33ed11/5

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

← 32ed11/5

33ed11/5

34ed11/5 →

Prime factorization	3 × 11
Step size	41.3638¢
Octave	29\33ed11/5 (1199.55¢) (convergent)
Twelfth	46\33ed11/5 (1902.73¢) (semiconvergent)
Consistency limit	16
Distinct consistency limit	4

33 equal divisions of 11/5 (abbreviated 33ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 33 equal parts of about 41.4 ¢ each. Each step represents a frequency ratio of (11/5)^1/33, or the 33rd root of 11/5.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	41.364
2	82.728	20/19, 21/20, 22/21, 23/22
3	124.091	14/13, 15/14
4	165.455	11/10, 21/19, 23/21
5	206.819	9/8, 26/23
6	248.183	15/13, 22/19, 23/20
7	289.546	13/11, 19/16
8	330.91	23/19
9	372.274	26/21
10	413.638	14/11, 19/15
11	455.001	13/10
12	496.365	4/3
13	537.729	15/11, 26/19
14	579.093	7/5
15	620.456	10/7, 23/16
16	661.82	19/13, 22/15
17	703.184	3/2
18	744.548	20/13, 23/15
19	785.912	11/7
20	827.275	21/13
21	868.639
22	910.003	22/13, 27/16
23	951.367	19/11, 26/15
24	992.73	16/9, 23/13
25	1034.094	20/11
26	1075.458	13/7, 28/15
27	1116.822	19/10, 21/11
28	1158.185
29	1199.549	2/1
30	1240.913
31	1282.277	21/10, 23/11
32	1323.64	15/7, 28/13
33	1365.004	11/5

Harmonics

Approximation of harmonics in 33ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.5	+0.8	-0.9	-14.9	+0.3	-18.4	-1.4	+1.6	-15.4	-14.9	-0.1
	Relative (%)	-1.1	+1.9	-2.2	-36.1	+0.8	-44.4	-3.3	+3.8	-37.2	-36.1	-0.3
Steps (reduced)		29 (29)	46 (13)	58 (25)	67 (1)	75 (9)	81 (15)	87 (21)	92 (26)	96 (30)	100 (1)	104 (5)

Approximation of harmonics in 33ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-14.6	-18.8	-14.2	-1.8	+17.3	+1.1	-9.8	-15.8	-17.6	-15.4	-9.6
	Relative (%)	-35.3	-45.5	-34.2	-4.4	+41.9	+2.7	-23.6	-38.3	-42.5	-37.2	-23.3
Steps (reduced)		107 (8)	110 (11)	113 (14)	116 (17)	119 (20)	121 (22)	123 (24)	125 (26)	127 (28)	129 (30)	131 (32)