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	22.6
2	45.3	37/36, 38/37, 39/38, 40/39, 41/40
3	67.9	25/24, 26/25, 27/26
4	90.6	19/18, 20/19, 39/37
5	113.2	16/15
6	135.9	13/12, 27/25, 40/37
7	158.5	23/21, 34/31
8	181.1	10/9
9	203.8	9/8
10	226.4	33/29, 41/36
11	249.1	15/13, 37/32
12	271.7	41/35
13	294.4	32/27
14	317	6/5
15	339.6	28/23, 39/32
16	362.3	16/13, 37/30
17	384.9	5/4
18	407.6	19/15
19	430.2	32/25, 41/32
20	452.8	13/10
21	475.5	25/19, 29/22
22	498.1	4/3
23	520.8	23/17, 27/20
24	543.4	26/19, 37/27, 41/30
25	566.1	18/13, 25/18
26	588.7	38/27
27	611.3	27/19, 37/26
28	634	13/9, 36/25
29	656.6	19/13
30	679.3	34/23, 37/25, 40/27
31	701.9	3/2
32	724.6	35/23, 38/25, 41/27
33	747.2	20/13, 37/24
34	769.8	25/16, 39/25
35	792.5	30/19
36	815.1	8/5
37	837.8	13/8
38	860.4	23/14
39	883.1	5/3
40	905.7	27/16
41	928.3	41/24
42	951	26/15
43	973.6
44	996.3	16/9
45	1018.9	9/5
46	1041.5	31/17
47	1064.2	24/13, 37/20
48	1086.8	15/8
49	1109.5	19/10
50	1132.1	25/13
51	1154.8	37/19, 39/20
52	1177.4
53	1200	2/1
54	1222.7
55	1245.3	37/18, 39/19, 41/20
56	1268	25/12, 27/13
57	1290.6	19/9, 40/19
58	1313.3	32/15
59	1335.9	13/6
60	1358.5
61	1381.2	20/9
62	1403.8	9/4
63	1426.5	41/18
64	1449.1	30/13, 37/16
65	1471.8
66	1494.4
67	1517	12/5
68	1539.7	39/16
69	1562.3	32/13, 37/15
70	1585	5/2
71	1607.6	38/15
72	1630.2	41/16
73	1652.9	13/5
74	1675.5	29/11
75	1698.2	8/3
76	1720.8	27/10
77	1743.5	41/15
78	1766.1	25/9, 36/13
79	1788.7
80	1811.4	37/13
81	1834	26/9
82	1856.7	38/13
83	1879.3
84	1902	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)