Overview

This section details how Meantonal stores and operates on musical data. It is intended to provide you with enough information to truly understand how Meantonal works, and to extend its functionality as your specific needs require. Or write your own implementation in another language!

Danger

Mathematics ahead. It’s not too bad, but you have been warned.

In order to understand how pitches and intervals are represented, and the various operations that can be carried out, you’ll need to know some elementary linear algebra. In particular:

• Vector addition and scalar multiplication.
• The dot product and what it means for two vectors to be orthogonal.
• Matrices and matrix multiplication.
• Linear maps and the null space of a matrix.

All of Meantonal’s operations are very simple, but understanding these concepts will help greatly with acquiring intuitions about what’s actually going on under the hood.

3Blue1Brown’s YouTube series is an excellent introduction to all the relevant topics.