65edt

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← 64edt65edt66edt →
Prime factorization 5 × 13
Step size 29.2608¢ 
Octave 41\65edt (1199.69¢)
(convergent)
Consistency limit 16
Distinct consistency limit 10

Division of the third harmonic into 65 equal parts (65EDT) is almost identical to 41 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 0.3053 cents compressed and the step size is about 29.2608 cents. It is consistent to the 16-integer-limit.

Harmonics

Approximation of harmonics in 65edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Error Absolute (¢) -0.31 +0.00 -0.61 -6.53 -0.31 -3.83 -0.92 +0.00 -6.84 +3.72 -0.61 +7.12 -4.13 -6.53 -1.22
Relative (%) -1.0 +0.0 -2.1 -22.3 -1.0 -13.1 -3.1 +0.0 -23.4 +12.7 -2.1 +24.3 -14.1 -22.3 -4.2
Steps
(reduced)
41
(41)
65
(0)
82
(17)
95
(30)
106
(41)
115
(50)
123
(58)
130
(0)
136
(6)
142
(12)
147
(17)
152
(22)
156
(26)
160
(30)
164
(34)
Degree Cent value Hekts Corresponding
JI intervals
Comments
0 exact 1/1
1 29.2608 20 57/56, 56/55
2 58.5217 40 30/29
3 87.7825 60 21/20, 20/19
4 117.0434 80 15/14
5 146.3042 100 49/45, 12/11
6 175.5651 120 21/19, 87/80, 72/65 pseudo-10/9
7 204.8259 140 9/8
8 234.0868 160 8/7
9 263.3476 180 7/6
10 292.6085 200 45/38, 32/27
11 321.8693 220 65/54 pseudo-6/5
12 351.1302 240 11/9, 27/22
13 380.391 260 56/45, 81/65 pseudo-5/4
14 409.6518 280 19/15
15 438.9127 300 9/7
16 468.1735 320 21/16
17 497.4344 340 4/3
18 526.6952 360 19/14
19 555.9561 380 40/29
20 585.2169 400 7/5
21 614.4778 420 10/7
22 643.7386 440 29/20
23 672.9995 460 28/19
24 702.2603 480 3/2
25 731.5212 500 32/21
26 760.782 520 45/29
27 790.0428 540 30/19
28 819.3037 560 45/28 pseudo-8/5
29 848.5645 580 18/11
30 877.8254 600 108/65 pseudo-5/3
31 907.0862 620 27/16
32 936.3471 640 12/7
33 965.6079 660 7/4
34 994.8688 680 16/9
35 1024.1296 700 65/36 pseudo-9/5
36 1053.3905 720 11/6
37 1082.6513 740 28/15
38 1111.9122 760 19/10
39 1141.173 780 29/15
40 1170.4338 800 55/28
41 1199.6947 820 2/1
42 1228.9555 840 57/28
43 1258.2164 860 60/29
44 1287.4772 880 21/10
45 1316.7381 900 15/7
46 1345.9989 920 87/40
47 1375.2598 940 42/19
48 1404.5206 960 9/4
49 1433.7815 980 16/7
50 1463.0423 1000 7/3
51 1492.3032 1020 45/19
52 1521.564 1040 65/27 pseudo-12/5
53 1550.8248 1060 22/9, 27/11
54 1580.0857 1080 162/65 pseudo-5/2
55 1609.3465 1100 38/15
56 1638.6074 1120 18/7
57 1667.8682 1140 21/8
58 1697.1291 1160 8/3
59 1726.3899 1180 19/7
60 1755.6508 1200 11/4
61 1784.9116 1220 14/5
62 1814.1725 1240 20/7
63 1843.4333 1260 29/10
64 1872.6942 1280 56/19
65 1901.9550 1300 exact 3/1 just perfect fifth plus an octave