To choose an appropriate model for a tuning, we must start with its absolute model. We can then discriminate between what information in the absolute model is essential and what information is incidental or redundant. This discrimination between the essential and inessential will suggest which (if any) of the more condensed models is most appropriate. The most appropriate model will factor out all incidental information and encode redundant information compactly.
Our absolute model of a diatonic tuning is a map from the diatonic pitch set (all pitches representable in traditional Western notation) to frequencies. We will consider the actual frequencies of a diatonic tuning to be incidental; therefore we will use at least a relative model. The diatonic pitch set is transposable, so this relative model is a transposable one. Finally, we will assume diatonic tunings to be register-doubling; therefore we will use a register-zero model in order to avoid redundant information about all registers. Briefly, what we consider to be essential about a diatonic tuning is the way it maps pitches in register zero to frequency ratios. Thus we will use a register-zero transposable tuning to model diatonic tunings.