84edt

← 83edt

84edt

85edt →

Prime factorization	22 × 3 × 7
Step size	22.6423¢
Octave	53\84edt (1200.04¢) (convergent)
Consistency limit	10
Distinct consistency limit	10

Division of the third harmonic into 84 equal parts (84EDT) is practically identical to 53 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 0.0430 cents stretched and the step size is about 22.6423 cents.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	22.642
2	45.285	37/36, 38/37, 39/38, 40/39, 41/40
3	67.927	25/24, 26/25, 27/26
4	90.569	19/18, 20/19, 39/37
5	113.212	16/15
6	135.854	13/12, 27/25, 40/37
7	158.496	23/21, 34/31
8	181.139	10/9
9	203.781	9/8
10	226.423	33/29, 41/36
11	249.066	15/13, 37/32
12	271.708	41/35
13	294.35	32/27
14	316.993	6/5
15	339.635	28/23, 39/32
16	362.277	16/13, 37/30
17	384.919	5/4
18	407.562	19/15
19	430.204	32/25, 41/32
20	452.846	13/10
21	475.489	25/19, 29/22
22	498.131	4/3
23	520.773	23/17, 27/20
24	543.416	26/19, 37/27, 41/30
25	566.058	18/13, 25/18
26	588.7	38/27
27	611.343	27/19, 37/26
28	633.985	13/9, 36/25
29	656.627	19/13
30	679.27	34/23, 37/25, 40/27
31	701.912	3/2
32	724.554	35/23, 38/25, 41/27
33	747.197	20/13, 37/24
34	769.839	25/16, 39/25
35	792.481	30/19
36	815.124	8/5
37	837.766	13/8
38	860.408	23/14
39	883.051	5/3
40	905.693	27/16
41	928.335	41/24
42	950.978	26/15
43	973.62
44	996.262	16/9
45	1018.904	9/5
46	1041.547	31/17
47	1064.189	24/13, 37/20
48	1086.831	15/8
49	1109.474	19/10
50	1132.116	25/13
51	1154.758	37/19, 39/20
52	1177.401
53	1200.043	2/1
54	1222.685
55	1245.328	37/18, 39/19, 41/20
56	1267.97	25/12, 27/13
57	1290.612	19/9, 40/19
58	1313.255	32/15
59	1335.897	13/6
60	1358.539
61	1381.182	20/9
62	1403.824	9/4
63	1426.466	41/18
64	1449.109	30/13, 37/16
65	1471.751
66	1494.393
67	1517.036	12/5
68	1539.678	39/16
69	1562.32	32/13, 37/15
70	1584.963	5/2
71	1607.605	38/15
72	1630.247	41/16
73	1652.889	13/5
74	1675.532	29/11
75	1698.174	8/3
76	1720.816	27/10
77	1743.459	41/15
78	1766.101	25/9, 36/13
79	1788.743
80	1811.386	37/13
81	1834.028	26/9
82	1856.67	38/13
83	1879.313
84	1901.955	3/1

Harmonics

Approximation of harmonics in 84edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.04	+0.00	+0.09	-1.31	+0.04	+4.88	+0.13	+0.00	-1.27	-7.77	+0.09
	Relative (%)	+0.2	+0.0	+0.4	-5.8	+0.2	+21.6	+0.6	+0.0	-5.6	-34.3	+0.4
Steps (reduced)		53 (53)	84 (0)	106 (22)	123 (39)	137 (53)	149 (65)	159 (75)	168 (0)	176 (8)	183 (15)	190 (22)

Approximation of harmonics in 84edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+4.92	-1.31	+0.17	+8.43	+0.04	-2.99	-1.22	+4.88	-7.73	+5.88
	Relative (%)	-11.6	+21.7	-5.8	+0.8	+37.2	+0.2	-13.2	-5.4	+21.6	-34.1	+26.0
Steps (reduced)		196 (28)	202 (34)	207 (39)	212 (44)	217 (49)	221 (53)	225 (57)	229 (61)	233 (65)	236 (68)	240 (72)