49edt

← 48edt

49edt

50edt →

Prime factorization	72
Step size	38.8154¢
Octave	31\49edt (1203.28¢)
Consistency limit	11
Distinct consistency limit	8

49 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 49edt or 49ed3), is a nonoctave tuning system that divides the interval of 3/1 into 49 equal parts of about 38.8⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/49, or the 49th root of 3.

49EDT is related to 31edo, but with the 3/1 rather than the 2/1 being just, which stretches the octave by about 3.2777 ¢. It is consistent through the 12-integer limit.

Lookalikes: 18edf, 31edo, 39cET, 80ed6

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	38.8	26.5
2	77.6	53.1	22/21, 23/22, 24/23
3	116.4	79.6	15/14, 16/15, 31/29
4	155.3	106.1	12/11, 23/21
5	194.1	132.7	19/17, 28/25, 29/26
6	232.9	159.2	8/7
7	271.7	185.7	7/6
8	310.5	212.2	6/5
9	349.3	238.8	11/9, 27/22
10	388.2	265.3	5/4
11	427	291.8	23/18, 32/25
12	465.8	318.4	17/13, 21/16
13	504.6	344.9
14	543.4	371.4	26/19
15	582.2	398	7/5
16	621	424.5	10/7
17	659.9	451	19/13, 22/15
18	698.7	477.6	3/2
19	737.5	504.1	23/15, 26/17, 29/19
20	776.3	530.6	25/16
21	815.1	557.1	8/5
22	853.9	583.7	18/11, 23/14
23	892.8	610.2
24	931.6	636.7	12/7
25	970.4	663.3	7/4
26	1009.2	689.8	25/14
27	1048	716.3	11/6
28	1086.8	742.9	15/8
29	1125.6	769.4	23/12
30	1164.5	795.9
31	1203.3	822.4	2/1
32	1242.1	849
33	1280.9	875.5	21/10, 23/11
34	1319.7	902	15/7
35	1358.5	928.6
36	1397.4	955.1
37	1436.2	981.6	16/7
38	1475	1008.2
39	1513.8	1034.7	12/5
40	1552.6	1061.2	22/9, 27/11
41	1591.4	1087.8	5/2
42	1630.2	1114.3	18/7
43	1669.1	1140.8	21/8
44	1707.9	1167.3
45	1746.7	1193.9	11/4
46	1785.5	1220.4	14/5
47	1824.3	1246.9	23/8
48	1863.1	1273.5
49	1902	1300	3/1

Harmonics

Approximation of harmonics in 49edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.3	+0.0	+6.6	+8.4	+3.3	+8.1	+9.8	+0.0	+11.7	+1.9	+6.6
	Relative (%)	+8.4	+0.0	+16.9	+21.6	+8.4	+20.9	+25.3	+0.0	+30.1	+5.0	+16.9
Steps (reduced)		31 (31)	49 (0)	62 (13)	72 (23)	80 (31)	87 (38)	93 (44)	98 (0)	103 (5)	107 (9)	111 (13)

Approximation of harmonics in 49edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-15.6	+11.4	+8.4	+13.1	-14.2	+3.3	-12.7	+15.0	+8.1	+5.2	+5.9
	Relative (%)	-40.1	+29.3	+21.6	+33.8	-36.6	+8.4	-32.7	+38.5	+20.9	+13.4	+15.2
Steps (reduced)		114 (16)	118 (20)	121 (23)	124 (26)	126 (28)	129 (31)	131 (33)	134 (36)	136 (38)	138 (40)	140 (42)

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