71zpi
71 zeta peak index (abbreviated 71zpi), is the equal-step tuning system obtained from the 71st peak of the Riemann zeta function.
Tuning | Strength | Closest EDO | Integer limit | ||||||
---|---|---|---|---|---|---|---|---|---|
ZPI | Steps per octave | Step size (cents) | Height | Integral | Gap | EDO | Octave (cents) | Consistent | Distinct |
71zpi | 20.2248393119540 | 59.3329806724710 | 3.531097 | 0.613581 | 12.986080 | 20edo | 1186.65961344942 | 6 | 6 |
Theory
71zpi marks the most prominent zeta peak index in the vicinity of 20edo. While 70zpi is the nearest peak to 20edo and closely competes with 71zpi in terms of strength, 71zpi remains superior across all measures of strength. 71zpi may also be viewed as a tritave compression of 32edt, a no-2s zeta peak EDT (consistent in the no-2s 19-integer-limit), but with less extreme stretch than the no-2s peak at 59.271105 cents.
71zpi features a good 3:5:9:11:14:15:16:19:25:26:33 chord, which differs a lot from the harmonic characteristics of 20edo.
The nearest zeta peaks to 71zpi that surpass its strength are 65zpi and 75zpi.
71zpi is distinguished by its extensive EDO-deviation and substantial zeta strength, qualifying it as a strong candidate for no-octave tuning systems. It is noteworthy that only 19zpi exhibits both a greater octave error and stronger zeta height and integral than 71zpi, although 71zpi still has a more pronounced zeta gap. Other notable zeta peak indices in this category include 61zpi, 84zpi, 110zpi, 137zpi, 151zpi, 222zpi, and 273zpi, each demonstrating characteristics that make them suitable for similar applications.
Harmonic series
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -13.3 | -3.3 | -26.7 | +2.3 | -16.6 | +13.2 | +19.3 | -6.6 | -11.0 | +2.0 | +29.4 | +9.4 | -0.2 | -1.0 | +6.0 |
Relative (%) | -22.5 | -5.6 | -45.0 | +3.9 | -28.0 | +22.2 | +32.5 | -11.1 | -18.5 | +3.4 | +49.5 | +15.9 | -0.3 | -1.6 | +10.1 | |
Steps | 20 | 32 | 40 | 47 | 52 | 57 | 61 | 64 | 67 | 70 | 73 | 75 | 77 | 79 | 81 |
Harmonic | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +19.7 | -19.9 | +5.1 | -24.3 | +9.9 | -11.3 | -29.0 | +16.0 | +4.7 | -3.9 | -9.9 | -13.5 | -14.9 | -14.3 | -11.7 | -7.4 | -1.3 |
Relative (%) | +33.2 | -33.6 | +8.6 | -41.0 | +16.6 | -19.1 | -48.8 | +27.0 | +7.9 | -6.6 | -16.7 | -22.8 | -25.2 | -24.1 | -19.8 | -12.4 | -2.2 | |
Steps | 83 | 84 | 86 | 87 | 89 | 90 | 91 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102 |
Intervals
There are multiple ways to approach notation. The simplest method is to use the notations from 20edo. However, this approach will not preserve octave compression when the audio is rendered by notation software. If maintaining accurate step compression in notation software is important, consider using the ups and downs notation from 182edo at every 9-degree step. With this method, the tonal difference will be less than 1 cent up to the 86th harmonic.
JI ratios are comprised of 33-integer-limit ratios, and are stylized as follows to indicate their accuracy:
|
Whole tone = 30 steps Limma = 16 steps Apotome = 14 steps | |||
Degree | Cents | Ratios | Ups and Downs Notation | Step |
---|---|---|---|---|
0 | 0.000 | P1 | 0 | |
1 | 59.333 | 33/32, 32/31, 31/30, 30/29, 29/28, 28/27, 27/26, 26/25, 25/24, 24/23, 23/22, 22/21, 21/20, 20/19 | v7m2 | 9 |
2 | 118.666 | 19/18, 18/17, 17/16, 33/31, 16/15, 31/29, 15/14, 29/27, 14/13, 27/25, 13/12, 25/23 | ^^m2 | 18 |
3 | 177.999 | 12/11, 23/21, 11/10, 32/29, 21/19, 31/28, 10/9, 29/26, 19/17, 28/25, 9/8 | vvvM2 | 27 |
4 | 237.332 | 26/23, 17/15, 25/22, 33/29, 8/7, 31/27, 23/20, 15/13, 22/19, 29/25, 7/6 | ^6M2 | 36 |
5 | 296.665 | 27/23, 20/17, 33/28, 13/11, 32/27, 19/16, 25/21, 31/26, 6/5 | vm3 | 45 |
6 | 355.998 | 29/24, 23/19, 17/14, 28/23, 11/9, 27/22, 16/13, 21/17, 26/21, 31/25 | v6M3 | 54 |
7 | 415.331 | 5/4, 29/23, 24/19, 19/15, 33/26, 14/11, 23/18, 32/25, 9/7, 31/24 | ^^^M3 | 63 |
8 | 474.664 | 22/17, 13/10, 30/23, 17/13, 21/16, 25/19, 29/22, 33/25, 4/3 | v44 | 72 |
9 | 533.997 | 31/23, 27/20, 23/17, 19/14, 15/11, 26/19, 11/8, 29/21, 18/13 | ^54 | 81 |
10 | 593.330 | 25/18, 32/23, 7/5, 31/22, 24/17, 17/12, 27/19, 10/7 | A4 | 90 |
11 | 652.663 | 33/23, 23/16, 13/9, 29/20, 16/11, 19/13, 22/15, 25/17, 28/19, 31/21 | ~5 | 99 |
12 | 711.996 | 3/2, 32/21, 29/19, 26/17, 23/15 | ^^5 | 108 |
13 | 771.329 | 20/13, 17/11, 31/20, 14/9, 25/16, 11/7, 30/19, 19/12, 27/17 | v5m6 | 117 |
14 | 830.662 | 8/5, 29/18, 21/13, 13/8, 31/19, 18/11, 23/14 | ^4m6 | 126 |
15 | 889.995 | 28/17, 33/20, 5/3, 32/19, 27/16, 22/13, 17/10 | vM6 | 135 |
16 | 949.328 | 29/17, 12/7, 31/18, 19/11, 26/15, 33/19, 7/4 | v6A6, ^6d7 | 144 |
17 | 1008.661 | 30/17, 23/13, 16/9, 25/14, 9/5, 29/16, 20/11 | ^m7 | 153 |
18 | 1067.994 | 31/17, 11/6, 24/13, 13/7, 28/15, 15/8, 32/17 | v4M7 | 162 |
19 | 1127.327 | 17/9, 19/10, 21/11, 23/12, 25/13, 27/14, 29/15, 31/16, 33/17 | ^5M7 | 171 |
20 | 1186.660 | 2/1 | vv1 +1 oct | 180 |
21 | 1245.993 | 33/16, 31/15, 29/14, 27/13, 25/12 | ^71 +1 oct | 189 |
22 | 1305.326 | 23/11, 21/10, 19/9, 17/8, 32/15, 15/7, 28/13 | m2 +1 oct | 198 |
23 | 1364.659 | 13/6, 24/11, 11/5, 31/14, 20/9, 29/13 | v5M2 +1 oct | 207 |
24 | 1423.992 | 9/4, 25/11, 16/7, 23/10, 30/13 | ^4M2 +1 oct | 216 |
25 | 1483.325 | 7/3, 33/14, 26/11, 19/8, 31/13 | vvvm3 +1 oct | 225 |
26 | 1542.657 | 12/5, 29/12, 17/7, 22/9, 27/11, 32/13 | ^6m3 +1 oct | 234 |
27 | 1601.990 | 5/2, 33/13, 28/11, 23/9 | ^M3 +1 oct | 243 |
28 | 1661.323 | 18/7, 31/12, 13/5, 21/8, 29/11 | v64 +1 oct | 252 |
29 | 1720.656 | 8/3, 27/10, 19/7, 30/11 | ^^^4 +1 oct | 261 |
30 | 1779.989 | 11/4, 25/9, 14/5, 31/11, 17/6 | vvA4 +1 oct | 270 |
31 | 1839.322 | 20/7, 23/8, 26/9, 29/10, 32/11 | ^5d5 +1 oct | 279 |
32 | 1898.655 | 3/1 | P5 +1 oct | 288 |
33 | 1957.988 | 31/10, 28/9, 25/8, 22/7 | v7m6 +1 oct | 297 |
34 | 2017.321 | 19/6, 16/5, 29/9, 13/4 | ^^m6 +1 oct | 306 |
35 | 2076.654 | 23/7, 33/10, 10/3, 27/8 | vvvM6 +1 oct | 315 |
36 | 2135.987 | 17/5, 24/7, 31/9 | ^6M6 +1 oct | 324 |
37 | 2195.320 | 7/2, 32/9, 25/7, 18/5 | vm7 +1 oct | 333 |
38 | 2254.653 | 29/8, 11/3, 26/7 | v6M7 +1 oct | 342 |
39 | 2313.986 | 15/4, 19/5, 23/6, 27/7 | ^^^M7 +1 oct | 351 |
40 | 2373.319 | 31/8, 4/1 | v41 +2 oct | 360 |
41 | 2432.652 | 33/8, 29/7 | ^51 +2 oct | 369 |
42 | 2491.985 | 25/6, 21/5, 17/4, 30/7 | vvm2 +2 oct | 378 |
43 | 2551.318 | 13/3, 22/5, 31/7 | ~2 +2 oct | 387 |
44 | 2610.651 | 9/2, 32/7 | ^^M2 +2 oct | 396 |
45 | 2669.984 | 23/5, 14/3, 33/7, 19/4 | v5m3 +2 oct | 405 |
46 | 2729.317 | 24/5, 29/6 | ^4m3 +2 oct | 414 |
47 | 2788.650 | 5/1 | vM3 +2 oct | 423 |
48 | 2847.983 | 31/6, 26/5, 21/4 | v6A3 +2 oct, ^6d4 +2 oct | 432 |
49 | 2907.316 | 16/3, 27/5 | ^4 +2 oct | 441 |
50 | 2966.649 | 11/2, 28/5 | v4A4 +2 oct | 450 |
51 | 3025.982 | 17/3, 23/4, 29/5 | ^^^d5 +2 oct | 459 |
52 | 3085.315 | 6/1 | vv5 +2 oct | 468 |
53 | 3144.648 | 31/5, 25/4 | ^75 +2 oct | 477 |
54 | 3203.981 | 19/3, 32/5 | m6 +2 oct | 486 |
55 | 3263.314 | 13/2, 33/5, 20/3 | v5M6 +2 oct | 495 |
56 | 3322.647 | 27/4 | ^4M6 +2 oct | 504 |
57 | 3381.980 | 7/1 | vvvm7 +2 oct | 513 |
58 | 3441.313 | 29/4, 22/3 | ^6m7 +2 oct | 522 |
59 | 3500.646 | 15/2, 23/3 | ^M7 +2 oct | 531 |
60 | 3559.979 | 31/4 | v61 +3 oct | 540 |
61 | 3619.312 | 8/1 | ^^^1 +3 oct | 549 |
62 | 3678.645 | 33/4, 25/3, 17/2 | v4m2 +3 oct | 558 |
63 | 3737.978 | 26/3 | ^5m2 +3 oct | 567 |
64 | 3797.311 | 9/1 | M2 +3 oct | 576 |
65 | 3856.644 | 28/3 | v7m3 +3 oct | 585 |
66 | 3915.977 | 19/2, 29/3 | ^^m3 +3 oct | 594 |
67 | 3975.310 | 10/1 | vvvM3 +3 oct | 603 |
68 | 4034.643 | 31/3 | ^6M3 +3 oct | 612 |
69 | 4093.976 | 21/2, 32/3 | v4 +3 oct | 621 |
70 | 4153.309 | 11/1 | v6A4 +3 oct | 630 |
71 | 4212.642 | 23/2 | ^d5 +3 oct | 639 |
72 | 4271.975 | v45 +3 oct | 648 | |
73 | 4331.308 | 12/1 | ^55 +3 oct | 657 |
74 | 4390.641 | 25/2 | vvm6 +3 oct | 666 |
75 | 4449.974 | 13/1 | ~6 +3 oct | 675 |
76 | 4509.307 | 27/2 | ^^M6 +3 oct | 684 |
77 | 4568.640 | 14/1 | v5m7 +3 oct | 693 |
78 | 4627.972 | 29/2 | ^4m7 +3 oct | 702 |
79 | 4687.305 | 15/1 | vM7 +3 oct | 711 |
80 | 4746.638 | 31/2 | v6A7 +3 oct, ^6d1 +4 oct | 720 |
81 | 4805.971 | 16/1 | ^1 +4 oct | 729 |
82 | 4865.304 | 33/2 | v6m2 +4 oct | 738 |
83 | 4924.637 | 17/1 | ^^^m2 +4 oct | 747 |
84 | 4983.970 | 18/1 | vvM2 +4 oct | 756 |
85 | 5043.303 | ^7M2 +4 oct | 765 | |
86 | 5102.636 | 19/1 | m3 +4 oct | 774 |
87 | 5161.969 | 20/1 | v5M3 +4 oct | 783 |
88 | 5221.302 | ^4M3 +4 oct | 792 | |
89 | 5280.635 | 21/1 | vvv4 +4 oct | 801 |
90 | 5339.968 | 22/1 | ^64 +4 oct | 810 |
91 | 5399.301 | 23/1 | ^A4 +4 oct, vd5 +4 oct | 819 |
92 | 5458.634 | v65 +4 oct | 828 | |
93 | 5517.967 | 24/1 | ^^^5 +4 oct | 837 |
94 | 5577.300 | 25/1 | v4m6 +4 oct | 846 |
95 | 5636.633 | 26/1 | ^5m6 +4 oct | 855 |
96 | 5695.966 | 27/1 | M6 +4 oct | 864 |
97 | 5755.299 | 28/1 | v7m7 +4 oct | 873 |
98 | 5814.632 | 29/1 | ^^m7 +4 oct | 882 |
99 | 5873.965 | 30/1 | vvvM7 +4 oct | 891 |
100 | 5933.298 | 31/1 | ^6M7 +4 oct | 900 |
101 | 5992.631 | 32/1 | v1 +5 oct | 909 |
102 | 6051.964 | 33/1 | v6A1 +5 oct, ^6d2 +5 oct | 918 |
Approximation to JI
Interval mappings
The following tables show how 33-integer-limit intervals are represented in 71zpi. Prime harmonics are in bold; inconsistent intervals are in italics.
