44ed11/5

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44ed11/5

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Prime factorization	22 × 11
Step size	31.0228¢
Octave	39\44ed11/5 (1209.89¢)
Twelfth	61\44ed11/5 (1892.39¢)
Consistency limit	2
Distinct consistency limit	2

44 equal divisions of 11/5 (abbreviated 44ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 44 equal parts of about 31 ¢ each. Each step represents a frequency ratio of (11/5)^1/44, or the 44th root of 11/5.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	31.023
2	62.046	26/25, 30/29, 31/30
3	93.068	18/17, 19/18
4	124.091
5	155.114	12/11, 23/21
6	186.137	19/17, 29/26
7	217.16	17/15, 25/22, 26/23
8	248.183	15/13
9	279.205
10	310.228	6/5, 31/26
11	341.251
12	372.274	21/17, 26/21, 31/25
13	403.297	19/15, 29/23
14	434.32
15	465.342	17/13, 30/23
16	496.365
17	527.388	23/17
18	558.411	18/13, 29/21
19	589.434	31/22
20	620.456	10/7
21	651.479	19/13
22	682.502
23	713.525
24	744.548	23/15
25	775.571
26	806.593
27	837.616
28	868.639
29	899.662
30	930.685	12/7, 29/17
31	961.708
32	992.73	23/13
33	1023.753
34	1054.776	11/6
35	1085.799
36	1116.822	21/11
37	1147.844
38	1178.867
39	1209.89
40	1240.913
41	1271.936	23/11, 25/12
42	1302.959
43	1333.981	13/6
44	1365.004	11/5

Harmonics

Approximation of harmonics in 44ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.9	-9.6	-11.2	+5.7	+0.3	+12.7	-1.4	+11.9	-15.4	+5.7	+10.2
	Relative (%)	+31.9	-30.8	-36.2	+18.5	+1.1	+40.8	-4.4	+38.4	-49.6	+18.5	+32.9
Steps (reduced)		39 (39)	61 (17)	77 (33)	90 (2)	100 (12)	109 (21)	116 (28)	123 (35)	128 (40)	134 (2)	139 (7)

Approximation of harmonics in 44ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.3	-8.5	-3.8	+8.5	-3.3	-9.2	-9.8	-5.5	+3.1	-15.4	+0.7
	Relative (%)	-13.7	-27.3	-12.3	+27.5	-10.8	-29.8	-31.5	-17.7	+10.0	-49.6	+2.3
Steps (reduced)		143 (11)	147 (15)	151 (19)	155 (23)	158 (26)	161 (29)	164 (32)	167 (35)	170 (38)	172 (40)	175 (43)