From eli@UX3.SP.CS.CMU.EDU Tue May 14 15:18:11 1996 14 May 96 18:18:03 +0500 14 May 96 17:34:31 +0500 Subject: m-6 lfo data Date: Tue, 14 May 1996 17:32:45 -0400 (EDT) From: Eli Brandt Cc: roberts@pharm.som.sunysb.edu, anders.wikholm@atcit.mil.se, Mark_Camp*@quickmail.apple.com, tgs1@aracnet.com X-Portmanteau: pantryptaminergeticallysisterrainbowtie OK, I did the lfo-ratio calculations out to 9:8. After each pair is the rate, in milliHertz, at which the oscillators go through a full cycle of drift. Basically if it's under one or two mHz the ratio sounds tight; otherwise it doesn't. The lfo speed data posted to the list was missing a few data points, so I added those. Unfortunately there also seems to be some systematic error -- either that or Cakewalk's timing is off. See the beginning of the revised listing for details. The non-revised listing is appended too. If anyone has a way to take accurate timings of a few of the slower rates, I'd appreciate it... also, are these numbers accurate for versions other than the M-6r 2.13? ========== lfo ratios lfo-speed ratios out to a factor-limit of nine and a beat rate of 5 mHz. beat rate (mHz) --- 2:1 --- 63 61 1.0 62 59 0.1 61 57 1.5 60 55 1.2 59 53 2.7 58 51 1.4 57 49 1.0 49 39 0.9 48 38 0.7 41 28 0.2 40 27 0.3 37 24 0.3 25 17 0.1 7 2 0.0 3 0 0.0 --- 3:1 --- 63 59 0.7 62 56 1.7 61 53 2.3 60 50 1.9 58 45 2.4 56 42 2.0 52 36 1.1 23 13 -3.9 18 9 0.6 6 0 0.7 --- 4:1 --- 63 57 2.5 62 53 2.8 61 49 2.5 57 39 1.9 54 33 2.8 52 30 1.4 44 21 0.7 43 20 0.7 22 10 -2.6 16 4 -1.4 15 3 -3.6 --- 5:1 --- 63 55 2.8 62 50 2.9 60 43 2.6 54 29 1.4 48 22 1.0 39 16 0.6 37 15 0.4 14 1 0.3 --- 6:1 --- 63 53 3.3 --- 7:1 --- 63 51 3.2 62 45 3.6 58 31 3.0 49 19 1.4 38 13 0.6 25 6 3.4 21 4 5.0 --- 8:1 --- 63 49 3.5 61 39 3.4 51 19 1.7 44 15 -4.5 29 7 -3.3 27 6 1.4 15 0 -3.5 --- 9:1 --- 62 42 3.7 38 11 0.4 31 7 -1.1 29 6 -0.5 25 4 -2.9 --- 3:2 --- 63 62 0.5 61 59 -0.3 59 56 1.6 57 53 0.8 55 50 0.7 51 45 1.0 22 18 4.0 6 3 0.6 --- 5:2 --- 63 60 1.6 61 55 1.8 59 50 2.8 55 43 1.4 38 22 0.4 24 15 0.1 --- 7:2 --- 63 58 1.7 61 51 2.1 59 45 3.4 51 31 1.6 39 19 0.5 17 6 3.3 --- 9:2 --- 63 56 2.2 59 42 3.6 35 15 -2.2 32 14 2.7 22 9 4.7 17 4 -3.0 --- 4:3 --- 62 61 0.5 59 57 1.8 56 53 1.1 53 49 0.2 39 34 -4.7 36 30 0.2 --- 5:3 --- 62 60 1.1 59 55 2.1 56 50 1.2 50 43 0.8 29 21 -3.5 26 19 -2.8 22 17 -2.2 18 14 3.2 --- 7:3 --- 62 58 1.2 59 51 2.5 56 45 1.9 45 31 0.6 38 23 4.5 34 20 0.8 23 15 -3.4 --- 8:3 --- 62 57 2.0 59 49 2.8 53 39 1.0 49 34 -3.8 43 26 -4.5 39 22 4.4 23 14 -1.3 15 6 -4.2 14 5 -0.9 --- 5:4 --- 61 60 0.6 57 55 0.3 53 50 0.1 36 31 -4.9 33 29 -1.4 11 9 4.7 --- 7:4 --- 61 58 0.7 57 51 0.6 53 45 0.8 43 33 -3.8 --- 9:4 --- 61 56 1.2 53 42 0.9 47 34 -1.9 44 30 -4.1 35 21 3.0 25 16 -1.4 --- 6:5 --- 60 59 -0.9 55 53 0.5 38 35 -4.8 36 32 -4.2 35 31 4.3 25 22 2.4 2 1 4.9 --- 7:5 --- 60 58 0.1 55 51 0.3 50 45 0.6 37 30 -3.6 --- 8:5 --- 60 57 0.9 55 49 0.7 44 37 -4.9 23 18 -4.6 20 16 0.0 13 9 0.0 --- 9:5 --- 60 56 0.6 50 42 0.8 41 30 4.1 35 24 -2.3 33 23 1.1 32 22 -4.5 27 19 -3.4 23 17 1.6 14 9 -2.6 --- 7:6 --- 59 58 1.0 53 51 -0.2 41 38 -4.9 32 29 -3.0 23 21 1.8 --- 8:7 --- 58 57 0.8 51 49 0.4 42 40 -4.5 38 36 -3.6 35 32 -2.9 34 31 0.2 27 25 -1.9 15 14 2.0 10 8 -0.3 5 4 4.2 --- 9:7 --- 58 56 0.5 45 42 0.2 43 39 4.6 39 35 3.6 38 33 -4.8 34 29 2.4 30 26 -2.2 29 25 -3.9 15 13 -0.6 14 12 4.0 