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	33.2
2	66.3	26/25
3	99.5
4	132.7	40/37, 41/38
5	165.9	11/10
6	199	28/25, 37/33
7	232.2
8	265.4
9	298.5
10	331.7	23/19, 40/33
11	364.9	21/17, 37/30
12	398	39/31
13	431.2
14	464.4	17/13
15	497.6	4/3
16	530.7	19/14, 34/25
17	563.9
18	597.1	41/29
19	630.2
20	663.4	22/15
21	696.6
22	729.7	29/19, 35/23
23	762.9
24	796.1
25	829.3	21/13
26	862.4	23/14, 28/17
27	895.6
28	928.8
29	961.9
30	995.1	16/9
31	1028.3	38/21
32	1061.5
33	1094.6
34	1127.8
35	1161	41/21
36	1194.1
37	1227.3
38	1260.5	29/14
39	1293.6
40	1326.8	28/13
41	1360
42	1393.2	38/17
43	1426.3
44	1459.5
45	1492.7
46	1525.8	41/17
47	1559
48	1592.2
49	1625.3
50	1658.5
51	1691.7
52	1724.9
53	1758
54	1791.2	31/11
55	1824.4
56	1857.5	38/13, 41/14
57	1890.7
58	1923.9
59	1957.1	31/10
60	1990.2	41/13
61	2023.4
62	2056.6	23/7
63	2089.7
64	2122.9
65	2156.1
66	2189.2	39/11
67	2222.4
68	2255.6
69	2288.8	15/4
70	2321.9
71	2355.1	39/10
72	2388.3
73	2421.4
74	2454.6	33/8
75	2487.8
76	2521
77	2554.1
78	2587.3
79	2620.5
80	2653.6	37/8
81	2686.8
82	2720
83	2753.1
84	2786.3	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