Contents. Iannis Xenakis s Achorripsis (1957) : The Matrix Game. Iannis Xenakis ( ) Iannis Xenakis Achorripsis (1957) Distribution of Events

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1 Contents Iannis Xenakis s Achorripsis (1957) : The Matrix Game Linda M. Arsenault (2002) Reviewed by Beomsoo Kim Iannis Xenakis Achorripsis (1957) Matrix Structure Distribution of Events 28 Columns (Time / Measures) 9 Rows (Timbres) Matrix Game (Rule followed) Iannis Xenakis ( ) Country: Greece/France Genres: Chamber, Keyboard, Orchestral, Ballet, Choral, Concerto, Vocal, Film He was a French composer of Greek heritage and Romanian birth, known for his revolutionary ideas regarding the systematic, mathematical organization of music and its structural parallels with architecture, and for his pioneering work in electronic music. (born May 29, 1922, Braila, Rom. died Feb. 4, 2001, Paris, France) Romanian-born Greek-French composer. His Greek family returned to Greece in 1932, and he studied engineering. A wartime resistance fighter, he was forced to flee Greece in 1947 when he was denounced as a communist. He worked closely with the architect Le Corbusier (194759), while studying composition with Olivier Messiaen and others. Interested in expressing mathematical structures in music, he used the term "stochastic music" to refer to situations in which the number of elements precludes prediction of what each element will do but the overall behaviour of the group is determinate (see stochastic process). He often based his compositions on standard concepts of mathematics and physics, such as the Fibonacci sequence (Metastasis, 1954), the Boltzmann constant (Pithoprakta, 1956), and Markov chains (Analogique A and Analogique B, ). (Britannica) 1

2 Achorripsis (The jets of sound) Rules of the game in every instance of applying probability theory Must follow the rule Imagine sudoku variations and my composed piece Think about aesthetically beautiful pieces Mathematical strategy : Poisson s law Poisson distribution Complexity USC ISE : Gaussian, 575c March 1, 2007 exponential, and uniform distribution Initial setup (Matrix structure) Clouds of sounds Densities of sound ~ # of events k Simeon Denis Poisson( ) s law used exp = , exp^-0.6 = CF) exp^-0.5 = , exp^-0.7 = Setup initial values (lamda=0.6) Event occurs under unit time, (mean, var)=(lamda,lamda) Calculate probabilities P according to event k Meaningful (large enough) P used into 28*7=196 blocks 7 timbres from 21 insts. # of sound 28 columns = 182 # of Event regarding to # of cells 1 block = min. piece Things to remember columns 2. 7 rows 3. Total 196 blocks , 65, 19, 4,1 as k= 0, 1, 2, 3, 4 5. New lamda for columns and rows 6. Altered version possible (for his aesthetic goal) to make 4. 2

3 Distribution of Events to columns & rows How to adjust # of columns How about rows?

4 Matrix game 7 timbres from 21 insts. # of sound 28 columns = 182 Structually completed Mapping those to physical domain Zero events : silence Single events : 2.5 ~ 6.5 sounds per measure Mean = 5, mean sound 5*6.5 = 32.5 in 1 block Goes to 10, 15, 20 as k increases Time sequence : under his creativity Timbres : 7 * 3 different insts. = 21 1 block = 6.5 Finalized = *0+65*1+19*2+4*3+1*4 = 119 LP Well-distributed / Equally distributed Follow Poisson s law, but minor change is okay. Aesthetically worthy Polla ta dhina, for children s chorus and orchestra. ST/ , for 10 inst. Akatra, for 16 wind insts. Achorripsis, for 21 insts. Sound recording, selections (1969) 1 Copies at Granddepos (r X5p) 4

5 Demonstrations (mp3, 128k) Glissando :easiest to follow up pp space 5