13 11 -0.2 --- 9:8 --- 57 56 -0.3 36 33 -1.3 31 29 2.2 29 27 -2.0 20 19 4.4 17 16 -1.5 14 13 -2.6 7 6 2.8 ========== revised lfo speeds these values are corrected(?) by increasing the measured rates by a factor of 1.01128. this causes a rate-15 lfo to not drift audibly against Cakewalk 3.0 at the new tempo, over the span of a minute. lfo; rate in Hz; period (sec.); beats per min. 63 20.23 0.04944 1214 62 13.49 0.07412 809.4 61 10.12 0.09879 607.4 60 8.1 0.1234 486.2 59 6.747 0.1482 404.8 58 5.789 0.1728 347.3 57 5.07 0.1973 304.2 56 4.505 0.222 270.3 55 4.056 0.2465 243.4 54 3.689 0.271 221.4 53 3.382 0.2957 203 52 3.122 0.3203 187.3 51 2.898 0.345 173.9 50 2.706 0.3695 162.4 49 2.537 0.3942 152.2 48 2.389 0.4187 143.3 47 2.137 0.468 128.2 46 2.137 0.468 128.2 45 1.934 0.517 116.1 44 1.766 0.5663 106 43 1.625 0.6154 97.5 42 1.505 0.6646 90.28 41 1.401 0.7137 84.07 40 1.311 0.763 78.64 39 1.27 0.7876 76.18 38 1.195 0.8368 71.7 37 1.098 0.9105 65.9 36 1.042 0.9598 62.52 35 0.9911 1.009 59.46 34 0.9479 1.055 56.87 33 0.925 1.081 55.5 32 0.8646 1.157 51.88 31 0.8295 1.206 49.77 30 0.7816 1.279 46.9 29 0.7389 1.353 44.33 28 0.7007 1.427 42.04 27 0.6555 1.525 39.33 26 0.6066 1.649 36.4 25 0.5725 1.747 34.34 24 0.5493 1.82 32.96 23 0.5145 1.944 30.86 22 0.4782 2.091 28.69 21 0.4418 2.264 26.51 20 0.4065 2.46 24.45 19 0.3629 2.755 21.77 18 0.3201 3.124 19.2 17 0.2863 3.493 17.17 16 0.2541 3.936 15.24 15 0.2197 4.551 13.19 14 0.1927 5.19 11.56 13 0.1708 5.854 10.24 12 0.1505 6.646 9.028 11 0.1328 7.528 7.97 10 0.1192 8.386 7.155 9 0.1068 9.367 6.405 8 0.1043 9.587 6.258 7 0.09206 10.86 5.524 6 0.08206 12.19 4.924 5 0.07219 13.85 4.331 4 0.06343 15.77 3.805 3 0.05474 18.27 3.285 2 0.04603 21.72 2.762 1 0.03855 25.94 2.313 0 0.02737 36.53 1.642 ========== original lfo speeds lfo rate; rate in Hz; period (sec.); beats per min. 63 20.0 0.05 1200 62 13.34 0.07496 800.4 61 10.01 0.09990 600.6 60 8.01 0.1248 480.8 59 6.672 0.1499 400.3 58 5.724 0.1747 343.4 57 5.013 0.1995 300.8 56 4.455 0.2245 267.3 55 4.011 0.2493 240.7 54 3.648 0.2741 218.9 53 3.344 0.2990 200.7 52 3.087 0.3239 185.2 51 2.866 0.3489 172.0 50 2.676 0.3737 160.6 49 2.509 0.3986 150.5 48 2.362 0.4234 141.7 47 2.113 0.4733 126.8 46 2.113 0.4733 126.8 45 1.9126 0.52285 114.8 44 1.7462 0.57267 104.8 43 1.6068 0.62236 96.41 42 1.4878 0.67213 89.27 41 1.3855 0.72176 83.13 40 1.2960 0.77161 77.76 39 1.2555 0.79650 75.33 38 1.1817 0.84624 70.90 37 1.0860 0.92081 65.16 36 1.0303 0.97059 61.82 35 0.9800 1.0204 58.80 34 0.9373 1.0670 56.24 33 0.9147 1.0933 54.88 32 0.8550 1.1696 51.30 31 0.8202 1.2192 49.21 30 0.7729 1.2938 46.38 29 0.7307 1.3686 43.84 28 0.6929 1.4432 41.57 27 0.6482 1.5427 38.89 26 0.5998 1.6672 35.99 25 0.5661 1.7665 33.96 24 0.54317 1.8410 32.59 23 0.50872 1.9657 30.52 22 0.47287 2.1148 28.37 21 0.43686 2.2891 26.21 20 0.40197 2.4878 24.18 19 0.35889 2.7864 21.53 18 0.31651 3.1595 18.99 17 0.28308 3.5326 16.98 16 0.25124 3.9803 15.07 15 0.21729 4.6021 13.04 14 0.19052 5.2488 11.43 13 0.16891 5.9203 10.13 12 0.14878 6.7213 8.927 11 0.13135 7.6133 7.881 10 0.11791 8.4810 7.075 9 0.10557 9.4724 6.334 8 0.10314 9.6956 6.188 7 0.09103 10.985 5.462 6 0.08114 12.324 4.869 5 0.07138 14.010 4.283 4 0.06272 15.944 3.763 3 0.054130 18.474 3.248 2 0.045516 21.970 2.731 1 0.038117 26.235 2.287 0 0.027066 36.947 1.624 -- Eli Brandt eli+@cs.cmu.edu