33ed5/2

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33ed5/2

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Prime factorization	3 × 11
Step size	48.0701¢
Octave	25\33ed5/2 (1201.75¢) (semiconvergent)
Twelfth	40\33ed5/2 (1922.8¢)
Consistency limit	6
Distinct consistency limit	6

33 equal divisions of 5/2 (abbreviated 33ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 33 equal parts of about 48.1⁠ ⁠¢ each. Each step represents a frequency ratio of (5/2)^1/33, or the 33rd root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	48.1
2	96.1	17/16, 20/19
3	144.2	25/23
4	192.3	19/17, 28/25
5	240.4	23/20
6	288.4	13/11, 20/17
7	336.5	17/14, 23/19, 28/23
8	384.6	5/4
9	432.6
10	480.7	25/19
11	528.8	19/14, 23/17
12	576.8	7/5
13	624.9	10/7, 23/16
14	673	25/17, 28/19
15	721.1
16	769.1	25/16
17	817.2	8/5
18	865.3	23/14, 28/17
19	913.3	17/10, 22/13
20	961.4	7/4
21	1009.5	25/14
22	1057.5
23	1105.6	19/10
24	1153.7
25	1201.8	2/1
26	1249.8
27	1297.9	17/8
28	1346
29	1394
30	1442.1	23/10
31	1490.2	19/8, 26/11
32	1538.2	17/7
33	1586.3	5/2

Harmonics

Approximation of harmonics in 33ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.8	+20.8	+3.5	+1.8	+22.6	-3.9	+5.3	-6.4	+3.5	-17.3	-23.7
	Relative (%)	+3.6	+43.4	+7.3	+3.6	+47.0	-8.2	+10.9	-13.3	+7.3	-36.0	-49.3
Steps (reduced)		25 (25)	40 (7)	50 (17)	58 (25)	65 (32)	70 (4)	75 (9)	79 (13)	83 (17)	86 (20)	89 (23)

Approximation of harmonics in 33ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-18.1	-2.2	+22.6	+7.0	-1.8	-4.6	-2.1	+5.3	+16.9	-15.5	+3.6
	Relative (%)	-37.6	-4.5	+47.0	+14.6	-3.8	-9.6	-4.3	+10.9	+35.2	-32.3	+7.6
Steps (reduced)		92 (26)	95 (29)	98 (32)	100 (1)	102 (3)	104 (5)	106 (7)	108 (9)	110 (11)	111 (12)	113 (14)