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.

Theory

This tuning tempers out 99/98 and 121/120 in the 11-limit; and 120/119 in the 17-limit.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	22.6	15.5
2	45.3	31	37/36, 38/37, 39/38, 40/39, 41/40
3	67.9	46.4	25/24, 26/25, 27/26
4	90.6	61.9	19/18, 20/19, 39/37
5	113.2	77.4	16/15
6	135.9	92.9	13/12, 27/25, 40/37
7	158.5	108.3	23/21, 34/31
8	181.1	123.8	10/9
9	203.8	139.3	9/8
10	226.4	154.8	33/29, 41/36
11	249.1	170.2	15/13, 37/32
12	271.7	185.7	41/35
13	294.4	201.2	32/27
14	317	216.7	6/5
15	339.6	232.1	28/23, 39/32
16	362.3	247.6	16/13, 37/30
17	384.9	263.1	5/4
18	407.6	278.6	19/15
19	430.2	294	32/25, 41/32
20	452.8	309.5	13/10
21	475.5	325	25/19, 29/22
22	498.1	340.5	4/3
23	520.8	356	23/17, 27/20
24	543.4	371.4	26/19, 37/27, 41/30
25	566.1	386.9	18/13, 25/18
26	588.7	402.4	38/27
27	611.3	417.9	27/19, 37/26
28	634	433.3	13/9, 36/25
29	656.6	448.8	19/13
30	679.3	464.3	34/23, 37/25, 40/27
31	701.9	479.8	3/2
32	724.6	495.2	35/23, 38/25, 41/27
33	747.2	510.7	20/13, 37/24
34	769.8	526.2	25/16, 39/25
35	792.5	541.7	30/19
36	815.1	557.1	8/5
37	837.8	572.6	13/8
38	860.4	588.1	23/14
39	883.1	603.6	5/3
40	905.7	619	27/16
41	928.3	634.5	41/24
42	951	650	26/15
43	973.6	665.5
44	996.3	681	16/9
45	1018.9	696.4	9/5
46	1041.5	711.9	31/17
47	1064.2	727.4	24/13, 37/20
48	1086.8	742.9	15/8
49	1109.5	758.3	19/10
50	1132.1	773.8	25/13
51	1154.8	789.3	37/19, 39/20
52	1177.4	804.8
53	1200	820.2	2/1
54	1222.7	835.7
55	1245.3	851.2	37/18, 39/19, 41/20
56	1268	866.7	25/12, 27/13
57	1290.6	882.1	19/9, 40/19
58	1313.3	897.6	32/15
59	1335.9	913.1	13/6
60	1358.5	928.6
61	1381.2	944	20/9
62	1403.8	959.5	9/4
63	1426.5	975	41/18
64	1449.1	990.5	30/13, 37/16
65	1471.8	1006
66	1494.4	1021.4
67	1517	1036.9	12/5
68	1539.7	1052.4	39/16
69	1562.3	1067.9	32/13, 37/15
70	1585	1083.3	5/2
71	1607.6	1098.8	38/15
72	1630.2	1114.3	41/16
73	1652.9	1129.8	13/5
74	1675.5	1145.2	29/11
75	1698.2	1160.7	8/3
76	1720.8	1176.2	27/10
77	1743.5	1191.7	41/15
78	1766.1	1207.1	25/9, 36/13
79	1788.7	1222.6
80	1811.4	1238.1	37/13
81	1834	1253.6	26/9
82	1856.7	1269	38/13
83	1879.3	1284.5
84	1902	1300	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)