34edt

← 33edt

34edt

35edt →

Prime factorization	2 × 17
Step size	55.9399¢
Octave	21\34edt (1174.74¢)
Consistency limit	2
Distinct consistency limit	2

34EDT is the equal division of the third harmonic into 34 parts of 55.9399 cents each, corresponding to 21.4516 edo. It is contorted in the no-twos 11-limit, tempering out 77/75, 245/243, and 1331/1323. Using the patent val, it tempers out 169/165 and 847/845 in the 13-limit (no-twos subgroup). With the patent 4, it tempers out 49/48, 81/80, and 16128/15625 in the 3.4.5.7 subgroup; 77/75, 176/175, 891/875, and 1331/1280 in the 3.4.5.7.11 subgroup; 65/64, 143/140, 169/165, 196/195, and 325/324 in the 3.4.5.7.11.13 subgroup.

Lookalikes: 43ED4

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	55.94
2	111.88
3	167.82	11/10, 21/19
4	223.759	17/15
5	279.699	27/23
6	335.639	23/19
7	391.579
8	447.519	13/10
9	503.459
10	559.399	18/13
11	615.338	10/7, 27/19
12	671.278	25/17
13	727.218
14	783.158	11/7
15	839.098
16	895.038
17	950.978	19/11
18	1006.917
19	1062.857
20	1118.797	19/10, 21/11
21	1174.737
22	1230.677
23	1286.617	19/9, 21/10
24	1342.556	13/6
25	1398.496
26	1454.436
27	1510.376
28	1566.316
29	1622.256	23/9
30	1678.196
31	1734.135	19/7
32	1790.075
33	1846.015
34	1901.955	3/1

Harmonics

Approximation of harmonics in 34edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-25.3	+0.0	+5.4	+10.7	-25.3	-12.4	-19.8	+0.0	-14.6	-11.8	+5.4
	Relative (%)	-45.2	+0.0	+9.7	+19.1	-45.2	-22.2	-35.5	+0.0	-26.1	-21.0	+9.7
Steps (reduced)		21 (21)	34 (0)	43 (9)	50 (16)	55 (21)	60 (26)	64 (30)	68 (0)	71 (3)	74 (6)	77 (9)

Approximation of harmonics in 34edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-21.3	+18.2	+10.7	+10.8	+17.8	-25.3	-7.0	+16.1	-12.4	+18.9	-2.1
	Relative (%)	-38.0	+32.6	+19.1	+19.4	+31.7	-45.2	-12.5	+28.8	-22.2	+33.8	-3.8
Steps (reduced)		79 (11)	82 (14)	84 (16)	86 (18)	88 (20)	89 (21)	91 (23)	93 (25)	94 (26)	96 (28)	97 (29)