Ratio | Error (abs, ¢) | Error (rel, %) |
---|---|---|
14/1 | -0.186 | -0.314 |
11/5 | -0.346 | -0.583 |
17/8 | +0.370 | +0.624 |
31/22 | -0.388 | -0.654 |
21/13 | +0.408 | +0.688 |
25/19 | -0.451 | -0.759 |
26/3 | -0.595 | -1.003 |
30/29 | +0.641 | +1.081 |
31/10 | -0.733 | -1.236 |
32/9 | -0.770 | -1.297 |
15/14 | -0.777 | -1.309 |
19/16 | -0.848 | -1.429 |
15/1 | -0.963 | -1.623 |
23/12 | +1.007 | +1.698 |
27/10 | +1.105 | +1.863 |
33/14 | -1.123 | -1.892 |
25/16 | -1.299 | -2.189 |
33/1 | -1.309 | -2.206 |
29/28 | -1.418 | -2.390 |
27/22 | +1.451 | +2.445 |
31/2 | +1.603 | +2.702 |
29/2 | -1.605 | -2.705 |
29/6 | +1.695 | +2.857 |
31/28 | +1.789 | +3.016 |
31/27 | -1.839 | -3.099 |
11/1 | +1.991 | +3.355 |
14/11 | -2.177 | -3.669 |
23/4 | -2.292 | -3.864 |
5/1 | +2.336 | +3.938 |
14/5 | -2.523 | -4.252 |
32/27 | +2.530 | +4.264 |
31/30 | +2.566 | +4.325 |
33/26 | +2.586 | +4.358 |
25/11 | +2.682 | +4.520 |
26/9 | +2.705 | +4.559 |
19/5 | +2.787 | +4.697 |
24/7 | +2.858 | +4.817 |
26/15 | -2.931 | -4.940 |
15/11 | -2.954 | -4.979 |
14/3 | +3.113 | +5.247 |
19/11 | +3.133 | +5.280 |
31/29 | +3.208 | +5.406 |
3/1 | -3.300 | -5.561 |
27/2 | +3.442 | +5.800 |
16/13 | -3.474 | -5.856 |
29/22 | -3.595 | -6.060 |
28/27 | -3.628 | -6.115 |
16/5 | +3.635 | +6.127 |
33/5 | -3.645 | -6.144 |
24/17 | -3.670 | -6.185 |
13/7 | -3.708 | -6.250 |
21/16 | +3.883 | +6.544 |
26/1 | -3.894 | -6.564 |
29/10 | -3.941 | -6.642 |
16/11 | +3.981 | +6.709 |
32/3 | -4.069 | -6.858 |
19/13 | -4.323 | -7.285 |
32/31 | +4.369 | +7.363 |
10/9 | -4.405 | -7.424 |
23/20 | -4.629 | -7.801 |
25/1 | +4.673 | +7.875 |
21/19 | +4.731 | +7.974 |
22/9 | -4.750 | -8.006 |
25/13 | -4.773 | -8.045 |
25/14 | +4.859 | +8.190 |
31/6 | +4.903 | +8.263 |
29/18 | +4.995 | +8.418 |
29/27 | -5.046 | -8.505 |
19/1 | +5.123 | +8.635 |
31/9 | -5.138 | -8.660 |
25/21 | -5.182 | -8.733 |
11/3 | +5.290 | +8.916 |
19/14 | +5.310 | +8.949 |
5/3 | +5.636 | +9.499 |
26/11 | -5.885 | -9.919 |
16/1 | +5.971 | +10.064 |
33/25 | -5.982 | -10.082 |
27/26 | -6.004 | -10.120 |
33/32 | +6.060 | +10.214 |
19/15 | +6.087 | +10.258 |
8/7 | +6.158 | +10.378 |
26/5 | -6.231 | -10.502 |
32/15 | -6.406 | -10.796 |
14/9 | +6.413 | +10.808 |
33/19 | -6.432 | -10.841 |
17/7 | +6.528 | +11.002 |
24/13 | +6.566 | +11.067 |
9/1 | -6.599 | -11.122 |
9/2 | +6.741 | +11.362 |
28/9 | -6.928 | -11.676 |
16/15 | +6.935 | +11.688 |
13/5 | +7.110 | +11.982 |
16/7 | -7.183 | -12.106 |
33/16 | -7.280 | -12.270 |
32/1 | -7.369 | -12.420 |
13/11 | +7.455 | +12.565 |
21/5 | +7.518 | +12.671 |
32/29 | +7.576 | +12.769 |
10/3 | -7.704 | -12.985 |
31/26 | -7.843 | -13.219 |
21/11 | +7.864 | +13.253 |
25/3 | +7.972 | +13.437 |
19/7 | -8.031 | -13.535 |
22/3 | -8.050 | -13.568 |
31/18 | +8.202 | +13.824 |
29/9 | -8.346 | -14.066 |
19/3 | +8.423 | +14.196 |
31/3 | -8.438 | -14.221 |
25/7 | -8.481 | -14.294 |
26/25 | -8.567 | -14.439 |
11/9 | +8.590 | +14.478 |
9/5 | -8.936 | -15.060 |
26/19 | -9.018 | -15.199 |
23/18 | -9.033 | -15.225 |
16/3 | +9.271 | +15.625 |
32/11 | -9.360 | -15.775 |
29/20 | +9.399 | +15.842 |
13/1 | +9.446 | +15.920 |
21/8 | -9.457 | -15.940 |
14/13 | -9.632 | -16.234 |
17/12 | -9.671 | -16.299 |
33/10 | +9.695 | +16.340 |
32/5 | -9.705 | -16.357 |
27/14 | -9.712 | -16.369 |
21/17 | -9.828 | -16.563 |
21/1 | +9.854 | +16.609 |
13/8 | -9.866 | -16.628 |
27/1 | -9.899 | -16.684 |
3/2 | +10.041 | +16.923 |
28/3 | -10.227 | -17.237 |
17/13 | +10.236 | +17.252 |
22/15 | -10.386 | -17.505 |
15/13 | -10.409 | -17.544 |
33/31 | +10.429 | +17.576 |
23/17 | +10.678 | +17.997 |
33/13 | -10.755 | -18.126 |
31/15 | -10.774 | -18.159 |
7/5 | +10.818 | +18.232 |
24/19 | +10.889 | +18.352 |
10/1 | -11.004 | -18.546 |
23/8 | +11.048 | +18.620 |
29/26 | -11.051 | -18.625 |
11/7 | -11.163 | -18.815 |
25/9 | +11.272 | +18.998 |
25/24 | -11.339 | -19.112 |
22/1 | -11.350 | -19.129 |
31/14 | -11.551 | -19.468 |
29/3 | -11.645 | -19.627 |
19/9 | +11.723 | +19.757 |
29/4 | +11.736 | +19.779 |
31/1 | -11.738 | -19.782 |
27/11 | -11.890 | -20.039 |
33/2 | +12.031 | +20.278 |
32/25 | -12.042 | -20.295 |
33/28 | +12.218 | +20.592 |
27/5 | -12.235 | -20.621 |
23/6 | -12.333 | -20.786 |
15/2 | +12.377 | +20.860 |
32/19 | -12.492 | -21.055 |
28/15 | -12.564 | -21.175 |
16/9 | +12.571 | +21.187 |
31/20 | +12.607 | +21.248 |
13/3 | +12.746 | +21.481 |
17/4 | -12.970 | -21.860 |
11/10 | +12.995 | +21.901 |
7/1 | +13.154 | +22.170 |
2/1 | -13.340 | -22.484 |
28/1 | -13.527 | -22.798 |
33/29 | +13.636 | +22.982 |
24/5 | +13.676 | +23.049 |
22/5 | -13.686 | -23.067 |
17/16 | +13.711 | +23.108 |
31/11 | -13.728 | -23.138 |
26/21 | -13.749 | -23.172 |
29/15 | -13.982 | -23.565 |
24/11 | +14.021 | +23.632 |
29/23 | +14.028 | +23.643 |
31/5 | -14.074 | -23.720 |
15/7 | -14.117 | -23.793 |
19/8 | -14.188 | -23.913 |
30/1 | -14.304 | -24.107 |
24/23 | -14.348 | -24.182 |
27/20 | +14.446 | +24.347 |
33/7 | -14.463 | -24.376 |
19/17 | -14.559 | -24.537 |
27/25 | -14.572 | -24.559 |
25/8 | -14.639 | -24.673 |
30/23 | +14.669 | +24.724 |
29/14 | -14.759 | -24.874 |
31/4 | +14.943 | +25.185 |
29/1 | -14.945 | -25.189 |
25/17 | -15.009 | -25.297 |
27/19 | -15.022 | -25.318 |
29/12 | +15.035 | +25.341 |
20/17 | +15.307 | +25.798 |
11/2 | +15.331 | +25.839 |
28/23 | +15.446 | +26.033 |
28/11 | -15.517 | -26.153 |
23/2 | -15.633 | -26.347 |
5/2 | +15.677 | +26.422 |
28/5 | -15.863 | -26.736 |
27/16 | -15.870 | -26.748 |
24/1 | +16.012 | +26.987 |
25/22 | +16.022 | +27.004 |
13/9 | +16.045 | +27.043 |
19/10 | +16.127 | +27.181 |
12/7 | +16.199 | +27.301 |
30/11 | -16.294 | -27.463 |
31/25 | -16.410 | -27.658 |
7/3 | +16.454 | +27.731 |
22/19 | -16.473 | -27.764 |
6/1 | -16.640 | -28.045 |
27/4 | +16.782 | +28.284 |
32/13 | -16.815 | -28.340 |
31/19 | -16.861 | -28.417 |
29/11 | -16.936 | -28.544 |
8/5 | +16.975 | +28.610 |
26/7 | -17.048 | -28.734 |
23/7 | +17.206 | +28.999 |
32/21 | -17.223 | -29.028 |
31/23 | +17.236 | +29.049 |
29/5 | -17.281 | -29.126 |
11/8 | -17.321 | -29.193 |
17/5 | +17.346 | +29.234 |
23/22 | -17.623 | -29.703 |
17/11 | +17.691 | +29.817 |
31/16 | -17.709 | -29.847 |
20/9 | -17.745 | -29.908 |
23/10 | -17.969 | -30.285 |
25/2 | +18.013 | +30.359 |
28/25 | -18.200 | -30.674 |
31/12 | +18.243 | +30.747 |
19/2 | +18.464 | +31.119 |
11/6 | +18.631 | +31.400 |
28/19 | -18.650 | -31.433 |
6/5 | -18.976 | -31.983 |
