84edt

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← 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)