; ; Bohlen-Pierce Scale ; ------------------- ; a Pitch Class Converter ; implemented using Csound's Python opcodes ; ; version 1.0.0 ; ; Includes comparative demo -- complete with emcee! ; ; Bruce H. McCosar ; ; $Id: bohlenpierce.csd 5 2008-04-18 21:28:55Z mccosar $ ; -d -W -o demobp.wav ; ------------------------------------------------------------ HEADER sr = 44100 kr = 4410 ksmps = 10 nchnls = 1 pyinit ; The only way to fly. pyruni {{ # Calculate standard value for Middle C, based on A=440 REFERENCE_FREQUENCY = 440*2**(-9/12.0) 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. By default, 8.00 in this system is the same base frequency as Middle C. However, since the octaves are stretched, the lowest audible note is at about 5.09 (20.731519 Hz). """ t = tritave - 8 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. By default, 8.00 in this system is the same base frequency as Middle C. However, since the octaves are stretched, the lowest audible note is at about 5.09 (20.763933 Hz). """ t = tritave - 8 f = REFERENCE_FREQUENCY * (3**t) a,b = INTONATION[int(pitchclass)].split('/') cps = f * int(a) / int(b) return cps }} ; ------------------------------------------------------- INSTRUMENTS instr 101 ; =====================> Triangle-Wave Voice ; (Uses Equal-Tempered BP Scale) ; . . . . . . . . . . . . . . . . . . . . . . . . . . . controls iamp = ampdbfs(p4) icps pycall1i "cpsbpet", int(p5), frac(p5)*100 ; . . . . . . . . . . . . . . . . . . . . . . . . interpretation ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . signal ; ; Bohlen-Pierce sounds best with signal generators ; that emphasize the odd harmonics. In this case, ; for demonstration purposes, I've chosen an ; analog-synth style triangle wave. ; ; vco xamp, xcps, iwave, kpw asrc vco iamp, icps, 3, 0.5 ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . filter ; ; Sweeps filter down to a spot just above ; the fundamental. ; ; expon ia, idur, ib kfco expon 8000, p3, 1.1*icps ; moogvcf2 asig, xfco, xres asig moogvcf2 asrc, kfco, 0.33 ; balance asig, acomp asig balance asig, asrc ; . . . . . . . . . . . . . . . . . . . . . . . . . . . envelope ; ; Removes clicks at the beginning and end. ; ; linen xamp, irise, idur, ide k1 linen 1, 0.05, p3, 0.05 ; ; Actual shape of the wave is exponential decay. ; Half life is p3/3. ; ; expon ia, idur, ib k2 expon 1, p3, 0.125 kenv = k1*k2 ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . output out asig*kenv ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . send endin ; ============================================ 101 instr 102 ; =====================> Triangle-Wave Voice ; (A duplicate of the above, but uses the ; just intonation Bohlen-Pierce scale.) iamp = ampdbfs(p4) icps pycall1i "cpsbpji", int(p5), frac(p5)*100 asrc vco iamp, icps, 3, 0.5 kfco expon 8000, p3, 1.1*icps asig moogvcf2 asrc, kfco, 0.33 asig balance asig, asrc k1 linen 1, 0.05, p3, 0.05 k2 expon 1, p3, 0.125 kenv = k1*k2 out asig*kenv endin ; ============================================ 102 instr 201 ; =================> Your Friendly Announcer asig diskin2 p4, 1 kenv linen 0.9, 0.05, p3, 0.05 out asig*kenv endin ; ===========================================> 201 ; ---------------------------------------------------------- F-TABLES ; # time size gen str1 f 1 0 32768 10 1 ; ------------------------------------------------------------- SCORE ; p1 p2 p3 p4 ; Your Friendly Announcer i 201 0.20 1.31 "et.wav" ; "Equal Temperament" i 201 7.00 1.25 "ji.wav" ; "Just Intonation" i 201 13.1 2.38 "end.wav" ; ;-) ; p1 p2 p3 p4 p5 p6 p7 p8 p9 ; inst start dur dBfs T.pc i 101 2.20 1.42 -7 7.10 i 101 2.30 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