A good friend of mine recently sent me a link to “Music: a Mathematical Offering” by Dave Benson. I’ve only briefly skimmed the text. However, I can already assure you this free online book is full of useful information. It does veer into the technical, as it is packed with equations that may seem a bit alien to some. Don’t let this dissuade you, as there is plenty of knowledge for people of all backgrounds.
Here is a list of chapters in the online version:
1. Waves and harmonics
2. Fourier theory
3. A mathematician’s guide to the orchestra
4. Consonance and dissonance
5. Scales and temperaments: the fivefold way
6. More scales and temperaments
7. Digital music
9. Symmetry in music
I would also like to point out that my synthesizer of choice, Csound, is covered.