73edt

← 72edt

73edt

74edt →

Prime factorization	73 (prime)
Step size	26.0542¢
Octave	46\73edt (1198.49¢)
Consistency limit	17
Distinct consistency limit	10

Division of the third harmonic into 73 equal parts (73EDT) is related to 46 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 1.5078 cents compressed and the step size is about 26.0542 cents. It is consistent to the 18-integer-limit. In comparison, 46edo is only consistent up to the 14-integer-limit.

Interval

degree	cents value	hekts	corresponding JI intervals	comments
0			exact 1/1
1	26.0542	17.8082	66/65
2	52.1084	35.6164	34/33
3	78.1625	53.4247	68/65
4	104.2167	71.2329	17/16
5	130.2709	89.0411	55/51
6	156.3251	106.8493	23/21
7	182.3792	124.6575	10/9
8	208.4334	142.46575	44/39	pseudo-9/8
9	234.4876	160.274	63/55	pseudo-8/7
10	260.5418	178.0822		pseudo-7/6
11	286.596	195.8904	13/11
12	312.6501	213.6986		pseudo-6/5
13	338.7043	231.50685	17/14
14	364.7585	249.3151	100/81
15	390.8127	267.1233		pseudo-5/4
16	416.8668	284.9315	14/11
17	442.921	302.7397	31/24
18	468.9752	320.54795	21/16
19	495.0294	338.3562		pseudo-4/3
20	521.0836	356.1644	27/20
21	547.1377	373.9726	11/8
22	573.1919	391.7808	39/28	pseudo-7/5
23	599.2461	409.589	140/99
24	625.3003	427.3973	56/39	pseudo-10/7
25	651.3545	445.2055	16/11
26	677.4086	463.0137	40/27
27	703.4628	480.8219		pseudo-3/2
28	729.517	498.6301	32/21
29	755.5712	516.4384	48/31
30	781.6253	534.2466	(11/7)
31	807.6795	552.0548		pseudo-8/5
32	833.7337	569.863	34/21
33	859.7879	587.6712	28/17
34	885.8421	605.47945		pseudo-5/3
35	911.8962	623.2877	22/13
36	937.9504	641.0959		pseudo-12/7
37	964.0046	658.9041	110/63	pseudo-7/4
38	990.0588	676.7123	39/22	pseudo-16/9
39	1016.1129	694.52055	9/5
40	1042.1671	712.3288	42/23
41	1068.2213	730.137	102/55
42	1094.2755	747.9452	17/8
43	1120.3297	765.7534	65/34
44	1146.3838	783.5616	64/33
45	1172.438	801.3699	63/32
46	1198.4922	819.1781		pseudo-octave
47	1224.5464	836.9863	81/40
48	1250.6005	854.7945	35/17
49	1276.6547	872.6027	23/11
50	1302.7089	890.411	17/8
51	1328.7631	908.2192	28/13
52	1354.8173	926.0274	24/11
53	1380.8714	943.8356	20/9
54	1406.9256	961.6438	9/4
55	1432.9798	979.45205	16/7
56	1459.034	997.2603		pseudo-7/3
57	1485.0882	1015.0685	26/11
58	1511.1423	1032.8767		pseudo-12/5
59	1537.1965	1050.6849	17/7
60	1563.2507	1068.49315	42/17
61	1589.3049	1086.3014		pseudo-5/2
62	1615.359	1104.1096	28/11
63	1641.4132	1121.9178		pseudo-18/7
64	1667.4674	1139.726	21/8
65	1693.5216	1157.53425	8/3
66	1719.5758	1175.3425	27/10
67	1745.6299	1193.1507	11/4
68	1771.6841	1210.9589	39/14
69	1797.7383	1228.7671	48/17
70	1823.7925	1246.5753	112/39
71	1849.8466	1264.3836	99/34
72	1875.9008	1282.1918	65/22
73	1901.9550	1300	exact 3/1	just perfect fifth plus an octave

Related regular temperaments

73edt is also related to the microtemperament which tempers out |73 -153 73> in the 5-limit, which is supported by 46, 783, 829, 1612, 2395, 3128, and 4007 EDOs.

5-limit 46&783

Comma: |73 -153 73>

POTE generator: ~|21 -44 21> = 26.0543

Mapping: [<1 0 -1|, <0 73 153|]

EDOs: 46, 737, 783, 829, 875, 1612, 2395, 2441, 3128, 4007, 5573, 6402

7-limit 46&783

Commas: 4375/4374, |-92 20 3 19>

POTE generator: ~335544320/330812181 = 26.0533

Mapping: [<1 0 -1 5|, <0 73 153 -101|]

EDOs: 46, 691, 737, 783, 829, 1520, 1612

11-limit 46&783

Commas: 4375/4374, 806736/805255, 2097152/2096325

POTE generator: ~3072/3025 = 26.0542

Mapping: [<1 0 -1 5 6|, <0 73 153 -101 -117|]

EDOs: 46, 737, 783, 829, 875