38edt

← 37edt

38edt

39edt →

Prime factorization	2 × 19
Step size	50.0514 ¢
Octave	24\38edt (1201.23 ¢) (→ 12\19edt)
Consistency limit	6
Distinct consistency limit	6

38 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 38edt or 38ed3), is a nonoctave tuning system that divides the interval of 3/1 into 38 equal parts of about 50.1 ¢ each. Each step represents a frequency ratio of 3^1/38, or the 38th root of 3.

38EDT is related to 24edo (quarter-tone tuning), but with the 3/1 rather than the 2/1 being just, which stretches the octave by about 1.2347 cents. It is consistent to the 6-integer-limit.

Lookalikes: 14edf, 24edo, 56ed5, 62ed6

Harmonics

Approximation of harmonics in 38edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.2	+0.0	+2.5	+16.6	+1.2	-15.4	+3.7	+0.0	+17.8	+3.0	+2.5
	Relative (%)	+2.5	+0.0	+4.9	+33.1	+2.5	-30.7	+7.4	+0.0	+35.6	+5.9	+4.9
Steps (reduced)		24 (24)	38 (0)	48 (10)	56 (18)	62 (24)	67 (29)	72 (34)	76 (0)	80 (4)	83 (7)	86 (10)

Approximation of harmonics in 38edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+14.1	-14.1	+16.6	+4.9	+0.1	+1.2	+7.7	+19.0	-15.4	+4.2	-22.7
	Relative (%)	+28.1	-28.3	+33.1	+9.9	+0.2	+2.5	+15.5	+38.0	-30.7	+8.4	-45.4
Steps (reduced)		89 (13)	91 (15)	94 (18)	96 (20)	98 (22)	100 (24)	102 (26)	104 (28)	105 (29)	107 (31)	108 (32)

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	50.1	34.2
2	100.1	68.4	17/16, 18/17, 19/18
3	150.2	102.6	12/11, 23/21
4	200.2	136.8	9/8, 19/17
5	250.3	171.1	15/13, 22/19
6	300.3	205.3	19/16
7	350.4	239.5	11/9, 27/22
8	400.4	273.7	24/19, 29/23
9	450.5	307.9	13/10, 22/17
10	500.5	342.1	4/3
11	550.6	376.3	11/8, 26/19
12	600.6	410.5	17/12, 24/17
13	650.7	444.7	16/11, 19/13
14	700.7	478.9	3/2
15	750.8	513.2	17/11, 20/13
16	800.8	547.4	19/12, 27/17
17	850.9	581.6	18/11
18	900.9	615.8	27/16
19	951	650	19/11, 26/15
20	1001	684.2	16/9
21	1051.1	718.4	11/6
22	1101.1	752.6	17/9
23	1151.2	786.8
24	1201.2	821.1	2/1
25	1251.3	855.3
26	1301.3	889.5	17/8
27	1351.4	923.7	24/11
28	1401.4	957.9	9/4
29	1451.5	992.1
30	1501.5	1026.3	19/8
31	1551.6	1060.5	22/9, 27/11
32	1601.6	1094.7
33	1651.7	1128.9	13/5
34	1701.7	1163.2	8/3
35	1751.8	1197.4	11/4
36	1801.9	1231.6	17/6
37	1851.9	1265.8
38	1902	1300	3/1

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