; ; Bohlen-Pierce Scale ; ------------------- ; a Pitch Class Converter ; implemented using Csound's Python opcodes ; ; version 1.1.0 ; ; Bruce H. McCosar ; ; $Id: cpsbpconv.csd 34 2008-04-25 23:03:39Z mccosar $ ; ; Changes: ; ; -- 1.1.0: Changed pitch correlation standard to that ; suggested on the Bohlen-Pierce site (see below). Also ; a new demo, featuring the modes of the Lambda scale. ; -d -W -o bpdemo.wav ; ------------------------------------------------------------ HEADER sr = 44100 kr = 4410 ksmps = 10 nchnls = 2 pyinit ; The quicker picker upper. pyruni {{ """ The pitch correlation standard suggested on the Bohlen-Pierce Site[1] is that the tritave below 'middle A' (BP pitch class 10) should correspond to the lowest 'E' on the guitar, about 82.4 Hz. Compositionally, it might be useful to redefine the tritave names in the following manner: T.pc ---- 0.10 = BP contrabass A, two tritaves below BP middle A, 27.46896 Hz: equivalent to lowest 'A' on the piano (A0). 1.10 = BP bass A, one tritave below BP middle A, 82.40689 Hz: exactly equal to low 'E' on the guitar (E2). 2.10 = BP middle A, 247.22066 Hz: just above the B below middle C on the piano (B3) 3.00 = BP middle C, 318.5588537 Hz (used as the definition below) 3.10 = BP treble A, one tritave above BP middle A, 741.66200 Hz. These, then, are the note names and corresponding pitch classes for each tritave (Lambda scale[2] shown) (10)(11)(12) 0 1 2 3 4 5 6 7 8 9 A B C --- --- --- --- --- --- --- --- --- --- --- --- --- C D E F G H J A B [1] http://members.aol.com/bpsite/tuning.html#anchor56508 [2] http://members.aol.com/bpsite/modes.html#anchor194521 """ REFERENCE_FREQUENCY = 318.5588537 # BP middle C def cpsbpet(tritave,pitchclass): """ Return cycles-per-second given the tritave and the pitch class for a note in the Bohlen-Pierce scale (equal tempered version) -- 00 to 12. """ t = tritave - 3 n = t + pitchclass / 13.0 cps = REFERENCE_FREQUENCY * (3**n) return cps INTONATION = """ 1/1 27/25 25/21 9/7 7/5 75/49 5/3 9/5 49/25 15/7 7/3 63/25 25/9 """.split() def cpsbpji(tritave,pitchclass): """ Return cycles-per-second given the tritave and the pitch class for a note in the Bohlen-Pierce scale (just intonation version) -- 00 to 12. """ t = tritave - 3 f = REFERENCE_FREQUENCY * (3**t) a,b = INTONATION[int(pitchclass)].split('/') cps = f * int(a) / int(b) return cps }} ; ------------------------------------------------------- INSTRUMENTS garvL init 0 garvR init 0 instr 101 iamp = ampdbfs(p4)*1.1 icps pycall1i "cpsbpji", int(p5), frac(p5)*100 ipan = 0.5+(log(icps)-6.10)/3 ; asig vibes iamp, icps, 0.5, 0.5, 1, 6.08, 0.03, 1, 0.1 kenv linen 1, 0.01, p3, 0.01 aL, aR pan2 asig*kenv, ipan ; outs aL, aR garvL = aL + garvL garvR = aR + garvR endin instr 201 ifblvl = p4 ifco = p5 aL, aR reverbsc garvL, garvR, ifblvl, ifco