1. Musical Applications of Constraint Programming using a Local Search Algorithm Charlotte Truchet Laboratoire d’Informatique de Nantes Atlantique Nantes University France

2. Overview Computer assisted composition and OpenMusic Modelling of musical CSPs Adaptive search OMClouds Guitar

3. Computer Assisted Composition Introduction

4. Computer Assisted Composition Common Music / Stella Rick Taube, ZKM, Germany EMI David Cope, USA OpenMusic Gérard Assayag, Carlos Agon, IRCAM, France Introduction

5. OpenMusic, visual Introduction

6. OpenMusic, object oriented Introduction

7. Overview Computer assisted composition and OpenMusic Modelling of musical CSPs Adaptive search OMClouds Guitar

8. Previous works Automatic harmonization: Ebcioglu 87, Tsang Aitken 91, Ballesta 98, Pachet Roy 01 BOXES (Beurivé, Desainte-Catherine 01), Mosaïcing (Zils, Pachet 01), Pico (Rueda, Valencia 01), MusicSpace (Delerue 04) In OpenMusic: Situation (Rueda, Bonnet 90), PWConstraints (Laurson 96) Modelling

9. Harmony, Georges Bloch Modelling Une empreinte sonore de la Fondation Beyeler (for ensemble)

10. Asynchronous rhythms, Mauro Lanza Variables: rhythmical patterns of fixed, relatively prime lengths L 1... L n Each pattern is played repetitively on one voice Constraint: not two onsets played simultaneously for a fixed duration D No solution as soon as D >= lcm(L i, L j ) for any i, j Modelling

11. Asynchronous rhythms, Mauro Lanza Erba nera che cresci segno nero tu vivi (for voice and eletronics) Burgertime (for tuba end electronics) Aschenblume (for ensemble) Modelling

12. Special features of these CSPs Modelling Expressivity of the constraint language Need for diverse solutions Many overconstrained problems Solutions are re-written afterwards The resolution process has to be understood by non-scientific users

13. Overview Computer assisted composition and OpenMusic Modelling of musical CSPs Adaptive search OMClouds Guitar

14. Adaptive search Local search method close to GSAT, WalkSAT, WSAT(OIP) Selman 92, Selman Kautz 94, Walser 99 Min Conflict Minton 92 Tabu-like heuristic Glover 89 Shown to be very efficient on classical academic CSPs Codognet Diaz 03

15. Local search Adaptive search constraint X = Y error function which measures how much the constraint is satisfied | X- Y | The goal is now to find a configuration with error zero.

16. Adaptive search constraint X = Y error function which measures how much the constraint is satisfied | X- Y | projection on each variable

17. Intuitively Adaptive search Directed search: the structure of the problem is used at the variable level at the constraint level Convergence on variables with bad values Any kind of constraint can be used, provided the appropriate error functions are defined

18. Overview Computer assisted composition and OpenMusic Modelling of musical CSPs Adaptive search and musical application OMClouds Guitar

19. OMClouds Homogeneous variables Three CSPs structures: lists, permutations, cycles Take advantage of existing musical knowledge in OpenMusic Visual definition of the constraints By default, automatic transformation of constraints into cost-functions Edition of approximate solutions OMClouds

20. OMClouds objects OMClouds asvarlist values domains current errors tabu status constraints... associated methods update initialize randomly descent resolution... musical object associated methods edit on a score play...

21. OMClouds instance of asvarlist method for asvarlist

22. OMClouds Variables Constraint primitive

23. OMClouds Edition of partial results

24. Overview Computer assisted composition and OpenMusic Modelling of musical CSPs Adaptive search and musical application OMClouds Guitar

25. C major chord : bass + third + fifth Find a playable realization and the associated fingering Guitar 5

26. Constraints for a single chord The guitarist uses only four fingers or three in case of a barré, and then no note can be played below the barré The hand has a limited size, depending on the position If the mute is possible, then a minimum of notes must be played ad lib Guitar

27. Constraints for two successive chords Minimize the number of cases in the position’s change Minimize the number of position changes Maximize the number of fingers which stay on the same note In case of barrés, stay on the same barré Optimize an ad hoc distance in order to combine all of these possibilities Several possibilities: Guitar

28. Resolution Solved in two steps first step : find all the solution for one chord complete method second step : find a tour in the solutions with minimal error adaptive search Visual integration to OM objects by adding the fingergings

29. Guitar Chords from Mikhaïl Malt

30. Musical application give new, original CSPs and shows a good example of non-academic use of CP CP is a flexible programming tool for the composers OMClouds takes advantage of the whole search process, and naturally copes with overconstrained CSPs Conclusion