33ed7/4

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33ed7/4

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Prime factorization	3 × 11
Step size	29.3584¢
Octave	41\33ed7/4 (1203.69¢)
Twelfth	65\33ed7/4 (1908.29¢)
Consistency limit	10
Distinct consistency limit	3

33 equal divisions of 7/4 (abbreviated 33ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 33 equal parts of about 29.4 ¢ each. Each step represents a frequency ratio of (7/4)^1/33, or the 33rd root of 7/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	29.4
2	58.7	28/27
3	88.1	19/18, 20/19, 21/20
4	117.4	15/14, 16/15
5	146.8	25/23
6	176.2	10/9, 21/19
7	205.5	9/8, 26/23
8	234.9	8/7, 23/20
9	264.2	7/6
10	293.6	13/11, 19/16, 25/21
11	322.9	6/5, 23/19
12	352.3
13	381.7	5/4
14	411	19/15, 24/19
15	440.4	9/7, 22/17
16	469.7	17/13, 21/16, 25/19
17	499.1	4/3
18	528.5	19/14, 23/17, 27/20
19	557.8
20	587.2	7/5
21	616.5	10/7, 27/19
22	645.9
23	675.2	25/17, 28/19
24	704.6	3/2
25	734	23/15, 26/17
26	763.3	14/9
27	792.7	19/12
28	822	8/5
29	851.4	23/14
30	880.8	5/3
31	910.1	17/10, 22/13, 27/16
32	939.5	12/7
33	968.8	7/4

Harmonics

Approximation of harmonics in 33ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.7	+6.3	+7.4	+2.7	+10.0	+7.4	+11.1	+12.7	+6.4	-11.8	+13.7
	Relative (%)	+12.6	+21.6	+25.2	+9.3	+34.2	+25.2	+37.7	+43.2	+21.9	-40.2	+46.7
Steps (reduced)		41 (8)	65 (32)	82 (16)	95 (29)	106 (7)	115 (16)	123 (24)	130 (31)	136 (4)	141 (9)	147 (15)

Approximation of harmonics in 33ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-7.4	+11.1	+9.1	-14.6	-2.1	-13.0	+10.8	+10.1	+13.7	-8.1	+3.0
	Relative (%)	-25.3	+37.7	+30.9	-49.7	-7.2	-44.2	+36.9	+34.5	+46.7	-27.6	+10.3
Steps (reduced)		151 (19)	156 (24)	160 (28)	163 (31)	167 (2)	170 (5)	174 (9)	177 (12)	180 (15)	182 (17)	185 (20)