outs aL, aR garvL = 0 garvR = 0 endin ; ---------------------------------------------------------- F-TABLES ; Table #1, the "marmstk1.wav" audio file. f 1 0 256 1 "marmstk1.wav" 0 0 0 ; Table #2, a sine wave for the vibrato. f 2 0 128 10 1 ; ------------------------------------------------------------- SCORE ; inst time dur fblvl fco i 201 0 58 0.605 10000 ; inst time dur dBfs T.pc i 101 0.0016 0.4752 -4.99 3.06 i 101 0.0166 0.7693 -5.02 3.00 i 101 0.5370 0.2607 -8.04 3.07 i 101 0.7503 0.5004 -5.99 3.04 i 101 0.7574 0.7484 -7.02 3.00 i 101 1.2794 0.2734 -9.04 3.07 i 101 1.5110 0.5046 -5.00 3.03 i 101 1.5069 0.7289 -6.00 3.00 i 101 2.0010 0.5058 -5.97 3.02 i 101 2.2666 0.7397 -7.97 3.00 i 101 2.5394 0.2380 -11.97 3.03 i 101 2.7674 0.2715 -9.96 3.04 ; inst time dur dBfs T.pc i 101 3.0321 0.4844 -5.03 3.06 i 101 3.0379 0.7341 -4.98 3.00 i 101 3.5176 0.2268 -8.03 3.07 i 101 3.7828 0.4974 -6.03 3.04 i 101 3.7884 0.7364 -6.99 3.00 i 101 4.2613 0.2294 -9.00 3.07 i 101 4.5372 0.4784 -4.96 3.03 i 101 4.5255 0.7618 -5.99 3.00 i 101 5.0137 0.5224 -6.01 3.02 i 101 5.2517 0.7550 -8.01 3.00 i 101 5.5454 0.2729 -12.02 3.03 i 101 5.7535 0.2350 -10.04 3.04 ; inst time dur dBfs T.pc i 101 6.0361 0.5174 -5.05 3.06 i 101 6.0454 0.7717 -5.03 3.00 i 101 6.5404 0.2426 -8.03 3.07 i 101 6.7796 0.5169 -5.98 3.04 i 101 6.7562 0.7606 -6.97 3.00 i 101 7.2788 0.2666 -8.96 3.07 i 101 7.5182 0.4931 -4.97 3.03 i 101 7.5375 0.7310 -5.96 3.00 i 101 8.0401 0.4786 -6.02 3.02 i 101 8.2638 0.7557 -8.03 3.00 i 101 8.5149 0.2253 -12.05 3.03 i 101 8.7773 0.2676 -10.04 3.04 ; inst time dur dBfs T.pc i 101 9.0104 0.4937 -5.05 3.06 i 101 9.0114 0.7273 -5.03 3.00 i 101 9.5028 0.2619 -8.02 3.07 i 101 9.7736 0.4972 -5.95 3.04 i 101 9.7933 0.7415 -7.03 3.00 i 101 10.2665 0.2711 -8.97 3.07 i 101 10.5261 0.5247 -4.97 3.03 i 101 10.5121 0.7731 -6.02 3.00 i 101 11.0182 0.4801 -5.98 3.02 i 101 11.2961 0.7518 -8.02 3.00 i 101 11.5345 0.2713 -12.03 3.03 i 101 11.7636 0.2419 -9.97 3.04 ; inst time dur dBfs T.pc i 101 12.0482 0.5186 -4.96 3.10 i 101 12.0475 0.7256 -5.01 3.03 i 101 12.5170 0.2670 -7.99 3.12 i 101 12.7882 0.4767 -6.04 3.09 i 101 12.7512 0.7266 -7.04 3.03 i 101 13.2532 0.2304 -9.04 3.12 i 101 13.5458 0.4832 -4.96 3.07 i 101 13.5033 0.7610 -6.00 3.03 i 101 14.0485 0.4771 -6.02 3.06 i 101 14.2862 0.7508 -8.05 3.03 i 101 14.5329 0.2529 -12.02 3.07 i 101 14.7547 0.2627 -10.04 3.05 ; inst time dur dBfs T.pc i 101 15.0150 0.4923 -4.96 3.10 i 101 15.0011 0.7710 -5.05 3.03 i 101 15.5422 0.2686 -7.95 3.12 i 101 15.7551 0.4960 -6.03 3.09 i 101 15.7649 0.7517 -7.03 3.03 i 101 16.2571 0.2689 -8.95 3.12 i 101 16.5324 0.4886 -5.02 3.07 i 101 16.5253 0.7704 -6.03 3.03 i 101 17.0185 0.5213 -6.03 3.06 i 101 17.2852 0.7254 -7.99 3.03 i 101 17.5489 0.2426 -12.03 3.07 i 101 17.7618 0.2377 -10.01 3.05 ; inst time