The comparison of the behaviours of software systems is an important concern in software engineering research. For example, in the areas of specification discovery and specification mining, it is important to measure the consistency between a collection of execution traces and the program specification that was automatically constructed from these traces. This problem is also tackled in process mining, where for almost two decades researchers propose measures to assess the quality of process specifications automatically discovered from execution logs of information systems. Though various measures have been proposed, it was recently observed that none of them fulfils essential properties, such as monotonicity. To address this research problem, we build on the following observation: If two behaviours are not equivalent, the extent of deviation can be quantified by a quotient of a certain aspect of one behaviour over the same aspect of the other behaviour. However, there is no systematic approach for defining such quotients and it is unclear which aspects shall be considered for meaningful comparison of systems that describe infinite behaviours, which is often the case for software systems. It is the contribution of this paper to introduce a framework to define behaviour quotients that apply once a system's behaviour is captured by a language over a set of actions. We instantiate the framework with measures for the cardinality and entropy as specific aspects of languages, thereby handling both finite and infinite behaviours. In addition, we prove important properties of these quotients. We demonstrate the application of the quotients to capture precision and recall between a collection of recorded executions of a system and a system specification, i.e., between the recorded and specified behaviours of a system. An experimental evaluation of the quotients using our open-source implementation demonstrates their feasibility and indicates that they enable a monotonic assessment.