Introduction

A few years ago, I decided to learn to play the guitar on my own. The last time I tried, I was a teenager, and it went nowhere. My initial goal was to learn something out of my comfort zone. Also, I always loved music, and I felt that I was missing something important in my life because I could not perform a bit of it.

After a year into the process, playing a few minutes consistently every day, I got stuck. I figured the problem was that I felt lost in the fretboard, and no matter how much I played, I was not getting any new insights about how music works other than what I gathered by my own very limited intuition.

So started learning some music theory. For the first time, I understood the importance of scales, particularly Major and Minor scales, triads, chord progression, etc. I felt like learning how to read and write for the first time. A world of patterns and traditions suddenly opened. At that moment, my most influential books were Guitar Theory for Dummies by Desi Serna¹, and Basic Music Theory by Jonathan Harnum². As usual, after I got some of the basics, I had way more questions than when I started.

I was a scientist until a few years ago, and now I am an engineer. In my experience, I learn better when having a model to guide me in my learning process. The model does not need to be complete or correct, and I always assume that its content requires constant revisions and updates.

More recently, I was learning some abstract algebra. As a physics, I did not know a whole lot about math applied to discrete objects. However, as an engineer related to computing projects, I needed to learn new conceptual tools from algebra to help me to describe some of the problems I was facing. As I was learning more about music and its representation, I found that algebra seems to be also an excellent language to synthesize some of the music concepts.

With this blog, I will start a new series of notes about what you may call music theory. However, my goal is to provide a model to help me learning, making and performing music. Most of the content is my way of describing what I am reading about music, its representation, and its internal structure. I will provide as many references as I can without any illusion to be exhaustive. This lack of knowledge about referential material is because I only offer sources I managed to read, however in some cases, in a hurry.

I will be using what I call a quasi-formal approach using abstract algebra as a foundation. I will concentrate on creating simple definitions without taking too much time to justify them completely. As a complement, I will provide as many references as I know about each topic for active readers interested in pursuing them further.

In no way am I claiming originality about this approach. I discovered early on that the music community knew about this for a long time, as you can see in the most recent referential work by Lewin³, Rings⁴, and Tymoczko⁵. However, I think this series has the added value of reusing modern algebra concepts and notations rather than reinventing them in a musical context. I will closely follow the notation and algebra concepts as presented by excellent Introduction to Abstract Algebra by Jonathan Smith⁶.

Initially, I will avoid going too deep into the physics/acoustics or psychoacoustics of music. However, it is likely I will not stay out of it for too long.

Finally, I have little or no expertise in the details discussed in this series of blogs. Therefore, I prepared a disclaimer inspired by MIT license wording.

Therefore expect conceptual errors and constant updates to the whole blog series. Be skeptical and critical of this series content. Ultimately, you are responsible for the information you consume.

References