Actually, there is lots of nice maths in music theory.
Yes, music theory is descriptive rather than prescriptive. But messing around (mathematically) with its ideas can help one find nice musical possibilities one might not otherwise have considered.
For example, the major scale, the (ascending) melodic minor scale, and the harmonic minor scale are all seven-note scales such that all scale-wise thirds are major or minor.
This is important, because people like using harmony built on stacking major and minor thirds.
But are there any other seven-note scales whose thirds are all major or minor, beside the aforementioned (and their modes)?
Yes, the harmonic major scale (and its modes). Not so well known, it presents lots of different, but still ultimately convential, possibilities.
After digging a bit into math approach to music, I'd agree with mhh__. Music is the business of making vibrations sound good. Definition of "good" is cultural and changes with times (see Devil's interval). The standard mathematical approach to music starts from axioms that are only applicable to western music and imply no evolution.
Maybe linguistic methods would serve composers better, as they deal in similar problems: how to to create meaningful whole from meaningless parts that relate to each other in complex way. Just as linguistics, music involves not only the mechanics of ear sensing, but also pattern recognition machine that likes to have just the right amount of repetition, and just the right amount of new stuff.
Yes, ultimately taste, or `what sounds good' decides. But mathematical approaches to all the building blocks of music can bring new materials to the ear which might sound good.
For example, I love the third mode of harmonic major (Phrygian flat 4) because I like the way it sounds. But I wouldn't have discovered it if I hadn't been thinking about scales in a systematic, mathematical kind of way.
Yes, music theory is descriptive rather than prescriptive. But messing around (mathematically) with its ideas can help one find nice musical possibilities one might not otherwise have considered.
For example, the major scale, the (ascending) melodic minor scale, and the harmonic minor scale are all seven-note scales such that all scale-wise thirds are major or minor.
This is important, because people like using harmony built on stacking major and minor thirds.
But are there any other seven-note scales whose thirds are all major or minor, beside the aforementioned (and their modes)?
Yes, the harmonic major scale (and its modes). Not so well known, it presents lots of different, but still ultimately convential, possibilities.