27/23 | +19.074 | +32.148 |
8/1 | +19.312 | +32.548 |
27/13 | -19.345 | -32.604 |
30/19 | -19.427 | -32.742 |
7/4 | -19.498 | -32.862 |
29/25 | -19.618 | -33.064 |
17/1 | +19.682 | +33.172 |
18/17 | +19.711 | +33.222 |
9/7 | -19.753 | -33.292 |
17/14 | +19.868 | +33.486 |
13/12 | -19.907 | -33.551 |
18/1 | -19.940 | -33.606 |
29/19 | -20.068 | -33.823 |
9/4 | +20.082 | +33.845 |
15/8 | -20.275 | -34.172 |
13/10 | +20.450 | +34.466 |
23/21 | +20.506 | +34.560 |
32/7 | -20.523 | -34.589 |
33/8 | -20.621 | -34.754 |
17/15 | +20.645 | +34.796 |
22/13 | -20.796 | -35.049 |
21/10 | +20.858 | +35.155 |
23/13 | +20.914 | +35.249 |
29/16 | -20.917 | -35.253 |
33/17 | -20.991 | -35.378 |
20/3 | -21.045 | -35.469 |
31/13 | -21.183 | -35.703 |
22/21 | -21.204 | -35.737 |
25/6 | +21.313 | +35.921 |
31/21 | -21.592 | -36.391 |
32/23 | +21.604 | +36.412 |
19/6 | +21.763 | +36.680 |
20/7 | +21.835 | +36.800 |
18/11 | -21.930 | -36.961 |
18/5 | -22.276 | -37.544 |
23/9 | -22.374 | -37.709 |
8/3 | +22.611 | +38.109 |
13/2 | +22.786 | +38.404 |
21/4 | -22.798 | -38.424 |
28/13 | -22.973 | -38.718 |
17/3 | +22.982 | +38.733 |
17/6 | -23.011 | -38.783 |
33/20 | +23.035 | +38.824 |
27/7 | -23.053 | -38.853 |
21/2 | +23.195 | +39.093 |
13/4 | -23.206 | -39.112 |
4/3 | -23.381 | -39.407 |
26/17 | -23.576 | -39.736 |
30/13 | -23.750 | -40.028 |
10/7 | -24.158 | -40.716 |
19/12 | -24.229 | -40.836 |
20/1 | -24.344 | -41.030 |
23/16 | +24.388 | +41.104 |
29/13 | -24.391 | -41.109 |
22/7 | -24.504 | -41.299 |
25/18 | +24.612 | +41.482 |
25/12 | -24.680 | -41.595 |
29/17 | +24.706 | +41.639 |
29/21 | -24.799 | -41.797 |
31/7 | -24.891 | -41.952 |
19/18 | +25.063 | +42.241 |
29/8 | +25.076 | +42.263 |
26/23 | +25.079 | +42.268 |
21/20 | -25.134 | -42.361 |
23/19 | +25.237 | +42.534 |
30/17 | +25.347 | +42.721 |
33/4 | +25.372 | +42.762 |
20/13 | +25.543 | +43.050 |
23/3 | -25.673 | -43.270 |
25/23 | -25.687 | -43.293 |
15/4 | +25.718 | +43.344 |
9/8 | -25.911 | -43.671 |
13/6 | +26.086 | +43.965 |
28/17 | +26.124 | +44.030 |
18/7 | +26.239 | +44.224 |
17/9 | +26.281 | +44.294 |
17/2 | -26.311 | -44.344 |
20/11 | -26.335 | -44.385 |
7/2 | +26.494 | +44.654 |
4/1 | -26.681 | -44.968 |
12/5 | +27.016 | +45.533 |
32/17 | -27.051 | -45.592 |
12/11 | +27.362 | +46.116 |
30/7 | -27.458 | -46.277 |
19/4 | -27.529 | -46.397 |
33/23 | +27.664 | +46.625 |
31/24 | -27.750 | -46.769 |
31/17 | +27.913 | +47.045 |
25/4 | -27.979 | -47.157 |
23/15 | -28.010 | -47.208 |
23/5 | +28.023 | +47.231 |
29/7 | -28.099 | -47.358 |
31/8 | +28.284 | +47.669 |
22/17 | +28.301 | +47.699 |
23/11 | +28.369 | +47.813 |
29/24 | +28.376 | +47.824 |
17/10 | -28.647 | -48.282 |
11/4 | +28.671 | +48.323 |
23/14 | -28.787 | -48.517 |
23/1 | -28.973 | -48.831 |
5/4 | +29.017 | +48.906 |
27/8 | -29.211 | -49.232 |
12/1 | +29.353 | +49.471 |
18/13 | -29.386 | -49.526 |
20/19 | -29.468 | -49.665 |
7/6 | -29.539 | -49.785 |
27/17 | -29.581 | -49.856 |
Ratio | Error (abs, ¢) | Error (rel, %) |
---|---|---|
14/1 | -0.186 | -0.314 |
11/5 | -0.346 | -0.583 |
31/22 | -0.388 | -0.654 |
21/13 | +0.408 | +0.688 |
25/19 | -0.451 | -0.759 |
26/3 | -0.595 | -1.003 |
30/29 | +0.641 | +1.081 |
31/10 | -0.733 | -1.236 |
15/14 | -0.777 | -1.309 |
15/1 | -0.963 | -1.623 |
23/12 | +1.007 | +1.698 |
27/10 | +1.105 | +1.863 |
33/14 | -1.123 | -1.892 |
33/1 | -1.309 | -2.206 |
29/28 | -1.418 | -2.390 |
27/22 | +1.451 | +2.445 |
31/2 | +1.603 | +2.702 |
29/2 | -1.605 | -2.705 |
29/6 | +1.695 | +2.857 |
31/28 | +1.789 | +3.016 |
31/27 | -1.839 | -3.099 |
11/1 | +1.991 | +3.355 |
14/11 | -2.177 | -3.669 |
23/4 | -2.292 | -3.864 |
5/1 | +2.336 | +3.938 |
14/5 | -2.523 | -4.252 |
31/30 | +2.566 | +4.325 |
33/26 | +2.586 | +4.358 |
25/11 | +2.682 | +4.520 |
26/9 | +2.705 | +4.559 |
19/5 | +2.787 | +4.697 |
26/15 | -2.931 | -4.940 |
15/11 | -2.954 | -4.979 |
14/3 | +3.113 | +5.247 |
19/11 | +3.133 | +5.280 |
31/29 | +3.208 | +5.406 |
3/1 | -3.300 | -5.561 |
27/2 | +3.442 | +5.800 |
29/22 | -3.595 | -6.060 |
28/27 | -3.628 | -6.115 |
33/5 | -3.645 | -6.144 |
13/7 | -3.708 | -6.250 |
26/1 | -3.894 | -6.564 |
29/10 | -3.941 | -6.642 |
19/13 | -4.323 | -7.285 |
10/9 | -4.405 | -7.424 |
23/20 | -4.629 | -7.801 |
25/1 | +4.673 | +7.875 |
21/19 | +4.731 | +7.974 |
22/9 | -4.750 | -8.006 |
25/13 | -4.773 | -8.045 |
25/14 | +4.859 | +8.190 |
31/6 | +4.903 | +8.263 |
29/18 | +4.995 | +8.418 |
29/27 | -5.046 | -8.505 |
19/1 | +5.123 | +8.635 |
31/9 | -5.138 | -8.660 |
25/21 | -5.182 | -8.733 |
11/3 | +5.290 | +8.916 |
19/14 | +5.310 | +8.949 |
5/3 | +5.636 | +9.499 |
26/11 | -5.885 | -9.919 |
33/25 | -5.982 | -10.082 |
27/26 | -6.004 | -10.120 |
19/15 | +6.087 | +10.258 |
26/5 | -6.231 | -10.502 |
14/9 | +6.413 | +10.808 |
33/19 | -6.432 | -10.841 |
17/7 | +6.528 | +11.002 |
9/1 | -6.599 | -11.122 |
9/2 | +6.741 | +11.362 |
28/9 | -6.928 | -11.676 |
13/5 | +7.110 | +11.982 |
13/11 | +7.455 | +12.565 |
21/5 | +7.518 | +12.671 |
10/3 | -7.704 | -12.985 |
31/26 | -7.843 | -13.219 |
21/11 | +7.864 | +13.253 |
25/3 | +7.972 | +13.437 |
19/7 | -8.031 | -13.535 |
22/3 | -8.050 | -13.568 |
31/18 | +8.202 | +13.824 |
29/9 | -8.346 | -14.066 |
19/3 | +8.423 | +14.196 |
31/3 | -8.438 | -14.221 |
25/7 | -8.481 | -14.294 |
26/25 | -8.567 | -14.439 |
11/9 | +8.590 | +14.478 |
9/5 | -8.936 | -15.060 |
26/19 | -9.018 | -15.199 |
23/18 | -9.033 | -15.225 |
29/20 | +9.399 | +15.842 |
13/1 | +9.446 | +15.920 |
14/13 | -9.632 | -16.234 |
33/10 | +9.695 | +16.340 |
27/14 | -9.712 | -16.369 |
21/17 | -9.828 | -16.563 |
21/1 | +9.854 | +16.609 |
27/1 | -9.899 | -16.684 |
3/2 | +10.041 | +16.923 |
28/3 | -10.227 | -17.237 |
17/13 | +10.236 | +17.252 |
22/15 | -10.386 | -17.505 |
15/13 | -10.409 | -17.544 |
33/31 | +10.429 | +17.576 |
33/13 | -10.755 | -18.126 |
31/15 | -10.774 | -18.159 |
7/5 | +10.818 | +18.232 |
10/1 | -11.004 | -18.546 |
23/8 | +11.048 | +18.620 |
29/26 | -11.051 | -18.625 |
11/7 | -11.163 | -18.815 |
25/9 | +11.272 | +18.998 |
22/1 | -11.350 | -19.129 |
31/14 | -11.551 | -19.468 |
29/3 | -11.645 | -19.627 |
19/9 | +11.723 | +19.757 |
29/4 | +11.736 | +19.779 |
31/1 | -11.738 | -19.782 |
27/11 | -11.890 | -20.039 |
33/2 | +12.031 | +20.278 |
33/28 | +12.218 | +20.592 |
27/5 | -12.235 | -20.621 |
23/6 | -12.333 | -20.786 |
15/2 | +12.377 | +20.860 |
28/15 | -12.564 | -21.175 |
31/20 | +12.607 | +21.248 |
13/3 | +12.746 | +21.481 |
11/10 | +12.995 | +21.901 |
