49edt

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49edt

50edt →

Prime factorization	72
Step size	38.8154 ¢
Octave	31\49edt (1203.28 ¢)
Consistency limit	12
Distinct consistency limit	9

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.

Theory

49edt is related to 31edo, but with the 3/1 rather than the 2/1 being just, which stretches the octave by about 3.28 ¢. Like 31edo, 49edt is consistent through the 12-integer-limit, but it has a sharp tendency, with prime harmonics 2, 5, 7, and 11 all tuned sharp.

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 (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-15.6	+11.4	+8.4	+13.1	-14.2	+3.3	-12.7	+15.0	+8.1	+5.2	+5.9	+9.8
	Relative (%)	-40.1	+29.3	+21.6	+33.8	-36.6	+8.4	-32.7	+38.5	+20.9	+13.4	+15.2	+25.3
Steps (reduced)		114 (16)	118 (20)	121 (23)	124 (26)	126 (28)	129 (31)	131 (33)	134 (36)	136 (38)	138 (40)	140 (42)	142 (44)

Subsets and supersets

Since 49 factors into primes as 7², 49edt contains 7edt as its only nontrivial subset edt.

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

See also

• 18edf – relative edf
• 31edo – relative edo
• 72ed5 – relative ed5
• 80ed6 – relative ed6
• 87ed7 – relative ed7
• 107ed11 – relative ed11
• 111ed12 – relative ed12
• 138ed22 – relative ed22
• 204ed96 – close to the zeta-optimized tuning for 31edo
• 39cET