68edt

← 67edt

68edt

69edt →

Prime factorization	22 × 17
Step size	27.9699¢
Octave	43\68edt (1202.71¢)
Consistency limit	5
Distinct consistency limit	5

68 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 68edt or 68ed3), is a nonoctave tuning system that divides the interval of 3/1 into 68 equal parts of about 28⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/68, or the 68th root of 3.

68EDT is related to 43edo (meride tuning), but with the 3/1 rather than the 2/1 being just. This results in octaves being stretched by about 2.707 cents. Unlike 43edo, it is only consistent up to the 6-integer-limit, with discrepancy for the 7th harmonic.

Lookalikes: 25edf, 28cET, 43edo, 100ed5, 111ed6

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	28	19.1
2	55.9	38.2	31/30, 32/31
3	83.9	57.4	22/21
4	111.9	76.5	16/15
5	139.8	95.6	13/12
6	167.8	114.7
7	195.8	133.8	19/17
8	223.8	152.9	33/29
9	251.7	172.1	22/19, 37/32
10	279.7	191.2	27/23
11	307.7	210.3	31/26, 37/31
12	335.6	229.4	17/14
13	363.6	248.5	21/17, 37/30
14	391.6	267.6
15	419.5	286.8	14/11
16	447.5	305.9	22/17, 35/27
17	475.5	325	29/22
18	503.5	344.1
19	531.4	363.2	19/14
20	559.4	382.4	29/21
21	587.4	401.5
22	615.3	420.6
23	643.3	439.7
24	671.3	458.8	28/19
25	699.2	477.9	3/2
26	727.2	497.1	35/23
27	755.2	516.2	17/11, 31/20
28	783.2	535.3	11/7
29	811.1	554.4	8/5
30	839.1	573.5	13/8
31	867.1	592.6	28/17
32	895	611.8
33	923	630.9	29/17
34	951	650	26/15
35	978.9	669.1
36	1006.9	688.2	34/19
37	1034.9	707.4
38	1062.9	726.5	24/13, 37/20
39	1090.8	745.6	15/8
40	1118.8	764.7	21/11
41	1146.8	783.8	31/16, 33/17
42	1174.7	802.9
43	1202.7	822.1	2/1
44	1230.7	841.2
45	1258.6	860.3	29/14, 31/15
46	1286.6	879.4
47	1314.6	898.5	32/15
48	1342.6	917.6
49	1370.5	936.8
50	1398.5	955.9
51	1426.5	975
52	1454.4	994.1	37/16
53	1482.4	1013.2	33/14
54	1510.4	1032.4
55	1538.3	1051.5	17/7
56	1566.3	1070.6	37/15
57	1594.3	1089.7
58	1622.3	1108.8	23/9
59	1650.2	1127.9
60	1678.2	1147.1	29/11
61	1706.2	1166.2
62	1734.1	1185.3
63	1762.1	1204.4	36/13
64	1790.1	1223.5
65	1818	1242.6
66	1846	1261.8
67	1874	1280.9
68	1902	1300	3/1

Harmonics

Approximation of harmonics in 68edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.7	+0.0	+5.4	+10.7	+2.7	-12.4	+8.1	+0.0	+13.4	-11.8	+5.4
	Relative (%)	+9.7	+0.0	+19.4	+38.2	+9.7	-44.5	+29.0	+0.0	+47.9	-42.1	+19.4
Steps (reduced)		43 (43)	68 (0)	86 (18)	100 (32)	111 (43)	120 (52)	129 (61)	136 (0)	143 (7)	148 (12)	154 (18)

Approximation of harmonics in 68edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.7	-9.7	+10.7	+10.8	-10.2	+2.7	-7.0	-11.9	-12.4	-9.1	-2.1
	Relative (%)	+23.9	-34.8	+38.2	+38.7	-36.5	+9.7	-25.0	-42.5	-44.5	-32.4	-7.5
Steps (reduced)		159 (23)	163 (27)	168 (32)	172 (36)	175 (39)	179 (43)	182 (46)	185 (49)	188 (52)	191 (55)	194 (58)