45edt

← 44edt

45edt

46edt →

Prime factorization	32 × 5
Step size	42.2657¢
Octave	28\45edt (1183.44¢)
Consistency limit	2
Distinct consistency limit	2

45EDT is the equal division of the third harmonic into 45 parts of 42.2657 cents each, corresponding to 28.3918 edo. It makes for a strong no-twos 17-limit system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit (no-twos subgroup). It is the tenth no-twos zeta peak edt.

Harmonics

Approximation of harmonics in 45edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-16.6	+0.0	+9.1	+3.2	-16.6	+12.4	-7.4	+0.0	-13.3	-9.3	+9.1
	Relative (%)	-39.2	+0.0	+21.6	+7.6	-39.2	+29.4	-17.6	+0.0	-31.6	-22.0	+21.6
Steps (reduced)		28 (28)	45 (0)	57 (12)	66 (21)	73 (28)	80 (35)	85 (40)	90 (0)	94 (4)	98 (8)	102 (12)

Approximation of harmonics in 45edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	-4.1	+3.2	+18.3	-2.1	-16.6	+16.6	+12.4	+12.4	+16.4	-18.3
	Relative (%)	-6.2	-9.8	+7.6	+43.3	-5.1	-39.2	+39.4	+29.3	+29.4	+38.9	-43.2
Steps (reduced)		105 (15)	108 (18)	111 (21)	114 (24)	116 (26)	118 (28)	121 (31)	123 (33)	125 (35)	127 (37)	128 (38)

Intervals of 45EDT

Degrees	Cents	hekts	Approximate Ratios
0			1/1
1	42.266	28.889
2	84.531	57.778	21/20
3	126.797	86.667	14/13, 15/14, 16/15, 29/27
4	169.063	115.556	11/10
5	211.328	144.444	9/8
6	253.594	173.333	15/13
7	295.86	202.222	19/16
8	338.125	231.111	17/14
9	380.391	260	5/4
10	422.657	288.889	14/11
11	464.922	317.778	21/16, 17/13
12	507.188	336.667	4/3
13	549.454	375.556	11/8
14	591.719	304.444	7/5
15	633.985	433.333	13/9
16	676.251	462.222	40/27. 189/128
17	718.516	491.111	50/33
18	760.782	520	14/9
19	803.048	548.889	8/5
20	845.313	577.778	13/8
21	887.579	606.667	5/3, 17/11
22	929.845	635.556	12/7
23	972.110	664.444	7/4
24	1014.376	693.333	9/5, 33/17
25	1056.642	722.222	24/13
26	1098.907	751.111	17/9
27	1141.173	780	27/14
28	1183.439	808.889	99/50
29	1225.704	837.778	81/40, 128/63
30	1267.97	866.667	27/13
31	1310.236	895.556	32/15
32	1352.501	924.444	24/11
33	1394.767	953.333	9/4 (9/8 plus an octave)
34	1437.033	982.222	16/7, 39/17
35	1479.298	1011.111	33/14
36	1521.564	1040	12/5 (6/5 plus an octave)
37	1563.83	1068.889	42/17
38	1606.095	1097.778	48/19
39	1648.361	1126.667	13/5 (13/10 plus an octave)
40	1690.627	1155.556	8/3
41	1732.892	1184.444	30/11
42	1775.158	1213.333	39/14, 14/5 (7/5 plus an octave), 45/16, 81/29
43	1817.424	1242.222	20/7
44	1859.689	1271.111
45	1901.955	1300	3/1