dur dBfs T.pc i 101 18.0016 0.5216 -5.02 3.10 i 101 18.0250 0.7422 -4.95 3.03 i 101 18.5239 0.2358 -7.97 3.12 i 101 18.7698 0.4767 -6.04 3.09 i 101 18.7711 0.7691 -7.02 3.03 i 101 19.2585 0.2322 -8.95 3.12 i 101 19.5334 0.4935 -4.97 3.07 i 101 19.5192 0.7627 -6.03 3.03 i 101 20.0059 0.4828 -6.01 3.06 i 101 20.2504 0.7355 -8.00 3.03 i 101 20.5075 0.2644 -12.01 3.07 i 101 20.7572 0.2344 -10.00 3.05 ; inst time dur dBfs T.pc i 101 21.0036 0.4909 -5.00 3.10 i 101 21.0033 0.7726 -5.03 3.03 i 101 21.5104 0.2704 -8.05 3.12 i 101 21.7521 0.4930 -5.96 3.09 i 101 21.7895 0.7483 -7.03 3.03 i 101 22.2933 0.2484 -9.02 3.12 i 101 22.5068 0.4806 -4.95 3.07 i 101 22.5045 0.7656 -6.04 3.03 i 101 23.0444 0.4944 -6.02 3.06 i 101 23.2991 0.7743 -7.95 3.03 i 101 23.5096 0.2366 -12.02 3.07 i 101 23.7593 0.2711 -10.00 3.05 ; inst time dur dBfs T.pc i 101 24.0061 0.5182 -3.95 3.06 i 101 24.0420 0.7502 -5.99 3.00 i 101 24.5347 0.2665 -6.98 3.07 i 101 24.7746 0.5144 -5.03 3.04 i 101 24.7772 0.7506 -8.03 3.00 i 101 25.2835 0.2340 -7.96 3.07 i 101 25.5364 0.4772 -4.99 3.03 i 101 25.5288 0.7472 -6.00 3.00 i 101 26.0085 0.5013 -6.96 3.02 i 101 26.2604 0.7380 -9.01 3.00 i 101 26.5486 0.2488 -10.00 3.03 i 101 26.7796 0.2453 -9.03 3.04 ; inst time dur dBfs T.pc i 101 27.0188 0.4952 -4.01 3.06 i 101 27.0320 0.7674 -6.01 3.00 i 101 27.5488 0.2330 -7.01 3.07 i 101 27.7748 0.5030 -4.97 3.04 i 101 27.7824 0.7279 -7.97 3.00 i 101 28.2563 0.2724 -7.97 3.07 i 101 28.5319 0.5124 -5.02 3.03 i 101 28.5360 0.7437 -6.01 3.00 i 101 29.0096 0.5200 -6.95 3.02 i 101 29.2923 0.7578 -9.02 3.00 i 101 29.5381 0.2617 -10.03 3.03 i 101 29.7991 0.2433 -9.03 3.04 ; inst time dur dBfs T.pc i 101 30.0356 0.4812 -3.99 3.06 i 101 30.0449 0.7673 -6.03 3.00 i 101 30.5035 0.2339 -7.02 3.07 i 101 30.7800 0.5006 -4.96 3.04 i 101 30.7940 0.7666 -8.03 3.00 i 101 31.2631 0.2455 -7.99 3.07 i 101 31.5394 0.4967 -5.01 3.03 i 101 31.5001 0.7598 -6.03 3.00 i 101 32.0051 0.5207 -7.03 3.02 i 101 32.2741 0.7381 -9.03 3.00 i 101 32.5247 0.2492 -10.01 3.03 i 101 32.7823 0.2463 -9.01 3.04 ; inst time dur dBfs T.pc i 101 33.0076 0.4972 -4.04 3.06 i 101 33.0112 0.7514 -6.05 3.00 i 101 33.5111 0.2685 -6.96 3.07 i 101 33.7661 0.5234 -4.96 3.04 i 101 33.7716 0.7644 -8.01 3.00 i 101 34.2597 0.2423 -8.01 3.07 i 101 34.5457 0.4938 -5.04 3.03 i 101 34.5404 0.7346 -5.97 3.00 i 101 35.0417 0.4847 -6.97 3.02 i 101 35.2946 0.7517 -9.00 3.00 i 101 35.5152 0.2627 -9.99 3.03 i 101 35.7741 0.2375 -8.99 3.04 ; inst time dur dBfs T.pc i 101 36.0009 0.4991 -4.02 3.03 i 101 36.0471 0.7500 -5.96 2.10 i 101 36.5101 0.2563 -6.95 3.04 i 101 36.7605 0.4941 -5.03 3.02 i 101 36.7894 0.7329 -8.03 2.10 i 101 37.2982 0.2430 -8.03 3.04 i 101 37.5095 0.5124 -5.01 3.00 i 101 37.5250 0.7391 -5.97 2.10 i 101 38.0431 0.4853 -7.01 2.12 i 101 38.2630 0.7713 -8.97 2.10 i 101 