Math/Modular-Arithmetic
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A Music Engine in $\mathbb{Z}_{12}$
This project began as a tool for visualizing chord shapes and progressions on a guitar fretboard, while being able to easily switch between different tunings.
It’s evolving into a more general music engine that can be used to explore various musical concepts, but the initial motivation was to have a tool to help me understand how different tunings work on the guitar.
The core insight is that music can be represented using modular arithmetic! In particular, the 12 notes in the chromatic scale can be represented as elements of the group $\mathbb{Z}_{12}$, which is the integers modulo 12. This allows us to use mathematical operations to manipulate musical concepts like chords and scales.