84edt
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Prime factorization
22 × 3 × 7
Step size
22.6423¢
Octave
53\84edt (1200.04¢)
(convergent)
Consistency limit
10
Distinct consistency limit
10
← 83edt | 84edt | 85edt → |
(convergent)
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
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) |
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) |