7/1 | +13.154 | +22.170 |
2/1 | -13.340 | -22.484 |
28/1 | -13.527 | -22.798 |
33/29 | +13.636 | +22.982 |
22/5 | -13.686 | -23.067 |
31/11 | -13.728 | -23.138 |
26/21 | -13.749 | -23.172 |
29/15 | -13.982 | -23.565 |
29/23 | +14.028 | +23.643 |
31/5 | -14.074 | -23.720 |
15/7 | -14.117 | -23.793 |
30/1 | -14.304 | -24.107 |
24/23 | -14.348 | -24.182 |
27/20 | +14.446 | +24.347 |
33/7 | -14.463 | -24.376 |
19/17 | -14.559 | -24.537 |
27/25 | -14.572 | -24.559 |
30/23 | +14.669 | +24.724 |
29/14 | -14.759 | -24.874 |
31/4 | +14.943 | +25.185 |
29/1 | -14.945 | -25.189 |
25/17 | -15.009 | -25.297 |
27/19 | -15.022 | -25.318 |
29/12 | +15.035 | +25.341 |
11/2 | +15.331 | +25.839 |
28/23 | +15.446 | +26.033 |
28/11 | -15.517 | -26.153 |
23/2 | -15.633 | -26.347 |
5/2 | +15.677 | +26.422 |
28/5 | -15.863 | -26.736 |
25/22 | +16.022 | +27.004 |
13/9 | +16.045 | +27.043 |
19/10 | +16.127 | +27.181 |
30/11 | -16.294 | -27.463 |
31/25 | -16.410 | -27.658 |
7/3 | +16.454 | +27.731 |
22/19 | -16.473 | -27.764 |
6/1 | -16.640 | -28.045 |
27/4 | +16.782 | +28.284 |
31/19 | -16.861 | -28.417 |
29/11 | -16.936 | -28.544 |
26/7 | -17.048 | -28.734 |
31/23 | +17.236 | +29.049 |
29/5 | -17.281 | -29.126 |
17/5 | +17.346 | +29.234 |
23/22 | -17.623 | -29.703 |
17/11 | +17.691 | +29.817 |
20/9 | -17.745 | -29.908 |
23/10 | -17.969 | -30.285 |
25/2 | +18.013 | +30.359 |
28/25 | -18.200 | -30.674 |
31/12 | +18.243 | +30.747 |
19/2 | +18.464 | +31.119 |
11/6 | +18.631 | +31.400 |
28/19 | -18.650 | -31.433 |
6/5 | -18.976 | -31.983 |
27/23 | +19.074 | +32.148 |
27/13 | -19.345 | -32.604 |
30/19 | -19.427 | -32.742 |
29/25 | -19.618 | -33.064 |
17/1 | +19.682 | +33.172 |
9/7 | -19.753 | -33.292 |
17/14 | +19.868 | +33.486 |
18/1 | -19.940 | -33.606 |
29/19 | -20.068 | -33.823 |
9/4 | +20.082 | +33.845 |
13/10 | +20.450 | +34.466 |
17/15 | +20.645 | +34.796 |
22/13 | -20.796 | -35.049 |
21/10 | +20.858 | +35.155 |
33/17 | -20.991 | -35.378 |
20/3 | -21.045 | -35.469 |
31/13 | -21.183 | -35.703 |
22/21 | -21.204 | -35.737 |
25/6 | +21.313 | +35.921 |
31/21 | -21.592 | -36.391 |
19/6 | +21.763 | +36.680 |
18/11 | -21.930 | -36.961 |
18/5 | -22.276 | -37.544 |
23/9 | -22.374 | -37.709 |
13/2 | +22.786 | +38.404 |
28/13 | -22.973 | -38.718 |
17/3 | +22.982 | +38.733 |
33/20 | +23.035 | +38.824 |
27/7 | -23.053 | -38.853 |
21/2 | +23.195 | +39.093 |
4/3 | -23.381 | -39.407 |
26/17 | -23.576 | -39.736 |
30/13 | -23.750 | -40.028 |
10/7 | -24.158 | -40.716 |
20/1 | -24.344 | -41.030 |
23/16 | +24.388 | +41.104 |
29/13 | -24.391 | -41.109 |
22/7 | -24.504 | -41.299 |
25/18 | +24.612 | +41.482 |
29/21 | -24.799 | -41.797 |
31/7 | -24.891 | -41.952 |
19/18 | +25.063 | +42.241 |
29/8 | +25.076 | +42.263 |
26/23 | +25.079 | +42.268 |
33/4 | +25.372 | +42.762 |
23/3 | -25.673 | -43.270 |
15/4 | +25.718 | +43.344 |
13/6 | +26.086 | +43.965 |
17/9 | +26.281 | +44.294 |
20/11 | -26.335 | -44.385 |
7/2 | +26.494 | +44.654 |
4/1 | -26.681 | -44.968 |
30/7 | -27.458 | -46.277 |
33/23 | +27.664 | +46.625 |
23/15 | -28.010 | -47.208 |
29/7 | -28.099 | -47.358 |
31/8 | +28.284 | +47.669 |
29/24 | +28.376 | +47.824 |
11/4 | +28.671 | +48.323 |
23/14 | -28.787 | -48.517 |
23/1 | -28.973 | -48.831 |
5/4 | +29.017 | +48.906 |
18/13 | -29.386 | -49.526 |
20/19 | -29.468 | -49.665 |
27/17 | -29.581 | -49.856 |
7/6 | +29.794 | +50.215 |
12/1 | -29.980 | -50.529 |
27/8 | +30.122 | +50.768 |
17/10 | +30.686 | +51.718 |
23/11 | -30.964 | -52.187 |
22/17 | -31.032 | -52.301 |
23/5 | -31.309 | -52.769 |
25/4 | +31.354 | +52.843 |
31/17 | -31.419 | -52.955 |
31/24 | +31.583 | +53.231 |
19/4 | +31.804 | +53.603 |
12/11 | -31.971 | -53.884 |
12/5 | -32.317 | -54.467 |
17/2 | +33.022 | +55.656 |
18/7 | -33.094 | -55.776 |
28/17 | -33.209 | -55.970 |
9/8 | +33.422 | +56.329 |
25/23 | +33.646 | +56.707 |
20/13 | -33.790 | -56.950 |
30/17 | -33.986 | -57.279 |
23/19 | -34.096 | -57.466 |
21/20 | +34.199 | +57.639 |
29/17 | -34.627 | -58.361 |
25/12 | +34.653 | +58.405 |
19/12 | +35.104 | +59.164 |
13/4 | +36.127 | +60.888 |
17/6 | +36.322 | +61.217 |
21/4 | +36.535 | +61.576 |
8/3 | -36.722 | -61.891 |
20/7 | -37.498 | -63.200 |
32/23 | -37.729 | -63.588 |
29/16 | +38.416 | +64.747 |
23/13 | -38.419 | -64.751 |
33/8 | +38.712 | +65.246 |
23/21 | -38.827 | -65.440 |
15/8 | +39.058 | +65.828 |
13/12 | +39.426 | +66.449 |
18/17 | -39.622 | -66.778 |
7/4 | +39.835 | +67.138 |
8/1 | -40.021 | -67.452 |
31/16 | +41.624 | +70.153 |
11/8 | +42.012 | +70.807 |
23/7 | -42.127 | -71.001 |
8/5 | -42.358 | -71.390 |
12/7 | -43.134 | -72.699 |
24/1 | -43.321 | -73.013 |
27/16 | +43.463 | +73.252 |
20/17 | -44.026 | -74.202 |
25/8 | +44.694 | +75.327 |
19/8 | +45.144 | +76.087 |
24/11 | -45.311 | -76.368 |
24/5 | -45.657 | -76.951 |
17/4 | +46.363 | +78.140 |
16/9 | -46.762 | -78.813 |
25/24 | +47.994 | +80.888 |
24/19 | -48.444 | -81.648 |
23/17 | -48.655 | -82.003 |
13/8 | +49.467 | +83.372 |
17/12 | +49.662 | +83.701 |
21/8 | +49.876 | +84.060 |
16/3 | -50.062 | -84.375 |
32/29 | -51.757 | -87.231 |
33/16 | +52.053 | +87.730 |
16/15 | -52.398 | -88.312 |
24/13 | -52.767 | -88.933 |
8/7 | -53.175 | -89.622 |
16/1 | -53.362 | -89.936 |
32/31 | -54.964 | -92.637 |
16/11 | -55.352 | -93.291 |
16/5 | -55.698 | -93.873 |
24/7 | -56.475 | -95.183 |
32/27 | -56.803 | -95.736 |
25/16 | +58.034 | +97.811 |
19/16 | +58.485 | +98.571 |
17/8 | +59.703 | +100.624 |
32/9 | -60.103 | -101.297 |
16/13 | -62.807 | -105.856 |
24/17 | -63.003 | -106.185 |
21/16 | +63.216 | +106.544 |
32/3 | -63.402 | -106.858 |
33/32 | +65.393 | +110.214 |
32/15 | -65.739 | -110.796 |
16/7 | -66.516 | -112.106 |
32/1 | -66.702 | -112.420 |
32/11 | -68.693 | -115.775 |
32/5 | -69.038 | -116.357 |
32/25 | -71.375 | -120.295 |
32/19 | -71.825 | -121.055 |
17/16 | +73.044 | +123.108 |
32/13 | -76.148 | -128.340 |
32/21 | -76.556 | -129.028 |
32/7 | -79.856 | -134.589 |
32/17 | -86.384 | -145.592 |
Record on the Riemann zeta function with prime 2 removed
71zpi sets a height record on the Riemann zeta function with prime 2 removed. The previous record is 53zpi and the next one is 93zpi. It is important to highlight that the optimal equal tunings obtained by excluding the prime number 2 from the Riemann zeta function differs slightly from the optimal equal tuning corresponding to the same peaks on the unmodified Riemann zeta function.