38.5050 0.2647 -9.98 3.00 i 101 38.7871 0.2269 -8.99 3.02 ; inst time dur dBfs T.pc i 101 39.0261 0.4918 -4.01 3.03 i 101 39.0444 0.7363 -6.04 2.10 i 101 39.5372 0.2617 -6.97 3.04 i 101 39.7812 0.4875 -4.99 3.02 i 101 39.7685 0.7495 -8.02 2.10 i 101 40.2619 0.2359 -8.03 3.04 i 101 40.5135 0.5089 -5.05 3.00 i 101 40.5261 0.7716 -6.01 2.10 i 101 41.0231 0.5123 -7.03 2.12 i 101 41.2747 0.7523 -8.96 2.10 i 101 41.5422 0.2701 -10.02 3.00 i 101 41.7947 0.2518 -8.99 3.02 ; inst time dur dBfs T.pc i 101 42.0344 0.5196 -4.02 3.03 i 101 42.0379 0.7388 -6.01 2.10 i 101 42.5351 0.2614 -7.01 3.04 i 101 42.7761 0.4793 -5.05 3.02 i 101 42.7825 0.7656 -7.96 2.10 i 101 43.2502 0.2491 -7.95 3.04 i 101 43.5003 0.4918 -4.99 3.00 i 101 43.5334 0.7397 -6.04 2.10 i 101 44.0473 0.5241 -6.96 2.12 i 101 44.2604 0.7731 -8.99 2.10 i 101 44.5439 0.2588 -10.01 3.00 i 101 44.7867 0.2320 -9.05 3.02 ; inst time dur dBfs T.pc i 101 45.0086 0.4910 -3.97 3.03 i 101 45.0034 0.7462 -5.97 2.10 i 101 45.5117 0.2460 -6.97 3.04 i 101 45.7517 0.5013 -5.03 3.02 i 101 45.7664 0.7425 -7.99 2.10 i 101 46.2667 0.2357 -8.00 3.04 i 101 46.5388 0.5032 -4.97 3.00 i 101 46.5426 0.7593 -5.95 2.10 i 101 47.0111 0.4970 -6.99 2.12 i 101 47.2760 0.7399 -8.99 2.10 i 101 47.5238 0.2719 -9.99 3.00 i 101 47.7796 0.2715 -8.96 3.02 ; inst time dur dBfs T.pc i 101 48.0379 0.5008 -3.97 3.06 i 101 48.0374 0.7557 -5.99 3.00 i 101 48.5057 0.2681 -7.03 3.07 i 101 48.7610 0.4881 -4.95 3.04 i 101 48.7620 0.7330 -8.00 3.00 i 101 49.2979 0.2632 -8.00 3.07 i 101 49.5057 0.5148 -5.00 3.03 i 101 49.5464 0.7276 -5.97 3.00 i 101 50.0359 0.4770 -6.96 3.02 i 101 50.2908 0.7512 -8.96 3.00 i 101 50.5226 0.2319 -9.97 3.03 i 101 50.7684 0.2676 -8.97 3.04 i 101 51.0410 0.4753 -5.96 3.06 i 101 51.0228 0.7487 -8.01 3.00 i 101 51.5018 0.2323 -7.95 3.07 i 101 51.7883 0.5244 -6.97 3.04 i 101 51.7832 0.7468 -10.05 3.00 i 101 52.2957 0.2661 -10.02 3.07 i 101 52.5249 0.4814 -7.97 3.03 i 101 52.5418 0.7629 -7.97 3.00 i 101 53.0491 0.4873 -9.03 3.02 i 101 53.2866 1.5024 -10.99 3.00 i 101 53.5436 0.2392 -13.05 3.03 i 101 53.7655 3.0048 -14.98 3.04 e UklGRiQCAABXQVZFZm10IBAAAAABAAEAIlYAAESsAAACABAAZGF0YQACAAAUAI//CwIt+w0I lhUI42n9MAIyBJwDlvccDazur/RUEb0E3AP//Hz5bw9n4xweGto7MXPRZBrYCWjePidR0/ot /NgTFOQC2/c7AiMD6/3L+PgLEvKVG5TSkijr6qkDKgzL6gEcZeFoF6P84P2a+k8KNfApCUH9 7v9DCuTniR3y6UUEPg6t7y8Pje7QCF4F2+8rEdH84PODEfjt3Q+29bD7cxUL52MTk/pW/PMD 0fUbCXQDUPYYDjX2cfoUCEPzoBH39AkG4QIa9A0JUvte/44GjfpkBeL84/qSCujzDQW+BCn4 WQoF98IEIAEA9goMzfk8AZkC2vvMAkb9wPsVDYT0xAbO//32Aw6q8uQOffZv/9oHY/RDBwn+ qv6EAggAyP1gCKnwgA1t+eH8AQs7854PWPPgBGUE3PYPBcr9yP8GBHP8sAG6AUX1Qg0d+HQD qgTt9W8LbPR3BH8CBvcgDez2FAWfAu/1Uggj+o4DjQGY/QACnv6B+vQHzvueAJoDVvf/Ce73 BgWUAU75hgna92YEwgFX+m4F9fmNAqEC5/o8BrT80/3sBNT44Qcq/gv9owYP950F3/1MAFIE 6vq2Aqv+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAA