44ed6

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44ed6

45ed6 →

Prime factorization	22 × 11
Step size	70.499 ¢
Octave	17\44ed6 (1198.48 ¢) (semiconvergent)
Twelfth	27\44ed6 (1903.47 ¢) (semiconvergent)
Consistency limit	4
Distinct consistency limit	4

44 equal divisions of the 6th harmonic (abbreviated 44ed6) is a nonoctave tuning system that divides the interval of 6/1 into 44 equal parts of about 70.5 ¢ each. Each step represents a frequency ratio of 6^1/44, or the 44th root of 6.

Theory

44ed6 is closely related to 17edo and 27edt, and like them is an excellent no-5 13-limit tuning. It also has good matches for the 23rd and 25th harmonics. Like 27edt, its octaves are slightly flat, albeit less so. The octave of 44ed6 is 1198.48 cents: about a cent and a half flat. The 3rd harmonic is sharp by the same amount, while the 7th, 11th, and 13th harmonics are all sharp by 15.1, 8.1, and 0.9 cents, respectively.

Harmonics

Approximation of harmonics in 44ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.5	+1.5	-3.0	+33.6	+0.0	+15.1	-4.6	+3.0	+32.1	+8.1	-1.5
	Relative (%)	-2.2	+2.2	-4.3	+47.7	+0.0	+21.5	-6.5	+4.3	+45.6	+11.5	-2.2
Steps (reduced)		17 (17)	27 (27)	34 (34)	40 (40)	44 (0)	48 (4)	51 (7)	54 (10)	57 (13)	59 (15)	61 (17)

Approximation of harmonics in 44ed6 (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+0.9	+13.6	+35.2	-6.1	+30.0	+1.5	-21.6	+30.6	+16.6	+6.6	+0.1	-3.0
	Relative (%)	+1.3	+19.3	+49.9	-8.6	+42.5	+2.2	-30.6	+43.4	+23.6	+9.4	+0.2	-4.3
Steps (reduced)		63 (19)	65 (21)	67 (23)	68 (24)	70 (26)	71 (27)	72 (28)	74 (30)	75 (31)	76 (32)	77 (33)	78 (34)

Subsets and supersets

Since 44 factors into primes as 2² × 11, 44ed6 has subset ed6's 2, 4, 11, and 22.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	70.5	23/22, 24/23, 27/26
2	141	13/12
3	211.5	17/15, 26/23
4	282	20/17, 27/23
5	352.5	11/9, 27/22
6	423	14/11, 23/18
7	493.5	4/3
8	564	18/13, 29/21
9	634.5	13/9, 23/16
10	705	3/2
11	775.5
12	846	13/8, 31/19
13	916.5	17/10, 22/13
14	987	23/13, 30/17
15	1057.5	24/13
16	1128	23/12
17	1198.5	2/1
18	1269	27/13
19	1339.5	13/6
20	1410	9/4
21	1480.5
22	1551	22/9, 27/11
23	1621.5	23/9, 28/11
24	1692	8/3
25	1762.5
26	1833	23/8, 26/9
27	1903.5	3/1
28	1974
29	2044.5	13/4
30	2115	17/5
31	2185.5
32	2256
33	2326.5	23/6
34	2397	4/1
35	2467.5
36	2538	13/3
37	2608.5	9/2
38	2679
39	2749.5
40	2820
41	2890.5
42	2961
43	3031.5	23/4
44	3102	6/1

See also

• 10edf – relative edf
• 17edo – relative edo
• 27edt – relative edt