Unmodified Riemann zeta function | Riemann zeta function with prime 2 removed | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Tuning | Strength | Closest EDO | Tuning | Strength | Closest EDO | |||||
ZPI | Steps per octave | Step size (cents) | Height | EDO | Octave (cents) | Steps per octave | Step size (cents) | Height | EDO | Octave (cents) |
53zpi | 16.3979501311478 | 73.1798786069366 | 2.518818 | 16edo | 1170.87805771099 | 16.4044889390925 | 73.1507092025500 | 4.100909 | 16edo | 1170.41134724080 |
71zpi | 20.2248393119540 | 59.3329806724710 | 3.531097 | 20edo | 1186.65961344942 | 20.2459529213541 | 59.2711049295348 | 4.137236 | 20edo | 1185.42209859070 |
93zpi | 24.5782550666850 | 48.8236449961234 | 2.810487 | 25edo | 1220.59112490308 | 24.5738316304204 | 48.8324335434323 | 4.665720 | 25edo | 1220.81083858581 |
Harmonic series in 71zpi with prime 2 removed
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -14.6 | -5.3 | -29.2 | -0.6 | -19.9 | +9.6 | +15.5 | -10.6 | -15.1 | -2.3 | +24.8 | +4.8 | -5.0 | -5.9 | +1.0 |
Relative (%) | -24.6 | -8.9 | -49.2 | -1.0 | -33.5 | +16.2 | +26.2 | -17.8 | -25.6 | -3.9 | +41.9 | +8.1 | -8.4 | -9.9 | +1.6 | |
Steps | 20 | 32 | 40 | 47 | 52 | 57 | 61 | 64 | 67 | 70 | 73 | 75 | 77 | 79 | 81 |
Harmonic | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +14.5 | -25.1 | -0.2 | +29.5 | +4.3 | -16.9 | +24.7 | +10.3 | -1.1 | -9.8 | -15.8 | -19.5 | -21.0 | -20.4 | -17.9 | -13.6 | -7.6 | -0.0 |
Relative (%) | +24.5 | -42.4 | -0.3 | +49.8 | +7.3 | -28.5 | +41.6 | +17.3 | -1.9 | -16.5 | -26.7 | -32.9 | -35.4 | -34.5 | -30.2 | -23.0 | -12.9 | -0.1 | |
Steps | 83 | 84 | 86 | 88 | 89 | 90 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 |
Intervals in 71zpi with prime 2 removed
JI ratios are comprised of 34-integer-limit ratios, and are stylized as follows to indicate their accuracy:
|
Whole tone = 13 steps Limma = 8 steps Apotome = 5 steps | |||
Degree | Cents | Ratios | Ups and Downs Notation | Step |
---|---|---|---|---|
0 | 0.000 | P1 | 0 | |
1 | 59.271 | 34/33, 33/32, 32/31, 31/30, 30/29, 29/28, 28/27, 27/26, 26/25, 25/24, 24/23, 23/22, 22/21, 21/20, 20/19 | vA1, ^d2 | 4 |
2 | 118.542 | 19/18, 18/17, 17/16, 33/31, 16/15, 31/29, 15/14, 29/27, 14/13, 27/25, 13/12, 25/23 | m2 | 8 |
3 | 177.813 | 12/11, 23/21, 34/31, 11/10, 32/29, 21/19, 31/28, 10/9, 29/26, 19/17, 28/25, 9/8 | vM2 | 12 |
4 | 237.084 | 26/23, 17/15, 25/22, 33/29, 8/7, 31/27, 23/20, 15/13, 22/19, 29/25 | vvA2 | 16 |
5 | 296.356 | 7/6, 34/29, 27/23, 20/17, 33/28, 13/11, 32/27, 19/16, 25/21, 31/26, 6/5 | vm3 | 20 |
6 | 355.627 | 29/24, 23/19, 17/14, 28/23, 11/9, 27/22, 16/13, 21/17, 26/21, 31/25 | vvM3 | 24 |
7 | 414.898 | 5/4, 34/27, 29/23, 24/19, 19/15, 33/26, 14/11, 23/18, 32/25, 9/7, 31/24 | ^^M3 | 28 |
8 | 474.169 | 22/17, 13/10, 30/23, 17/13, 21/16, 25/19, 29/22, 33/25, 4/3 | vv4 | 32 |
9 | 533.440 | 31/23, 27/20, 23/17, 19/14, 34/25, 15/11, 26/19, 11/8, 29/21 | ^^4 | 36 |
10 | 592.711 | 18/13, 25/18, 32/23, 7/5, 31/22, 24/17, 17/12, 27/19, 10/7 | ^A4 | 40 |
11 | 651.982 | 33/23, 23/16, 13/9, 29/20, 16/11, 19/13, 22/15, 25/17, 28/19, 31/21, 34/23 | ^^d5 | 44 |
12 | 711.253 | 3/2, 32/21, 29/19, 26/17, 23/15 | ^5 | 48 |
13 | 770.524 | 20/13, 17/11, 31/20, 14/9, 25/16, 11/7, 30/19, 19/12 | ^^d6 | 52 |
14 | 829.795 | 27/17, 8/5, 29/18, 21/13, 34/21, 13/8, 31/19, 18/11 | ^m6 | 56 |
15 | 889.067 | 23/14, 28/17, 33/20, 5/3, 32/19, 27/16, 22/13, 17/10 | M6 | 60 |
16 | 948.338 | 29/17, 12/7, 31/18, 19/11, 26/15, 33/19, 7/4 | vA6, ^d7 | 64 |
17 | 1007.609 | 30/17, 23/13, 16/9, 25/14, 34/19, 9/5, 29/16, 20/11 | m7 | 68 |
18 | 1066.880 | 31/17, 11/6, 24/13, 13/7, 28/15, 15/8, 32/17 | vM7 | 72 |
19 | 1126.151 | 17/9, 19/10, 21/11, 23/12, 25/13, 27/14, 29/15, 31/16, 33/17 | vvA7 | 76 |
20 | 1185.422 | 2/1 | v1 +1 oct | 80 |
21 | 1244.693 | 33/16, 31/15, 29/14, 27/13, 25/12 | vvA1 +1 oct | 84 |
22 | 1303.964 | 23/11, 21/10, 19/9, 17/8, 32/15, 15/7, 28/13 | vm2 +1 oct | 88 |
23 | 1363.235 | 13/6, 24/11, 11/5, 31/14, 20/9, 29/13 | vvM2 +1 oct | 92 |
24 | 1422.507 | 9/4, 34/15, 25/11, 16/7, 23/10, 30/13 | ^^M2 +1 oct | 96 |
25 | 1481.778 | 7/3, 33/14, 26/11, 19/8, 31/13 | vvm3 +1 oct | 100 |
26 | 1541.049 | 12/5, 29/12, 17/7, 22/9, 27/11, 32/13 | ^^m3 +1 oct | 104 |
27 | 1600.320 | 5/2, 33/13, 28/11, 23/9 | ^M3 +1 oct | 108 |
28 | 1659.591 | 18/7, 31/12, 13/5, 34/13, 21/8, 29/11 | ^^d4 +1 oct | 112 |
29 | 1718.862 | 8/3, 27/10, 19/7, 30/11 | ^4 +1 oct | 116 |
30 | 1778.133 | 11/4, 25/9, 14/5, 31/11, 17/6 | A4 +1 oct | 120 |
31 | 1837.404 | 20/7, 23/8, 26/9, 29/10, 32/11 | ^d5 +1 oct | 124 |
32 | 1896.675 | 3/1 | P5 +1 oct | 128 |
33 | 1955.946 | 34/11, 31/10, 28/9, 25/8, 22/7 | vA5 +1 oct, ^d6 +1 oct | 132 |
34 | 2015.218 | 19/6, 16/5, 29/9, 13/4 | m6 +1 oct | 136 |
35 | 2074.489 | 23/7, 33/10, 10/3 | vM6 +1 oct | 140 |
36 | 2133.760 | 27/8, 17/5, 24/7, 31/9 | vvA6 +1 oct | 144 |
37 | 2193.031 | 7/2, 32/9, 25/7, 18/5 | vm7 +1 oct | 148 |
38 | 2252.302 | 29/8, 11/3, 26/7 | vvM7 +1 oct | 152 |
39 | 2311.573 | 15/4, 34/9, 19/5, 23/6, 27/7 | ^^M7 +1 oct | 156 |
40 | 2370.844 | 31/8, 4/1 | vv1 +2 oct | 160 |
41 | 2430.115 | 33/8 | ^^1 +2 oct | 164 |
42 | 2489.386 | 29/7, 25/6, 21/5, 17/4 | vvm2 +2 oct | 168 |
43 | 2548.658 | 30/7, 13/3, 22/5, 31/7 | ^^m2 +2 oct | 172 |
44 | 2607.929 | 9/2, 32/7 | ^M2 +2 oct | 176 |
45 | 2667.200 | 23/5, 14/3, 33/7 | ^^d3 +2 oct | 180 |
46 | 2726.471 | 19/4, 24/5, 29/6, 34/7 | ^m3 +2 oct | 184 |
47 | 2785.742 | 5/1 | M3 +2 oct | 188 |
48 | 2845.013 | 31/6, 26/5, 21/4 | vA3 +2 oct, ^d4 +2 oct | 192 |
49 | 2904.284 | 16/3, 27/5 | P4 +2 oct | 196 |
50 | 2963.555 | 11/2, 28/5 | vA4 +2 oct | 200 |
51 | 3022.826 | 17/3, 23/4, 29/5 | d5 +2 oct | 204 |
52 | 3082.097 | 6/1 | v5 +2 oct | 208 |
53 | 3141.369 | 31/5 | vvA5 +2 oct | 212 |
54 | 3200.640 | 25/4, 19/3, 32/5 | vm6 +2 oct | 216 |
55 | 3259.911 | 13/2, 33/5, 20/3 | vvM6 +2 oct | 220 |
56 | 3319.182 | 27/4, 34/5 | ^^M6 +2 oct | 224 |
57 | 3378.453 | 7/1 | vvm7 +2 oct | 228 |
58 | 3437.724 | 29/4, 22/3 | ^^m7 +2 oct | 232 |
59 | 3496.995 | 15/2, 23/3 | ^M7 +2 oct | 236 |
60 | 3556.266 | 31/4 | ^^d1 +3 oct | 240 |
61 | 3615.537 | 8/1 | ^1 +3 oct | 244 |
62 | 3674.809 | 33/4, 25/3 | ^^d2 +3 oct | 248 |
63 | 3734.080 | 17/2, 26/3 | ^m2 +3 oct | 252 |
64 | 3793.351 | 9/1 | M2 +3 oct | 256 |
65 | 3852.622 | 28/3 | vA2 +3 oct, ^d3 +3 oct | 260 |
66 | 3911.893 | 19/2, 29/3 | m3 +3 oct | 264 |
67 | 3971.164 | 10/1 | vM3 +3 oct | 268 |
68 | 4030.435 | 31/3 | vvA3 +3 oct | 272 |
69 | 4089.706 | 21/2, 32/3 | v4 +3 oct | 276 |
70 | 4148.977 | 11/1 | vvA4 +3 oct | 280 |
71 | 4208.248 | 34/3, 23/2 | vd5 +3 oct | 284 |
72 | 4267.520 | vv5 +3 oct | 288 | |
73 | 4326.791 | 12/1 | ^^5 +3 oct | 292 |
74 | 4386.062 | 25/2 | vvm6 +3 oct | 296 |
75 | 4445.333 | 13/1 | ^^m6 +3 oct | 300 |
76 | 4504.604 | 27/2 | ^M6 +3 oct | 304 |
77 | 4563.875 | 14/1 | ^^d7 +3 oct | 308 |
78 | 4623.146 | 29/2 | ^m7 +3 oct | 312 |
79 | 4682.417 | 15/1 | M7 +3 oct | 316 |
80 | 4741.688 | 31/2 | vA7 +3 oct, ^d1 +4 oct | 320 |
81 | 4800.959 | 16/1 | P1 +4 oct | 324 |
82 | 4860.231 | 33/2 | vA1 +4 oct, ^d2 +4 oct | 328 |
83 | 4919.502 | 17/1 | m2 +4 oct | 332 |
84 | 4978.773 | 18/1 | vM2 +4 oct | 336 |
85 | 5038.044 | vvA2 +4 oct | 340 | |
86 | 5097.315 | 19/1 | vm3 +4 oct | 344 |
87 | 5156.586 | vvM3 +4 oct | 348 | |
88 | 5215.857 | 20/1 | ^^M3 +4 oct | 352 |
89 | 5275.128 | 21/1 | vv4 +4 oct | 356 |
90 | 5334.399 | 22/1 | ^^4 +4 oct | 360 |
91 | 5393.671 | ^A4 +4 oct | 364 | |
92 | 5452.942 | 23/1 | ^^d5 +4 oct | 368 |
93 | 5512.213 | 24/1 | ^5 +4 oct | 372 |
94 | 5571.484 | 25/1 | ^^d6 +4 oct | 376 |
95 | 5630.755 | 26/1 | ^m6 +4 oct | 380 |
96 | 5690.026 | 27/1 | M6 +4 oct | 384 |
97 | 5749.297 | 28/1 | vA6 +4 oct, ^d7 +4 oct | 388 |
98 | 5808.568 | 29/1 | m7 +4 oct | 392 |
99 | 5867.839 | 30/1 | vM7 +4 oct | 396 |
100 | 5927.110 | 31/1 | vvA7 +4 oct | 400 |
101 | 5986.382 | 32/1 | v1 +5 oct | 404 |
102 | 6045.653 | 33/1 | vvA1 +5 oct | 408 |
103 | 6104.924 | 34/1 | vm2 +5 oct | 412 |
Approximation to JI in 71zpi with prime 2 removed
Interval mappings in 71zpi with prime 2 removed
The following tables show how 34-integer-limit intervals are represented in 71zpi with prime 2 removed. Prime harmonics are in bold; inconsistent intervals are in italics.
