79edt

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79edt

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Prime factorization	79 (prime)
Step size	24.0754¢
Octave	50\79edt (1203.77¢)
Consistency limit	10
Distinct consistency limit	8

Division of the third harmonic into 79 equal parts (79EDT) is related to 50 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 3.7690 cents stretched and the step size is about 24.0754 cents. It is consistent to the 10-integer-limit.

Additionally, it is an 18-strong consistent circle of the interval 17/15.

Lookalikes: 50edo, 116ed5, 129ed6, 140ed7, 29edf

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	24.1
2	48.2	35/34, 36/35, 37/36, 38/37
3	72.2	25/24
4	96.3	18/17, 19/18, 37/35
5	120.4	15/14
6	144.5	37/34, 38/35
7	168.5
8	192.6	19/17
9	216.7	17/15
10	240.8	31/27
11	264.8	7/6
12	288.9	13/11
13	313	6/5
14	337.1	17/14
15	361.1	37/30
16	385.2	5/4
17	409.3	19/15
18	433.4	9/7
19	457.4
20	481.5	29/22, 37/28
21	505.6
22	529.7	19/14, 34/25
23	553.7
24	577.8
25	601.9	17/12
26	626	33/23
27	650	35/24
28	674.1	28/19, 31/21
29	698.2
30	722.3	38/25
31	746.3	37/24
32	770.4	25/16
33	794.5	19/12
34	818.6
35	842.6
36	866.7	28/17
37	890.8
38	914.9	39/23
39	938.9	31/18
40	963
41	987.1	23/13
42	1011.2
43	1035.2
44	1059.3	35/19
45	1083.4	28/15
46	1107.5	36/19
47	1131.5
48	1155.6	37/19
49	1179.7
50	1203.8
51	1227.8
52	1251.9	35/17
53	1276	23/11
54	1300.1	36/17
55	1324.1
56	1348.2	37/17
57	1372.3
58	1396.4
59	1420.4
60	1444.5
61	1468.6	7/3
62	1492.7
63	1516.7	12/5
64	1540.8
65	1564.9	37/15
66	1589	5/2
67	1613.1	33/13
68	1637.1	18/7
69	1661.2
70	1685.3	37/14
71	1709.4
72	1733.4
73	1757.5
74	1781.6	14/5
75	1805.7	17/6
76	1829.7
77	1853.8	35/12
78	1877.9
79	1902	3/1

Harmonics

79edt's representation of most primes is rather mediocre, however it has the property that many prime harmonics lie close to a quarter of the way or halfway between its steps, which is important in that 316edt, which quadruples it, is one of the strongest systems less than 1000 notes in the no-twos 19-limit, and among them has the best representation of primes beyond 19.

Approximation of prime harmonics in 79edt

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	+3.8	+0.0	+6.4	+1.7	-10.4	-10.7	+6.4	+6.5	-11.3
	Relative (%)	+15.7	+0.0	+26.7	+7.2	-43.0	-44.3	+26.7	+26.9	-47.0
Steps (reduced)		50 (50)	79 (0)	116 (37)	140 (61)	172 (14)	184 (26)	204 (46)	212 (54)	225 (67)

Approximation of odd harmonics in 79edt

Harmonic		25	27	29	31	33	35	37	39	41	43	45
Error	Absolute (¢)	-11.2	+0.0	-3.3	+1.6	-10.4	+8.2	+8.3	-10.7	-0.9	-11.2	+6.4
	Relative (%)	-46.6	+0.0	-13.9	+6.6	-43.0	+33.9	+34.3	-44.3	-3.9	-46.4	+26.7
Steps (reduced)		231 (73)	237 (0)	242 (5)	247 (10)	251 (14)	256 (19)	260 (23)	263 (26)	267 (30)	270 (33)	274 (37)