I'm aware of a number of different ways of representing pitch as numbers (including one I developed for use in my own software) but am interested if there are others.
The most widespread is probably MIDI (where C4 is 60 and each semitone up/down adds/substracts 1 from the value).
The MIDI note value system conflates enharmonics (which is problematic for a lot of the work I'm interested in and pretty much a deal breaker) and can really only handle a 12eq but it does have the advantage that both pitch class and octave are incorporated in one number.
I've written a lot of code that uses my own circle of fifths system http://jtauber.com/blog/2007/12/13/numerical_representation_of_pitch/ assigning D to 0 and +1 means a fifth above and -1 a fifth below. This allows for distinct enharmonic spelling, and easy interval arithmetic (which makes it easy to give the correct answer to questions like: what's the augmented fourth above D♯?) and can easily test for enharmonic equivalence via a modulo operation. It can, however, extend beyond the 35 note names for non-12eq tunings. One disadvantage is it only represents pitch class so you need a second number to indicate octave.
Hewlett's Base-40 system http://www.ccarh.org/publications/reprints/base40/ is very clever in supporting distinct enharmonic spelling plus representing pitch class and octave in a single number in such a way that allows easy interval arithmetic. The only disadvantage I can see is it does assume 35 note names and so has a 12-note octave assumption built in.
Hewlett's page (linked to above) does mention work by Clements and Zimmerman.
Is Hewlett's Base-40 the dominant one used in computational musicology or are there other systems (that maintain interval invariance and enharmonic spelling differentiation) in use, and, if so, what are they?