Ratio | Error (abs, ¢) | Error (rel, %) |
---|---|---|
34/1 | -0.032 | -0.053 |
34/19 | +0.166 | +0.281 |
23/12 | -0.168 | -0.284 |
19/1 | -0.198 | -0.334 |
14/3 | +0.329 | +0.555 |
19/5 | +0.374 | +0.631 |
21/13 | -0.458 | -0.772 |
34/5 | +0.540 | +0.911 |
5/1 | -0.572 | -0.965 |
30/29 | +0.580 | +0.978 |
24/7 | +0.631 | +1.064 |
27/10 | -0.689 | -1.163 |
26/9 | +0.787 | +1.327 |
15/14 | -0.901 | -1.519 |
25/19 | -0.946 | -1.595 |
16/1 | +0.959 | +1.619 |
17/8 | -0.991 | -1.672 |
31/22 | -1.007 | -1.698 |
27/22 | +1.080 | +1.821 |
34/25 | +1.112 | +1.876 |
25/1 | -1.144 | -1.929 |
29/6 | -1.151 | -1.943 |
19/16 | -1.157 | -1.953 |
25/11 | +1.197 | +2.020 |
27/2 | -1.261 | -2.128 |
29/28 | -1.480 | -2.497 |
16/5 | +1.531 | +2.584 |
31/28 | +1.604 | +2.706 |
11/5 | -1.769 | -2.984 |
31/6 | +1.932 | +3.260 |
31/27 | -2.086 | -3.520 |
25/16 | -2.103 | -3.548 |
19/11 | +2.143 | +3.615 |
33/26 | +2.152 | +3.632 |
32/27 | +2.221 | +3.746 |
34/11 | +2.309 | +3.896 |
11/1 | -2.341 | -3.949 |
31/30 | +2.504 | +4.225 |
14/11 | -2.610 | -4.404 |
33/14 | -2.669 | -4.504 |
31/10 | -2.775 | -4.683 |
11/3 | +2.939 | +4.959 |
32/9 | -3.059 | -5.161 |
31/29 | +3.084 | +5.203 |
16/11 | +3.300 | +5.568 |
31/2 | -3.347 | -5.647 |
21/16 | +3.388 | +5.716 |
15/11 | -3.511 | -5.923 |
28/27 | -3.690 | -6.225 |
25/14 | +3.807 | +6.423 |
16/13 | -3.846 | -6.488 |
26/15 | -3.921 | -6.616 |
9/2 | +4.019 | +6.780 |
29/22 | -4.090 | -6.901 |
29/18 | +4.128 | +6.965 |
25/3 | +4.136 | +6.978 |
24/17 | -4.289 | -7.235 |
32/31 | +4.307 | +7.266 |
21/1 | +4.347 | +7.335 |
34/21 | -4.379 | -7.388 |
14/5 | -4.379 | -7.388 |
26/3 | -4.493 | -7.581 |
21/19 | +4.545 | +7.669 |
10/9 | -4.590 | -7.745 |
5/3 | +4.708 | +7.943 |
19/14 | +4.753 | +8.019 |
13/1 | +4.805 | +8.107 |
13/7 | -4.822 | -8.135 |
34/13 | -4.837 | -8.160 |
23/20 | -4.876 | -8.227 |
21/5 | +4.919 | +8.300 |
17/7 | +4.919 | +8.300 |
14/1 | -4.951 | -8.353 |
19/13 | -5.003 | -8.441 |
19/3 | +5.082 | +8.574 |
29/27 | -5.170 | -8.723 |
34/3 | +5.248 | +8.854 |
3/1 | -5.280 | -8.908 |
13/5 | +5.377 | +9.072 |
23/4 | -5.448 | -9.192 |
24/13 | +5.453 | +9.199 |
25/21 | -5.491 | -9.264 |
14/9 | +5.608 | +9.462 |
19/15 | +5.653 | +9.538 |
34/15 | +5.820 | +9.819 |
15/1 | -5.851 | -9.872 |
29/10 | -5.859 | -9.885 |
8/7 | +5.910 | +9.972 |
25/13 | -5.949 | -10.037 |
33/32 | +5.998 | +10.120 |
27/26 | -6.066 | -10.235 |
16/3 | +6.239 | +10.526 |
22/9 | -6.359 | -10.729 |
29/2 | -6.431 | -10.850 |
33/25 | -6.477 | -10.927 |
21/11 | +6.688 | +11.284 |
16/15 | +6.811 | +11.491 |
33/2 | +6.958 | +11.739 |
33/5 | -7.048 | -11.892 |
13/11 | +7.146 | +12.056 |
31/18 | +7.212 | +12.168 |
31/9 | -7.366 | -12.427 |
32/29 | +7.391 | +12.469 |
33/19 | -7.422 | -12.523 |
26/11 | -7.432 | -12.539 |
33/10 | +7.529 | +12.703 |
34/33 | +7.589 | +12.803 |
33/1 | -7.620 | -12.857 |
32/15 | -7.767 | -13.104 |
29/4 | +8.147 | +13.745 |
31/26 | -8.152 | -13.754 |
11/9 | +8.219 | +13.866 |
32/3 | -8.339 | -14.069 |
33/16 | -8.580 | -14.475 |
26/25 | -8.629 | -14.559 |
16/7 | -8.668 | -14.624 |
29/20 | +8.719 | +14.710 |
15/2 | +8.726 | +14.723 |
28/9 | -8.969 | -15.133 |
23/8 | +9.130 | +15.404 |
26/5 | -9.201 | -15.523 |
3/2 | +9.298 | +15.688 |
25/9 | +9.416 | +15.886 |
23/18 | -9.467 | -15.972 |
26/19 | -9.575 | -16.154 |
7/1 | +9.627 | +16.242 |
34/7 | -9.659 | -16.296 |
17/13 | +9.741 | +16.435 |
14/13 | -9.756 | -16.460 |
26/1 | -9.773 | -16.488 |
19/7 | -9.825 | -16.576 |
10/3 | -9.870 | -16.652 |
9/5 | -9.988 | -16.851 |
13/3 | +10.085 | +17.015 |
23/17 | +10.121 | +17.076 |
7/5 | +10.199 | +17.207 |
21/17 | -10.199 | -17.207 |
24/1 | +10.258 | +17.307 |
17/12 | -10.289 | -17.360 |
33/31 | +10.305 | +17.386 |
19/9 | +10.361 | +17.481 |
29/9 | -10.450 | -17.630 |
24/19 | +10.456 | +17.641 |
34/9 | +10.528 | +17.762 |
9/1 | -10.559 | -17.815 |
15/13 | -10.657 | -17.979 |
13/8 | -10.732 | -18.107 |
25/7 | -10.771 | -18.172 |
24/5 | +10.830 | +18.271 |
27/14 | -10.888 | -18.370 |
22/15 | -11.067 | -18.672 |
21/8 | -11.190 | -18.879 |
31/4 | +11.231 | +18.948 |
29/26 | -11.236 | -18.957 |
32/11 | -11.278 | -19.027 |
25/24 | -11.401 | -19.236 |
16/9 | +11.519 | +19.434 |
22/3 | -11.639 | -19.637 |
31/20 | +11.803 | +19.913 |
33/28 | +11.908 | +20.092 |
11/7 | -11.968 | -20.191 |
31/15 | -12.074 | -20.370 |
11/2 | +12.237 | +20.646 |
33/13 | -12.425 | -20.964 |
32/25 | -12.475 | -21.047 |
24/11 | +12.598 | +21.255 |
31/3 | -12.645 | -21.335 |
11/10 | +12.809 | +21.611 |
31/14 | -12.974 | -21.890 |
32/5 | -13.047 | -22.012 |
27/4 | +13.317 | +22.468 |
33/29 | +13.389 | +22.589 |
32/19 | -13.420 | -22.642 |
29/12 | +13.427 | +22.653 |
25/2 | +13.434 | +22.666 |
27/11 | -13.498 | -22.774 |
17/16 | +13.587 | +22.923 |
29/23 | +13.595 | +22.937 |
32/1 | -13.618 | -22.976 |
28/15 | -13.677 | -23.076 |
27/20 | +13.889 | +23.432 |
5/2 | +14.006 | +23.631 |
26/21 | -14.120 | -23.823 |
30/23 | +14.174 | +23.915 |
28/3 | -14.249 | -24.041 |
19/2 | +14.380 | +24.261 |
24/23 | -14.410 | -24.311 |
17/1 | +14.546 | +24.542 |
2/1 | -14.578 | -24.595 |
27/25 | -14.695 | -24.793 |
19/17 | -14.744 | -24.876 |
23/6 | -14.746 | -24.879 |
7/3 | +14.907 | +25.150 |
19/10 | +14.952 | +25.226 |
20/17 | +14.997 | +25.303 |
23/7 | +15.040 | +25.375 |
28/23 | +15.075 | +25.434 |
17/5 | +15.118 | +25.507 |
10/1 | -15.150 | -25.560 |
29/15 | -15.157 | -25.573 |
12/7 | +15.209 | +25.659 |
27/5 | -15.267 | -25.758 |
13/9 | +15.364 | +25.922 |
15/7 | -15.478 | -26.115 |
8/1 | +15.537 | +26.214 |
17/4 | -15.569 | -26.267 |
31/11 | -15.584 | -26.294 |
27/19 | -15.641 | -26.389 |
25/17 | -15.690 | -26.471 |
29/3 | -15.729 | -26.538 |
19/8 | -15.735 | -26.548 |
25/22 | +15.775 | +26.615 |
34/27 | +15.807 | +26.670 |
27/1 | -15.839 | -26.723 |
29/14 | -16.058 | -27.093 |
8/5 | +16.109 | +27.179 |
22/5 | -16.347 | -27.580 |
31/12 | +16.510 | +27.856 |
31/23 | +16.679 | +28.140 |
25/8 | -16.681 | -28.144 |
22/19 | -16.721 | -28.210 |
31/25 | -16.782 | -28.313 |
27/16 | -16.798 | -28.342 |
17/11 | +16.887 | +28.491 |
22/1 | -16.918 | -28.544 |
28/11 | -17.188 | -28.999 |
33/7 | -17.247 | -29.099 |
31/5 | -17.353 | -29.278 |
11/6 | +17.517 | +29.554 |
23/22 | -17.685 | -29.838 |
31/19 | -17.727 | -29.908 |
11/8 | -17.878 | -30.163 |
34/31 | +17.893 | +30.189 |
31/1 | -17.925 | -30.243 |
32/21 | -17.966 | -30.311 |
30/11 | -18.089 | -30.519 |
28/25 | -18.385 | -31.019 |
32/13 | -18.424 | -31.084 |
9/4 | +18.597 | +31.375 |
29/11 | -18.668 | -31.496 |
25/6 | +18.714 | +31.574 |
27/23 | +18.765 | +31.659 |
