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	55.9
2	111.9
3	167.8	11/10, 21/19
4	223.8	17/15
5	279.7	27/23
6	335.6	23/19
7	391.6
8	447.5	13/10
9	503.5
10	559.4	18/13
11	615.3	10/7, 27/19
12	671.3	25/17
13	727.2
14	783.2	11/7
15	839.1
16	895
17	951	19/11
18	1006.9
19	1062.9
20	1118.8	19/10, 21/11
21	1174.7
22	1230.7
23	1286.6	19/9, 21/10
24	1342.6	13/6
25	1398.5
26	1454.4
27	1510.4
28	1566.3
29	1622.3	23/9
30	1678.2
31	1734.1	19/7
32	1790.1
33	1846
34	1902	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)

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