84ed5

← 83ed5

84ed5

85ed5 →

Prime factorization	22 × 3 × 7
Step size	33.1704¢
Octave	36\84ed5 (1194.13¢) (→3\7ed5)
Twelfth	57\84ed5 (1890.71¢) (→19\28ed5)
Consistency limit	4
Distinct consistency limit	4

Division of the 5th harmonic into 84 equal parts (84ed5) is related to 36edo but the 5/1 rather than the 2/1 being just. The octave is compressed (about 5.8656 cents) and the step size is about 33.1704 cents.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	33.17
2	66.341	26/25
3	99.511
4	132.682	40/37, 41/38
5	165.852	11/10
6	199.022	28/25, 37/33
7	232.193
8	265.363
9	298.534
10	331.704	23/19, 40/33
11	364.874	21/17, 37/30
12	398.045	39/31
13	431.215
14	464.386	17/13
15	497.556	4/3
16	530.726	19/14, 34/25
17	563.897
18	597.067	41/29
19	630.238
20	663.408	22/15
21	696.578
22	729.749	29/19, 35/23
23	762.919
24	796.09
25	829.26	21/13
26	862.43	23/14, 28/17
27	895.601
28	928.771
29	961.942
30	995.112	16/9
31	1028.282	38/21
32	1061.453
33	1094.623
34	1127.794
35	1160.964	41/21
36	1194.134
37	1227.305
38	1260.475	29/14
39	1293.646
40	1326.816	28/13
41	1359.986
42	1393.157	38/17
43	1426.327
44	1459.498
45	1492.668
46	1525.838	41/17
47	1559.009
48	1592.179
49	1625.35
50	1658.52
51	1691.69
52	1724.861
53	1758.031
54	1791.202	31/11
55	1824.372
56	1857.542	38/13, 41/14
57	1890.713
58	1923.883
59	1957.054	31/10
60	1990.224	41/13
61	2023.394
62	2056.565	23/7
63	2089.735
64	2122.906
65	2156.076
66	2189.246	39/11
67	2222.417
68	2255.587
69	2288.758	15/4
70	2321.928
71	2355.098	39/10
72	2388.269
73	2421.439
74	2454.61	33/8
75	2487.78
76	2520.951
77	2554.121
78	2587.291
79	2620.462
80	2653.632	37/8
81	2686.803
82	2719.973
83	2753.143
84	2786.314	5/1

Harmonics

Approximation of harmonics in 84ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.9	-11.2	-11.7	+0.0	+16.1	+14.6	+15.6	+10.7	-5.9	-5.0	+10.2
	Relative (%)	-17.7	-33.9	-35.4	+0.0	+48.4	+43.9	+47.0	+32.2	-17.7	-15.1	+30.7
Steps (reduced)		36 (36)	57 (57)	72 (72)	84 (0)	94 (10)	102 (18)	109 (25)	115 (31)	120 (36)	125 (41)	130 (46)

Approximation of harmonics in 84ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.3	+8.7	-11.2	+9.7	+4.3	+4.8	+10.7	-11.7	+3.3	-10.9	+11.7
	Relative (%)	+13.0	+26.2	-33.9	+29.3	+12.9	+14.5	+32.3	-35.4	+10.0	-32.8	+35.2
Steps (reduced)		134 (50)	138 (54)	141 (57)	145 (61)	148 (64)	151 (67)	154 (70)	156 (72)	159 (75)	161 (77)	164 (80)

Music

• Not From This World by Francium