What is a Model?

For our purposes, a model is any form of computation that predicts the state $\underline{x}(t)$ at some future time $t$ of a physical object or phenomenon based on

1. the object's initial state $\underline{x}(0)$
2. any ``input'' (external) forces $\underline{f}(t)$ on the object

In our case, typically,

$$\begin{eqnarray*} \underline{f}(t) &=& \mbox{vector of \emph{performance control} variables}\\ \mbox{Object} &=& \mbox{\emph{musical instrument} and/or \emph{audio effects}}\\ \underline{x}(t) &=& \mbox{\emph{object state}} \end{eqnarray*}$$

The output sound is some function of the object state $\underline{x}(t)$ .