Chapter 13. Meeting 13, Approaches: Non-Standard Synthesis 13.1. Announcements • Musical Design Report 3 due 6 April • Start thinking about sonic system projects 13.2. The Xenakis Sieve • A system (notation) for generating complex periodic integer sequences • Described by Xenakis in at least six articles between 1965 and 1990 • Xenakis demonstrated application to pitch scales and rhythms, and suggested application to many other parameters • “the basic problem for the originator of computer music is how to distribute points on a line” (Xenakis 1996, p. 150) • “the image of a line with points on it, which is close to the musician and to the tradition of music, is very useful” (Xenakis 1996, p. 147) 13.3. The Xenakis Sieve: Basic Components • Residual Classes: integer sequences based on a modulus (period) and a shift • Residual class 2@0: {..., 0, 2, 4, 6, 8, 10, 12, ...} • Residual class 2@1: {..., 1, 3, 5, 7, 9, 11, 13, ...} • Residual class 3@0: {..., 0, 3, 6, 9, 12, 15, ...} • Sieves combine residual classes with logical operators • Sieve 3@0 | 4@0 : {..., 0, 3, 4, 6, 8, 9, 12, ...} • Sieve 3@0 & 4@0 : {..., 0, 12, 24, ...} • Sieve {-3@2&4} | {-3@1&4@1} | {3@2&4@2} | {-3@0&4@3}: {..., 0, 2, 4, 5, 7, 9, 11, 12, ...} • Notation • Notations used by Xenakis: 136• A new notation (Ariza 2005c) Modulus number “at” shift value: 3@5 Logical operators and (&), or (|), and not (-) Nested groups with braces: {-3@2&4}|{-3@1&4@1}|{3@2&4@2}|{-3@0&4@3} 13.4. An Object Oriented Implementation of the Sieve in Python • sieve.py: a modular, object oriented sieve implementation in Python (Ariza 2005c) • A low level, portable interface • >>> from athenaCL.libATH import sieve, pitchTools >>> a = sieve.Sieve('{-3@2&4}|{-3@1&4@1}|{3@2&4@2}|{-3@0&4@3}') >>> print a {-3@2&4@0}|{-3@1&4@1}|{3@2&4@2}|{-3@0&4@3} >>> a.period() 12 >>> a(0, range(0,13)) # one octave segment as pitch class [0, 2, 4, 5, 7, 9, 11, 12] >>> a.compress() >>> print a 6@5|12@0|12@2|12@4|12@7|12@9 >>> a.expand() >>> print a {-3@2&4@0}|{-3@1&4@1}|{3@2&4@2}|{-3@0&4@3} 137 3434󰇛34󰇜3 4 󰇝󰇛3,2󰇜󰇛4,7󰇝󰇛15,5󰇜󰇛󰇜6,11󰇛8,6󰇜󰇜󰇛8,7󰇛4,2󰇜󰇞󰇜󰇞󰇝󰇛6,9󰇝󰇛6,9󰇜󰇜󰇛15󰇛,1815,19󰇜󰇞󰇜󰇞 󰇟󰇛3,2󰇜󰇛4,7󰇜󰇠󰇟󰇛6,9󰇜󰇛15,18󰇜󰇠>>> a(0, range(0,12), 'wid') [2, 2, 1, 2, 2, 2] >>> a(0, range(0,12), 'bin') [1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1] >>> a(0, range(0,12), 'unit') [0.0, 0.18181818181818182, 0.36363636363636365, 0.45454545454545453, 0.63636363636363635, 0.81818181818181823, 1.0] >>> [pitchTools.psToNoteName(x) for x in a(0, range(49))] ['C4', 'D4', 'E4', 'F4', 'G4', 'A4', 'B4', 'C5', 'D5', 'E5', 'F5', 'G5', 'A5', 'B5', 'C6', 'D6', 'E6', 'F6', 'G6', 'A6', 'B6', 'C7', 'D7', 'E7', 'F7', 'G7', 'A7', 'B7', 'C8'] • sieve.py: SievePitch objects specialized for pitch space usage >>> from athenaCL.libATH import sieve >>> a = sieve.SievePitch('6@5|12@0|12@2|12@4|12@7|12@9,c2,c4') >>> a() [-24, -22, -20, -19, -17, -15, -13, -12, -10, -8, -7, -5, -3, -1, 0] >>> [x + 60 for x in a()] [36, 38, 40, 41, 43, 45, 47, 48, 50, 52, 53, 55, 57, 59, 60] • athenaObj.py: can create an athenaCL Interpreter object to automate athenaCL commands >>> from athenaCL.libATH import athenaObj >>> ath = athenaObj.Interpreter() >>> ath.cmd('tmo da') >>> ath.cmd('pin a 5@3|7@2,c3,c8 4@2|6@3,c2,c4') >>> ath.cmd('pih') 13.5. The Sieve in athenaCL: Interactive Command Line • Using the interactive command-line, pitch sieves can be created, viewed, and deployed • Comma-separated arguments for complete specification: sieveString, lowerBoundaryPitch, upperBoundaryPitch, originPitch, unitSpacing • Example: PIn a 5@3|7@2,c2,c4,c2,1 • Multiple sieve-based multisets can be defined • Example: PIn b 5@3|7@2,c2,c4,c2,.5 5@1|7@8,c3,c6,c2,.5 13.6. Avoiding Octave Redundancy • Pitch sieves with large periods (or not a divisor or multiple of 12) are desirable • Can be achieved simply through the union of two or more moduli with a high LCMs >>> a = sieve.Sieve('3@0|4@0')Æ 13812 >>> a.period() >>> a = sieve.Sieve('3@0|5@0|7@0') >>> a.period() 105 139143 • Can be achieved through the use of moduli deviating from octave multiples (11, 13, 23, 25, 35, 37) >>> a = sieve.Sieve('11@0|13@0') >>> a.period() >>> a = sieve.Sieve('11@1|13@2|23@5|25@6') >>> a.period() 82225 13.7. Deploying Pitch Sieves with HarmonicAssembly • Provide complete sieve over seven octaves • TM HarmonicAssembly used to create chords • Chord size randomly selected between 2 and 3 • Rhythms and rests created with zero-order Markov chains • Command sequence: • emo m 140• pin a 11@1|13@2|23@5|25@6,c1,c7 • tmo ha • tin a 0 • tie t 0,30 • tie a rb,.2,.2,.6,1 • tie b c,120 • zero-order Markov chains building pulse triples tie r pt,(c,4),(mv,a{1}b{3}:{a=12|b=1}),(mv,a{1}b{0}:{a=9|b=1}),(c,.8) • index position of multiset: there is only one at zero tie d0 c,0 • selecting pitches from the multiset (indices 0-15) with a tendency mask tie d1 ru,(bpl,t,l,[(0,0),(30,12)]),(bpl,t,l,[(0,3),(30,15)]) • repetitions of each chord tie d2 c,1 • chord size tie d3 bg,rc,(2,3) • eln; elh 13.8. Reading: Berg. Composing Sound Structures with Rules • Berg, P. 2009. “Composing Sound Structures with Rules.” Contemporary Music Review 28(1): 75-87. • How did the PDP-15 affect what techniques were explored at the Institute of Sonology • Given the music, find the rules: how is this different than analytical approaches? • What is non standard about non-standard synthesis? • What is the relationship of Berg’s ASP to PILE 14113.9. Non-Standard Synthesis: Xenakis and Koenig • Both began with techniques for creating score tables • Both explored apply this techniques to sound construction • Both rejected acoustic models of sound creation • Both employed techniques of dynamic, algorithmic waveform generation 13.10. Tutorial: a Dynamic Stochastic Wavetable • Looping through an array at the audio rate creates a wave table [tabread4~] interpolates between points for any [phasor~] rate • Randomly place points within the table at a variable rate controlled by a [metro] [tabwrite] lets us specify index position, value to write to Can only be