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Wepropose { PiCO}, a calculus integrating concurrentobjects and constraints, as a base for music composition tools.In contrast with calculi such as NiehrenMueller:Free, milner.parrow.ea:calculus-mobileor TyCO vasconcelos:typed-concurrent, both constraints and objectsare primitive notions in { PiCO}. In { PiCO}a base object model is extended with constraints by orthogonallyadding the notion of constraint system found in the \rho-calculusOzCalculus. Concurrent processes make use of a constraint storeto synchronize communications either via the ask and tell operationsof the constraint model or the standard message-passing mechanismof the object model. A message delegation mechanism built intothe calculus allows encoding of general forms of inheritance.This paper includes encodings in { PiCO} of theconcepts of class and sub-class. These allow us to representcomplex partially defined objects such as musical structuresin a compact way. We illustrate the transparent interaction ofconstraints and objects by a musical example involving harmonicand temporal relations. The relationship between Cordial, avisual language for music composition applications, and its underlyingmodel { PiCO} is described.