The tuning theory presented in this thesis is based on the hypothesis that beat rate determines dissonance for chords that are considered consonant. This hypothesis leads to the establishment of beatless P5 and M3 as the goals of intonation. But a more sophisticated view of dissonance is probably necessary. For example, the prevalent use of detuning as a synthesis technique suggests that at least when it is at a slow rate, beating has some desirable affects.
In addition, it would be desirable to have a model of dissonance that covers grossly dissonant cases, such as diminished seventh chords, or even wolf fifths. As it is, beating models dissonance only for chords that are considered consonant. A model of gross dissonance could help establish limits of how far away from beatless one can go while still having acceptable P5 and M3. In addition, it might shed light onto what particular tunings are desirable for dissonant chords, since surely not only the fact that they are dissonant, but how dissonant they are, and what the ``color'' of this dissonance is, is important to their musical meaning.
Another feature of an advanced model of dissonance would be its ability to explain timbre's role in dissonance. In particular, it would be nice to have a model of the somewhat puzzling masking of beating by certain timbres. Along the lines of timbre, other considerations such as the interaction of vibrato with tuning and the hairy subject of intonation in large ensembles, where clouds of frequencies per pitch rather than individual frequencies occur, should be addressed.
Further research into current work in psycho-acoustics might yield some help in developing a more powerful theory of dissonance, although much work in this field studies the perception of sinusoidal dyads only, a case much simpler than real music.
Even if dissonance and consonance were completely understood, they are fundamentally harmonic phenomenon, so an important extension to the tuning theory of this work would be the consideration of melodic criteria. The most obvious and oft-cited tension between harmonic and melodic goals in intonation surrounds the leading tone. In its harmonic function, it should be close to 5/4 the frequency of the dominant. In its melodic function, many musicians like to make it lead into the tonic by playing it quite high, even higher than it is in 12TET. Melodic considerations like this one should be part of any complete tuning theory.