44ed5/2

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44ed5/2

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Prime factorization	22 × 11
Step size	36.0526 ¢
Octave	33\44ed5/2 (1189.74 ¢) (→ 3\4ed5/2)
Twelfth	53\44ed5/2 (1910.79 ¢)
Consistency limit	2
Distinct consistency limit	2

44 equal divisions of 5/2 (abbreviated 44ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 44 equal parts of about 36.1 ¢ each. Each step represents a frequency ratio of (5/2)^1/44, or the 44th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	36.1
2	72.1	25/24, 26/25
3	108.2
4	144.2	12/11, 13/12
5	180.3
6	216.3	17/15, 25/22
7	252.4	15/13, 22/19
8	288.4	13/11
9	324.5
10	360.5	21/17
11	396.6	29/23
12	432.6
13	468.7	17/13, 25/19
14	504.7
15	540.8	15/11, 26/19
16	576.8	7/5
17	612.9	10/7
18	648.9
19	685
20	721.1
21	757.1	17/11
22	793.2	19/12, 30/19
23	829.2	21/13, 29/18
24	865.3
25	901.3
26	937.4	12/7, 31/18
27	973.4	7/4
28	1009.5	25/14
29	1045.5	11/6, 31/17
30	1081.6
31	1117.6	19/10, 21/11
32	1153.7
33	1189.7
34	1225.8
35	1261.8	31/15
36	1297.9
37	1333.9	13/6
38	1370	11/5
39	1406.1
40	1442.1	30/13
41	1478.2
42	1514.2	12/5
43	1550.3
44	1586.3	5/2

Harmonics

Approximation of harmonics in 56ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-10.3	-4.0	+7.8	-10.3	+14.0	+2.1	-2.5	-8.1	+7.8	+12.8	+3.8
	Relative (%)	-36.2	-14.3	+27.5	-36.2	+49.5	+7.4	-8.7	-28.6	+27.5	+45.0	+13.3
Steps (reduced)		42 (42)	67 (11)	85 (29)	98 (42)	110 (54)	119 (7)	127 (15)	134 (22)	141 (29)	147 (35)	152 (40)

Approximation of harmonics in 56ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.8	-8.2	+14.0	-12.7	-4.4	+10.0	+1.4	-2.5	-2.0	+2.5	+10.5
	Relative (%)	+24.1	-28.9	+49.5	-44.9	-15.5	+35.2	+4.8	-8.7	-6.9	+8.8	+37.1
Steps (reduced)		157 (45)	161 (49)	166 (54)	169 (1)	173 (5)	177 (9)	180 (12)	183 (15)	186 (18)	189 (21)	192 (24)