Hello! This page describes the personal projects, academic ideas, and topics I have explored and/or am currently exploring.
Most of these began as simple questions arising from observation or reflection, often leading me to pick up new mathematical tools and frameworks as needed along the way. It is through these curiosity-led projects that I’ve discovered a desire to pursue research, and share it through writing.
Once completed, they will be made available here.
🎼Music
Piano By Ear • Piano Arrangement • Music Theory
Learning to Play Piano By Ear: A Player’s Handbook (WIP, 2025-)
Music Theory, Learning Piano, Autodidacticism, Music Pedagogy
Project Description
Since 2020, I have been teaching myself to play the piano by ear, a skill which I have found useful at church, where I often learn, improvise and transpose songs after just hearing them. A few people are curious as to how I developed this skill, and so I am now compiling a book to share my experience and insights on the subject.
This book will present an alternative, self-directed approach to learning the piano. My hope is that readers will come away with the fun and practical skill of playing by ear, a new way of engaging with music, as well as insights on how to approach learning new things.
An Algebraic Theory of Functional Harmony (WIP, 2025-)
Towards and Algebraic Theory of Functional Harmony
Mathematics and Music Theory
Project Description
Fixing a tonic (key), gives rise to a coordinate map that assigns each of the chords a unique coordinate that describes its function. This structure can be simply represented by the direct product (cyclic) group , derived solely from the spacing constraints that define the major, minor, and diminished chords. This structure can be unwrapped and visualised in 3D, which proves promising for application.
The complicated part? A different choice of tonic (key) will give rise to a different coordinate system. The question is, is there a consistent rule (morphism) that maps the functional coordinates under one key to those in another? So far, I have managed to tabulate it completely, but it turns out that finding and writing down this precise map is a nontrivial task.
So currently whenever I have time, I am trying to wrap my head around torsors, holonomies, and groupoid morphisms… as well as reading papers on various geometric approaches to music theory (Tymozcko, Lewin, NR Theory).