https://blog.phasewalk.xyz/tags/music/ Recent content in Music on phasewalk Hugo en-us Tue, 21 Apr 2026 00:00:00 +0000 https://blog.phasewalk.xyz/posts/z12/ Tue, 21 Apr 2026 00:00:00 +0000 https://blog.phasewalk.xyz/posts/z12/ <p>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.</p> <p>It&rsquo;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.</p> <p>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.</p>