33ed7/3

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33ed7/3

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Prime factorization	3 × 11
Step size	44.4506¢
Octave	27\33ed7/3 (1200.17¢) (→9\11ed7/3)
Twelfth	43\33ed7/3 (1911.38¢)
Consistency limit	10
Distinct consistency limit	4

33 equal divisions of 7/3 (abbreviated 33ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 33 equal parts of about 44.5⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/33, or the 33rd root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	44.5
2	88.9	19/18, 20/19, 21/20
3	133.4	13/12, 14/13, 27/25
4	177.8	10/9, 21/19
5	222.3	8/7
6	266.7	7/6
7	311.2	6/5
8	355.6	16/13
9	400.1	24/19
10	444.5	22/17
11	489
12	533.4	19/14
13	577.9	7/5
14	622.3	10/7, 23/16
15	666.8	28/19
16	711.2
17	755.7	17/11
18	800.1	19/12
19	844.6	13/8
20	889	5/3
21	933.5	12/7
22	977.9
23	1022.4	9/5
24	1066.8	13/7, 24/13
25	1111.3	19/10
26	1155.7
27	1200.2	2/1
28	1244.6
29	1289.1	19/9, 21/10
30	1333.5	13/6, 28/13
31	1378	20/9
32	1422.4	16/7
33	1466.9	7/3

Harmonics

Approximation of harmonics in 33ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.2	+9.4	+0.3	+14.1	+9.6	+9.4	+0.5	+18.8	+14.2	-17.4	+9.8
	Relative (%)	+0.4	+21.2	+0.8	+31.7	+21.6	+21.2	+1.1	+42.4	+32.0	-39.2	+21.9
Steps (reduced)		27 (27)	43 (10)	54 (21)	63 (30)	70 (4)	76 (10)	81 (15)	86 (20)	90 (24)	93 (27)	97 (31)

Approximation of harmonics in 33ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.5	+9.6	-21.0	+0.7	-15.4	+19.0	+14.3	+14.4	+18.8	-17.2	-5.3
	Relative (%)	+10.2	+21.6	-47.1	+1.5	-34.6	+42.8	+32.2	+32.4	+42.4	-38.8	-11.9
Steps (reduced)		100 (1)	103 (4)	105 (6)	108 (9)	110 (11)	113 (14)	115 (16)	117 (18)	119 (20)	120 (21)	122 (23)