61	+3.90	+4.52	+9.07	-4.08
	Relative (%)	+24.4	+21.2	-40.3	+34.5	+41.0	-24.2	+35.8	+18.3	+21.2	+42.6	-19.2
Steps (reduced)		209 (11)	215 (17)	220 (22)	226 (28)	231 (0)	235 (4)	240 (9)	244 (13)	248 (17)	252 (21)	255 (24)

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