Symbolic pitch modelling is a way of incorporating knowledge about relations between pitches into the process of analysing musical information or signals. In this paper, we propose a family of probabilistic symbolic polyphonic pitch models, which account for both the ''horizontal'' and the ''vertical'' pitch structure. These models are formulated as linear or log-linear interpolations of up to five sub-models, each of which is responsible for modelling a different type of relation. The ability of the models to predict symbolic pitch data is evaluated in terms of their cross-entropy, and of a newly proposed ''contextual cross-entropy'' measure. Their performance is then measured on synthesised polyphonic audio signals in terms of the accuracy of multiple pitch estimation in combination with a Nonnegative Matrix Factorisation-based acoustic model. In both experiments, the log-linear combination of at least one ''vertical'' (e.g., harmony) and one ''horizontal'' (e.g., note duration) sub-model outperformed a pitch-dependent Bernoulli prior by more than 60% in relative cross-entropy and 3% in absolute multiple pitch estimation accuracy. This work provides a proof of concept of the usefulness of model interpolation, which may be used for improved symbolic modelling of other aspects of music in the future.