29edt

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29edt

30edt →

Prime factorization	29 (prime)
Step size	65.5847 ¢
Octave	18\29edt (1180.52 ¢)
Consistency limit	3
Distinct consistency limit	3

29EDT is the equal division of the third harmonic into 29 parts of 65.5847 cents each, corresponding to 18.2970 edo. It is related to the luminal temperament.

While not possessing good approximations to most integer harmonics, it does have a few very good rational intervals: notably 27/26, 17/10, 45/32, and 11/6.

Intervals

steps	cents	hekts	corresponding JI intervals	comments
0			1/1
1	65.5847	44.8276	27/26
2	131.1693	89.6552	14/13, 27/25, 55/51
3	196.7540	134.4828	9/8, 28/25	pseudo-10/9
4	262.3386	179.3103	7/6
5	327.9233	224.1379		pseudo-6/5
6	393.5079	268.9655	64/51	pseudo-5/4
7	459.0926	313.7931	13/10
8	524.6772	358.6206	65/48, 27/20
9	590.2619	403.4483	45/32
10	655.8466	448.2759	16/11
11	721.4312	493.1034		pseudo-3/2
12	787.0159	537.9310	63/40, 52/33	pseudo-8/5
13	852.6005	582.7586	18/11	flat pseudo-5/3
14	918.1852	627.5862	17/10	sharp pseudo-5/3
15	983.7698	672.4138	30/17	flat pseudo-9/5
16	1049.3545	717.2414	11/6	sharp pseudo-9/5
17	1114.9391	772.0690	99/52, 40/21	pseudo-15/8
18	1180.5238	806.8966		pseudooctave
19	1246.1084	851.7241	33/16
20	1311.6931	896.5517	32/15
21	1377.2778	941.3794	144/65, 20/9
22	1442.8624	986.2069	30/13	pseudo-7/3 (7/6 plus pseudooctave)
23	1508.4471	1031.0345	153/64	pseudo-12/5
24	1574.0317	1075.8621		pseudo-5/2
25	1639.6164	1120.6897	18/7
26	1705.2010	1165.5172	8/3, 75/28	pseudo-27/10
27	1770.7857	1210.3448	39/14, 25/9, 153/55
28	1836.3703	1255.1724	26/9
29	1901.9550	1300.0000	3/1	just perfect fifth plus an octave

Harmonics

Approximation of harmonics in 29edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-19.5	+0.0	+26.6	-31.8	-19.5	-24.0	+7.2	+0.0	+14.4	-19.5	+26.6
	Relative (%)	-29.7	+0.0	+40.6	-48.4	-29.7	-36.6	+10.9	+0.0	+21.9	-29.7	+40.6
Steps (reduced)		18 (18)	29 (0)	37 (8)	42 (13)	47 (18)	51 (22)	55 (26)	58 (0)	61 (3)	63 (5)	66 (8)

Approximation of harmonics in 29edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+19.2	+22.1	-31.8	-12.3	+13.9	-19.5	+18.1	-5.1	-24.0	+26.6	+15.3
	Relative (%)	+29.3	+33.7	-48.4	-18.8	+21.2	-29.7	+27.6	-7.8	-36.6	+40.6	+23.3
Steps (reduced)		68 (10)	70 (12)	71 (13)	73 (15)	75 (17)	76 (18)	78 (20)	79 (21)	80 (22)	82 (24)	83 (25)