31/16 | -18.885 | -31.861 |
21/2 | +18.925 | +31.930 |
28/5 | -18.957 | -31.983 |
20/9 | -19.168 | -32.340 |
6/5 | -19.286 | -32.538 |
28/19 | -19.331 | -32.614 |
13/2 | +19.383 | +32.702 |
26/7 | -19.400 | -32.731 |
23/10 | -19.454 | -32.822 |
21/10 | +19.497 | +32.895 |
17/14 | +19.497 | +32.895 |
28/1 | -19.529 | -32.948 |
18/17 | +19.588 | +33.047 |
19/6 | +19.660 | +33.169 |
17/3 | +19.826 | +33.450 |
6/1 | -19.858 | -33.503 |
23/13 | +19.862 | +33.511 |
29/25 | -19.865 | -33.516 |
20/7 | +19.916 | +33.602 |
13/10 | +19.955 | +33.667 |
23/2 | -20.026 | -33.787 |
13/12 | -20.030 | -33.795 |
9/7 | -20.186 | -34.058 |
30/19 | -20.231 | -34.134 |
23/21 | +20.320 | +34.283 |
17/15 | +20.398 | +34.414 |
30/1 | -20.429 | -34.468 |
29/5 | -20.437 | -34.481 |
7/4 | -20.488 | -34.567 |
27/13 | -20.644 | -34.830 |
29/19 | -20.811 | -35.111 |
8/3 | +20.817 | +35.122 |
34/29 | +20.977 | +35.392 |
32/23 | +20.985 | +35.406 |
29/1 | -21.009 | -35.445 |
22/21 | -21.266 | -35.879 |
15/8 | -21.389 | -36.086 |
33/4 | +21.536 | +36.334 |
22/13 | -21.724 | -36.651 |
29/16 | -21.968 | -37.064 |
33/20 | +22.107 | +37.299 |
33/17 | -22.167 | -37.399 |
31/21 | -22.273 | -37.577 |
29/8 | +22.725 | +38.340 |
31/13 | -22.730 | -38.350 |
18/11 | -22.797 | -38.462 |
33/8 | -23.158 | -39.071 |
32/7 | -23.245 | -39.219 |
15/4 | +23.304 | +39.318 |
23/16 | +23.708 | +39.999 |
29/17 | +23.716 | +40.013 |
4/3 | -23.876 | -40.283 |
25/18 | +23.994 | +40.481 |
23/9 | -24.045 | -40.567 |
7/2 | +24.205 | +40.838 |
30/17 | +24.295 | +40.990 |
26/17 | -24.319 | -41.030 |
28/13 | -24.334 | -41.055 |
20/3 | -24.448 | -41.248 |
18/7 | +24.507 | +41.347 |
18/5 | -24.565 | -41.446 |
13/6 | +24.663 | +41.610 |
23/1 | +24.667 | +41.618 |
34/23 | -24.699 | -41.671 |
20/13 | +24.738 | +41.738 |
10/7 | -24.777 | -41.802 |
26/23 | +24.831 | +41.894 |
12/1 | +24.836 | +41.902 |
23/19 | +24.865 | +41.952 |
17/6 | -24.867 | -41.955 |
19/18 | +24.939 | +42.076 |
19/12 | -25.034 | -42.236 |
17/9 | +25.106 | +42.357 |
18/1 | -25.137 | -42.411 |
28/17 | +25.196 | +42.510 |
21/20 | -25.196 | -42.510 |
30/13 | -25.235 | -42.575 |
23/5 | +25.239 | +42.582 |
13/4 | -25.310 | -42.702 |
29/21 | -25.356 | -42.780 |
12/5 | +25.407 | +42.866 |
27/7 | -25.466 | -42.965 |
21/4 | -25.768 | -43.475 |
31/8 | +25.809 | +43.543 |
25/23 | -25.811 | -43.547 |
29/13 | -25.814 | -43.553 |
25/12 | -25.979 | -43.831 |
9/8 | -26.097 | -44.029 |
22/7 | -26.546 | -44.787 |
31/17 | +26.800 | +45.215 |
11/4 | +26.815 | +45.242 |
33/23 | +26.984 | +45.526 |
23/11 | +27.008 | +45.567 |
12/11 | +27.176 | +45.851 |
20/11 | -27.387 | -46.206 |
31/7 | -27.552 | -46.485 |
22/17 | +27.806 | +46.914 |
27/8 | +27.895 | +47.063 |
29/24 | +28.004 | +47.248 |
25/4 | +28.012 | +47.261 |
32/17 | -28.165 | -47.518 |
31/24 | -28.183 | -47.549 |
5/4 | +28.584 | +48.226 |
29/7 | +28.635 | +48.312 |
23/15 | -28.752 | -48.510 |
27/17 | +28.886 | +48.735 |
19/4 | +28.958 | +48.857 |
17/2 | +29.124 | +49.137 |
4/1 | -29.156 | -49.191 |
30/7 | +29.215 | +49.290 |
23/3 | -29.324 | -49.475 |
18/13 | +29.329 | +49.482 |
7/6 | +29.485 | +49.745 |
20/19 | -29.530 | -49.821 |
20/1 | +29.544 | +49.845 |
17/10 | -29.575 | -49.898 |
23/14 | +29.618 | +49.971 |
Ratio | Error (abs, ¢) | Error (rel, %) |
---|---|---|
34/1 | -0.032 | -0.053 |
34/19 | +0.166 | +0.281 |
19/1 | -0.198 | -0.334 |
14/3 | +0.329 | +0.555 |
19/5 | +0.374 | +0.631 |
21/13 | -0.458 | -0.772 |
34/5 | +0.540 | +0.911 |
5/1 | -0.572 | -0.965 |
30/29 | +0.580 | +0.978 |
27/10 | -0.689 | -1.163 |
26/9 | +0.787 | +1.327 |
15/14 | -0.901 | -1.519 |
25/19 | -0.946 | -1.595 |
31/22 | -1.007 | -1.698 |
27/22 | +1.080 | +1.821 |
34/25 | +1.112 | +1.876 |
25/1 | -1.144 | -1.929 |
29/6 | -1.151 | -1.943 |
25/11 | +1.197 | +2.020 |
27/2 | -1.261 | -2.128 |
29/28 | -1.480 | -2.497 |
31/28 | +1.604 | +2.706 |
11/5 | -1.769 | -2.984 |
31/6 | +1.932 | +3.260 |
31/27 | -2.086 | -3.520 |
19/11 | +2.143 | +3.615 |
33/26 | +2.152 | +3.632 |
34/11 | +2.309 | +3.896 |
11/1 | -2.341 | -3.949 |
31/30 | +2.504 | +4.225 |
14/11 | -2.610 | -4.404 |
33/14 | -2.669 | -4.504 |
31/10 | -2.775 | -4.683 |
11/3 | +2.939 | +4.959 |
31/29 | +3.084 | +5.203 |
31/2 | -3.347 | -5.647 |
15/11 | -3.511 | -5.923 |
28/27 | -3.690 | -6.225 |
25/14 | +3.807 | +6.423 |
26/15 | -3.921 | -6.616 |
9/2 | +4.019 | +6.780 |
29/22 | -4.090 | -6.901 |
29/18 | +4.128 | +6.965 |
25/3 | +4.136 | +6.978 |
21/1 | +4.347 | +7.335 |
34/21 | -4.379 | -7.388 |
14/5 | -4.379 | -7.388 |
26/3 | -4.493 | -7.581 |
21/19 | +4.545 | +7.669 |
10/9 | -4.590 | -7.745 |
5/3 | +4.708 | +7.943 |
19/14 | +4.753 | +8.019 |
13/1 | +4.805 | +8.107 |
13/7 | -4.822 | -8.135 |
34/13 | -4.837 | -8.160 |
21/5 | +4.919 | +8.300 |
17/7 | +4.919 | +8.300 |
14/1 | -4.951 | -8.353 |
19/13 | -5.003 | -8.441 |
19/3 | +5.082 | +8.574 |
29/27 | -5.170 | -8.723 |
34/3 | +5.248 | +8.854 |
3/1 | -5.280 | -8.908 |
13/5 | +5.377 | +9.072 |
25/21 | -5.491 | -9.264 |
14/9 | +5.608 | +9.462 |
19/15 | +5.653 | +9.538 |
34/15 | +5.820 | +9.819 |
15/1 | -5.851 | -9.872 |
29/10 | -5.859 | -9.885 |
25/13 | -5.949 | -10.037 |
27/26 | -6.066 | -10.235 |
22/9 | -6.359 | -10.729 |
29/2 | -6.431 | -10.850 |
33/25 | -6.477 | -10.927 |
21/11 | +6.688 | +11.284 |
33/2 | +6.958 | +11.739 |
33/5 | -7.048 | -11.892 |
13/11 | +7.146 | +12.056 |
31/18 | +7.212 | +12.168 |
31/9 | -7.366 | -12.427 |
33/19 | -7.422 | -12.523 |
26/11 | -7.432 | -12.539 |
33/10 | +7.529 | +12.703 |
34/33 | +7.589 | +12.803 |
33/1 | -7.620 | -12.857 |
29/4 | +8.147 | +13.745 |
31/26 | -8.152 | -13.754 |
11/9 | +8.219 | +13.866 |
26/25 | -8.629 | -14.559 |
29/20 | +8.719 | +14.710 |
15/2 | +8.726 | +14.723 |
28/9 | -8.969 | -15.133 |
26/5 | -9.201 | -15.523 |
3/2 | +9.298 | +15.688 |
25/9 | +9.416 | +15.886 |
26/19 | -9.575 | -16.154 |
7/1 | +9.627 | +16.242 |
34/7 | -9.659 | -16.296 |
17/13 | +9.741 | +16.435 |
14/13 | -9.756 | -16.460 |
26/1 | -9.773 | -16.488 |
19/7 | -9.825 | -16.576 |
10/3 | -9.870 | -16.652 |
9/5 | -9.988 | -16.851 |
13/3 | +10.085 | +17.015 |
23/17 | +10.121 | +17.076 |
7/5 | +10.199 | +17.207 |
21/17 | -10.199 | -17.207 |
33/31 | +10.305 | +17.386 |
19/9 | +10.361 | +17.481 |
29/9 | -10.450 | -17.630 |
34/9 | +10.528 | +17.762 |
9/1 | -10.559 | -17.815 |
15/13 | -10.657 | -17.979 |
25/7 | -10.771 | -18.172 |
27/14 | -10.888 | -18.370 |
22/15 | -11.067 | -18.672 |
31/4 | +11.231 | +18.948 |
29/26 | -11.236 | -18.957 |
22/3 | -11.639 | -19.637 |
31/20 | +11.803 | +19.913 |
33/28 | +11.908 | +20.092 |
11/7 | -11.968 | -20.191 |
