48edt

← 47edt

48edt

49edt →

Prime factorization	24 × 3
Step size	39.6241¢
Octave	30\48edt (1188.72¢) (→5\8edt)
Consistency limit	2
Distinct consistency limit	2
Special properties	Highly composite

48 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 48edt or 48ed3), is a nonoctave tuning system that divides the interval of 3/1 into 48 equal parts of about 39.6 ¢ each. Each step represents a frequency ratio of 3^1/48, or the 48th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	39.6
2	79.2	22/21, 23/22
3	118.9	15/14, 29/27, 31/29
4	158.5	23/21
5	198.1	19/17, 28/25
6	237.7	31/27
7	277.4	27/23
8	317	6/5
9	356.6	27/22
10	396.2	29/23
11	435.9	9/7
12	475.5	29/22
13	515.1	31/23
14	554.7	29/21
15	594.4	31/22
16	634	13/9
17	673.6	31/21
18	713.2
19	752.9	17/11
20	792.5
21	832.1	21/13
22	871.7
23	911.4	22/13
24	951	19/11, 26/15
25	990.6	23/13
26	1030.2
27	1069.8	13/7
28	1109.5
29	1149.1
30	1188.7
31	1228.3
32	1268	25/12, 27/13
33	1307.6
34	1347.2
35	1386.8	29/13
36	1426.5
37	1466.1	7/3
38	1505.7	31/13
39	1545.3	22/9
40	1585	5/2
41	1624.6	23/9
42	1664.2
43	1703.8
44	1743.5
45	1783.1	14/5
46	1822.7
47	1862.3
48	1902	3/1

Harmonics

Approximation of harmonics in 48edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.3	+0.0	+17.1	-12.6	-11.3	-0.8	+5.8	+0.0	+15.7	+9.2	+17.1
	Relative (%)	-28.5	+0.0	+43.1	-31.9	-28.5	-2.0	+14.6	+0.0	+39.7	+23.2	+43.1
Steps (reduced)		30 (30)	48 (0)	61 (13)	70 (22)	78 (30)	85 (37)	91 (43)	96 (0)	101 (5)	105 (9)	109 (13)

Approximation of harmonics in 48edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	-12.1	-12.6	-5.5	+8.4	-11.3	+14.0	+4.4	-0.8	-2.1	+0.2
	Relative (%)	-6.6	-30.4	-31.9	-13.9	+21.3	-28.5	+35.3	+11.2	-2.0	-5.2	+0.6
Steps (reduced)		112 (16)	115 (19)	118 (22)	121 (25)	124 (28)	126 (30)	129 (33)	131 (35)	133 (37)	135 (39)	137 (41)

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