COMPOSING MUSIC BY SIMULATION FROM MULTIPLE POINT PROCESSES

      Iannis Xenakis (also spelt as Yannis Xenakis) (Greek: Γιάννης (Ιάννης) Ξενάκης [ˈʝanis kseˈnacis]; 29 May 1922 – 4 February 2001) was a Greek-French composer, music theorist, architect, performance director and engineer. After 1947, he fled Greece, becoming a naturalized citizen of France.^[1] He is considered an important post-World War II composer whose works helped revolutionize 20th-century classical music.^[2] Xenakis pioneered the use of mathematical models in music such as applications of set theory, stochastic processes and game theory and was also an important influence on the development of electronic and computer music. He integrated music with architecture, designing music for pre-existing spaces, and designing spaces to be integrated with specific music compositions and performances.

Among his most important works are Metastaseis (1953–54) for orchestra, which introduced independent parts for every musician of the orchestra; percussion works such as Psappha (1975) and Pléïades (1979); compositions that introduced spatialization by dispersing musicians among the audience, such as Terretektorh (1966); electronic works created using Xenakis's UPIC system; and the massive multimedia performances Xenakis called polytopes, that were a summa of his interests and skills.^[3] Among the numerous theoretical writings he authored, the book Formalized Music: Thought and Mathematics in Composition (French edition 1963, English translation 1971) is regarded as one of his most important. As an architect, Xenakis is primarily known for his early work under Le Corbusier: the Sainte Marie de La Tourette, on which the two architects collaborated, and the Philips Pavilion at Expo 58, which Xenakis designed by himself

                     

                                                     IANNIS XENAKIS




      They are lots of articles in the literature about using stochastic processes e,g.Markov Chains to compose music. I don't know whether the following suggestion is original.


                                                           

                 A log-Gaussian Cox Process driven by an Ornstein-Uhlenbeck Process.

   This process was first proposed by Tom Leonard (Journal of the Royal Society, Series B, 1978) . It is a special case of the Doubly Stochastic Poisson Process described by my undergraduate mentor David Cox in the same journal in 1955

          Suppose you wish  to compose a piece of music on the time interval (0,T) and assume that each note may assume one of M different characteristics, Then the times of occurrences of any particular characteristic in the tune may be represented by points in the interval (0,T), These could be specified by the composer  (see above diagram) . If repeated for each of the N characteristics, then the N sets of points (when superimposed with different labels on the same interval) defines the entire composition.

         For any particular characteristic, it would instead be possible to simulate the points from a random point process on the interval (0,T). If a different point process is used to generate the points for each characteristic, then the entire composition can be simulated.

         A log-Gaussian Cox Process can  be parameterised using a mean value function M(t) for t assuming values in the interval (0,T),  See, for example, the smoother curve in the above diagram.

         If the Cox Process is driven by an Ornstein-Uhlenbeck process. then a variance V and a correlation parameter R also need to be specified.

         It is left to the composer to come up with an imaginative choice of the continuous function M. He may then use a standard computer package to simulate the points of occurrence of that particular characteristic, for specified V and R (which could of course be fiddled with to improve the quality of the tune).

         If the composer can devise a different choice of continuous function M for each of the N characteristics, then his entire composition can be simulated from the N thus defined Cox Processes, e.g.by keeping V and R fixed and specified across all simulations.

          This suggests to me to suggest a whole new ball park, where the ingenuity of the composer is still an essential ingredient.

                                                   See also

                             CAMERON'S STEADY STATE METHOD   



   Hi Cameron, I enjoyed your music. This seems to be equivalent to simulating from a Markov Chain, It'd be a 2 state Markov Chain if there

In response to disturbing video that emerged this week that appears to show a Washtenaw County sheriff punching Sha’Teina Grady El in the head multiple times...

vvere 2 possible tones or levels to each note.  But it'd be possible to generalise this by a simple graphical procedure that'd permit lots of input from the composer. Suppose there are 20  levels for each note. Then dravv a series of vertical lines on the graph paper, each dotted and labelled from 1 to 20 at regular intervals, Then dravv a vvobbly curve across the graph paper (composer's choice!) in similar fashion to the curve in the above diagram. On each of the vertical lines, highlight the dots that are immediately belovv and above the curve, Then each time you choose a tone or note, choose the upper dot vvith probability P and the lovver dot vvith probability 1-P vvhere P is different according to the level of the preceding note,.

             I hope that explains the idea vvell enough, and I'm sorry that my double u is key is stuck.. Good luck on your endeavours! Best vvishes, Tom.

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