31/15 | -12.074 | -20.370 |
11/2 | +12.237 | +20.646 |
33/13 | -12.425 | -20.964 |
31/3 | -12.645 | -21.335 |
11/10 | +12.809 | +21.611 |
31/14 | -12.974 | -21.890 |
27/4 | +13.317 | +22.468 |
33/29 | +13.389 | +22.589 |
29/12 | +13.427 | +22.653 |
25/2 | +13.434 | +22.666 |
27/11 | -13.498 | -22.774 |
28/15 | -13.677 | -23.076 |
27/20 | +13.889 | +23.432 |
5/2 | +14.006 | +23.631 |
26/21 | -14.120 | -23.823 |
28/3 | -14.249 | -24.041 |
19/2 | +14.380 | +24.261 |
17/1 | +14.546 | +24.542 |
2/1 | -14.578 | -24.595 |
27/25 | -14.695 | -24.793 |
19/17 | -14.744 | -24.876 |
7/3 | +14.907 | +25.150 |
19/10 | +14.952 | +25.226 |
23/7 | +15.040 | +25.375 |
17/5 | +15.118 | +25.507 |
10/1 | -15.150 | -25.560 |
29/15 | -15.157 | -25.573 |
27/5 | -15.267 | -25.758 |
13/9 | +15.364 | +25.922 |
15/7 | -15.478 | -26.115 |
31/11 | -15.584 | -26.294 |
27/19 | -15.641 | -26.389 |
25/17 | -15.690 | -26.471 |
29/3 | -15.729 | -26.538 |
25/22 | +15.775 | +26.615 |
34/27 | +15.807 | +26.670 |
27/1 | -15.839 | -26.723 |
29/14 | -16.058 | -27.093 |
22/5 | -16.347 | -27.580 |
31/12 | +16.510 | +27.856 |
22/19 | -16.721 | -28.210 |
31/25 | -16.782 | -28.313 |
17/11 | +16.887 | +28.491 |
22/1 | -16.918 | -28.544 |
28/11 | -17.188 | -28.999 |
33/7 | -17.247 | -29.099 |
31/5 | -17.353 | -29.278 |
11/6 | +17.517 | +29.554 |
31/19 | -17.727 | -29.908 |
34/31 | +17.893 | +30.189 |
31/1 | -17.925 | -30.243 |
30/11 | -18.089 | -30.519 |
28/25 | -18.385 | -31.019 |
9/4 | +18.597 | +31.375 |
29/11 | -18.668 | -31.496 |
25/6 | +18.714 | +31.574 |
21/2 | +18.925 | +31.930 |
28/5 | -18.957 | -31.983 |
20/9 | -19.168 | -32.340 |
6/5 | -19.286 | -32.538 |
28/19 | -19.331 | -32.614 |
13/2 | +19.383 | +32.702 |
26/7 | -19.400 | -32.731 |
21/10 | +19.497 | +32.895 |
17/14 | +19.497 | +32.895 |
28/1 | -19.529 | -32.948 |
19/6 | +19.660 | +33.169 |
17/3 | +19.826 | +33.450 |
6/1 | -19.858 | -33.503 |
23/13 | +19.862 | +33.511 |
29/25 | -19.865 | -33.516 |
13/10 | +19.955 | +33.667 |
9/7 | -20.186 | -34.058 |
30/19 | -20.231 | -34.134 |
23/21 | +20.320 | +34.283 |
17/15 | +20.398 | +34.414 |
30/1 | -20.429 | -34.468 |
29/5 | -20.437 | -34.481 |
27/13 | -20.644 | -34.830 |
29/19 | -20.811 | -35.111 |
34/29 | +20.977 | +35.392 |
29/1 | -21.009 | -35.445 |
22/21 | -21.266 | -35.879 |
33/4 | +21.536 | +36.334 |
22/13 | -21.724 | -36.651 |
33/20 | +22.107 | +37.299 |
33/17 | -22.167 | -37.399 |
31/21 | -22.273 | -37.577 |
29/8 | +22.725 | +38.340 |
31/13 | -22.730 | -38.350 |
18/11 | -22.797 | -38.462 |
15/4 | +23.304 | +39.318 |
4/3 | -23.876 | -40.283 |
25/18 | +23.994 | +40.481 |
7/2 | +24.205 | +40.838 |
26/17 | -24.319 | -41.030 |
28/13 | -24.334 | -41.055 |
20/3 | -24.448 | -41.248 |
18/5 | -24.565 | -41.446 |
13/6 | +24.663 | +41.610 |
23/1 | +24.667 | +41.618 |
34/23 | -24.699 | -41.671 |
10/7 | -24.777 | -41.802 |
23/19 | +24.865 | +41.952 |
19/18 | +24.939 | +42.076 |
17/9 | +25.106 | +42.357 |
18/1 | -25.137 | -42.411 |
30/13 | -25.235 | -42.575 |
23/5 | +25.239 | +42.582 |
29/21 | -25.356 | -42.780 |
27/7 | -25.466 | -42.965 |
31/8 | +25.809 | +43.543 |
25/23 | -25.811 | -43.547 |
29/13 | -25.814 | -43.553 |
22/7 | -26.546 | -44.787 |
11/4 | +26.815 | +45.242 |
23/11 | +27.008 | +45.567 |
20/11 | -27.387 | -46.206 |
31/7 | -27.552 | -46.485 |
27/8 | +27.895 | +47.063 |
29/24 | +28.004 | +47.248 |
25/4 | +28.012 | +47.261 |
5/4 | +28.584 | +48.226 |
19/4 | +28.958 | +48.857 |
17/2 | +29.124 | +49.137 |
4/1 | -29.156 | -49.191 |
7/6 | +29.485 | +49.745 |
20/19 | -29.530 | -49.821 |
23/14 | +29.618 | +49.971 |
17/10 | +29.696 | +50.102 |
20/1 | -29.728 | -50.155 |
18/13 | -29.942 | -50.518 |
23/3 | +29.947 | +50.525 |
30/7 | -30.056 | -50.710 |
27/17 | -30.385 | -51.265 |
23/15 | +30.519 | +51.490 |
29/7 | -30.636 | -51.688 |
31/24 | +31.088 | +52.451 |
22/17 | -31.465 | -53.086 |
12/11 | -32.095 | -54.149 |
33/23 | -32.288 | -54.474 |
31/17 | -32.471 | -54.785 |
9/8 | +33.174 | +55.971 |
25/12 | +33.292 | +56.169 |
21/4 | +33.503 | +56.525 |
12/5 | -33.864 | -57.134 |
13/4 | +33.961 | +57.298 |
21/20 | +34.075 | +57.490 |
28/17 | -34.075 | -57.490 |
19/12 | +34.237 | +57.764 |
17/6 | +34.404 | +58.045 |
12/1 | -34.435 | -58.098 |
26/23 | -34.440 | -58.106 |
20/13 | -34.533 | -58.262 |
18/7 | -34.764 | -58.653 |
30/17 | -34.976 | -59.010 |
23/9 | +35.227 | +59.433 |
29/17 | -35.555 | -59.987 |
33/8 | +36.113 | +60.929 |
29/16 | +37.303 | +62.936 |
15/8 | +37.882 | +63.914 |
8/3 | -38.454 | -64.878 |
7/4 | +38.783 | +65.433 |
13/12 | +39.241 | +66.205 |
23/2 | +39.245 | +66.213 |
20/7 | -39.355 | -66.398 |
18/17 | -39.683 | -66.953 |
23/10 | +39.817 | +67.178 |
31/16 | +40.387 | +68.139 |
27/23 | -40.506 | -68.341 |
11/8 | +41.393 | +69.837 |
23/22 | +41.586 | +70.162 |
27/16 | +42.473 | +71.658 |
25/8 | +42.590 | +71.856 |
31/23 | -42.592 | -71.860 |
8/5 | -43.162 | -72.821 |
19/8 | +43.536 | +73.452 |
17/4 | +43.702 | +73.733 |
8/1 | -43.734 | -73.786 |
12/7 | -44.063 | -74.341 |
28/23 | -44.196 | -74.566 |
20/17 | -44.274 | -74.697 |
23/6 | +44.525 | +75.121 |
30/23 | -45.097 | -76.085 |
29/23 | -45.676 | -77.063 |
24/11 | -46.673 | -78.745 |
16/9 | -47.752 | -80.566 |
25/24 | +47.870 | +80.764 |
21/8 | +48.081 | +81.121 |
24/5 | -48.442 | -81.729 |
13/8 | +48.539 | +81.893 |
24/19 | -48.815 | -82.359 |
17/12 | +48.982 | +82.640 |
24/1 | -49.013 | -82.693 |
23/18 | +49.804 | +84.028 |
33/16 | +50.691 | +85.525 |
32/29 | -51.881 | -87.531 |
16/15 | -52.460 | -88.509 |
16/3 | -53.032 | -89.474 |
8/7 | -53.361 | -90.028 |
24/13 | -53.819 | -90.801 |
23/4 | +53.823 | +90.808 |
23/20 | +54.395 | +91.773 |
32/31 | -54.964 | -92.734 |
16/11 | -55.971 | -94.432 |
32/27 | -57.051 | -96.254 |
25/16 | +57.168 | +96.452 |
16/5 | -57.740 | -97.416 |
19/16 | +58.114 | +98.047 |
17/8 | +58.280 | +98.328 |
16/1 | -58.312 | -98.381 |
24/7 | -58.640 | -98.936 |
23/12 | +59.103 | +99.716 |
32/9 | -62.330 | -105.161 |
21/16 | +62.659 | +105.716 |
16/13 | -63.117 | -106.488 |
24/17 | -63.560 | -107.235 |
33/32 | +65.269 | +110.120 |
32/15 | -67.038 | -113.104 |
32/3 | -67.610 | -114.069 |
16/7 | -67.939 | -114.624 |
23/8 | +68.401 | +115.404 |
32/11 | -70.549 | -119.027 |
32/25 | -71.746 | -121.047 |
32/5 | -72.318 | -122.012 |
32/19 | -72.692 | -122.642 |
17/16 | +72.858 | +122.923 |
32/1 | -72.890 | -122.976 |
24/23 | -73.681 | -124.311 |
32/21 | -77.237 | -130.311 |
32/13 | -77.695 | -131.084 |
32/7 | -82.517 | -139.219 |
23/16 | +82.979 | +139.999 |
32/17 | -87.436 | -147.518 |
32/23 | -97.557 | -164.594 |