Microtonality Is Rad

Psst. Hey, kid. You want some new music? You ever tried microtones?

Microtonal music is rad. It has new sounds - some haunting, some abrasive, some exotic, and some familiar. If you have a western musical ear, those novel sounds are the reason to listen to it, learn about it, compose it - you have to want more from music than what you're already getting. If you're from a culture with a microtonal tradition, then you're already ahead of the curve, but there are rad new sounds for you too, and also there's new theory to explain what you have already been exposed to.

A side benefit of learning about microtonal music is that you'll understand regular western music better. If you learn this text, you may even become frustrated when you hear people talk about regular music theory, because people are very confused about it. Since you will have superior knowledge, it will help if you don't mind feeling a little superior.

There is a lot to learn about. Some of it has cool math. Some of the subject matter is hardly developed and you could pioneer it, as a performer, composer, theorist, or mathematician. There are lots of opportunities for innovators.

The core idea of microtonal music is this: there are more notes than found on a piano, and they *work*. They're useful. You can make music from them. They have harmonic and melodic functions. These dark forbidden notes can also sound terrible, and some people with aesthetic fetishes for novelty or pain are into those too. 

Or maybe people who enjoy the sounds that are rough to me just have more advanced aesthetics, and they can appreciate beauty I find incomprehensible. Any new music you hear gives you an opportunity to develop new aesthetics, but microtonality does this on a really fundamental level. 

If you people know you as a microtonalist, and they hear music that they hate, they will ask you, "Does this have microtones?", and you'll know that they're really asking, "Is this good for you, you little freak?". And it might be good for you! Because when you engage with microtonal music, you become receptive to new beauty. We're all on different levels of that. If you want to gain a level in being a musical bad ass, this book is for you.

We have two primary tools; microtonal music is phrased in terms of intervals and frequency ratios.

Frequency ratios are easy. One note has a fundamental frequency of 220 hz. Another has a frequency of 440 hz. The ratio between these is

440 hz / 220 hz = 2/1.

Not all frequency ratios are rational numbers: you might have frequencies separated by an irrational number like 2^(7/19) or something more exotic. This is a huge divide in microtonal music: if the frequency ratios are rational, then you're working in "just intonation", which just means "rational tuning". The main framework for analyzing all other music is that of "regular temperaments", which describes useful mis-tunings of just intonation. There are some other niche frameworks we'll also explore, like for analyzing inharmonic musical instruments in Javanese gamelan music.

The next core concept in the language of microtonal music theory is the musical interval. Musical intervals describe the distance between notes, but abstractly, not as a fixed number like a frequency ratio. We use intervals to talk about music in a way which is somewhat agnostic to tuning. The interval between C4 and D4 is a major second, and people have some leeway in how they tune their major seconds.

Intervals will be familiar to the student of western music theory. Let's write out some intervals as distances between pitches to get a feel for them. Here's a chromatic scale's worth of pitches and intervals:

C4 − C4 = P1, the unison (or perfect unison)

Db4 − C4 = m2, the minor second

D4 − C4 = M2, the major second

Eb4 − C4 = m3, the minor third

E4 − C4 = M3, the major third

F4 − C4 = P4, the perfect fourth

Gb4 − C4 = d5, the diminished fifth

G4 − C4 = P5, the perfect fifth

Ab4 − C4 = m6, the minor sixth

A4 − C4 = M6, the major sixth

Bb4 − C4 = m7, the minor seventh

B4 − C4 = M7, the major seventh

C5 − C4 = P8, the octave (or perfect eighth)

If those aren't already familiar to you, it's no trouble. You'll learn them quickly, and then you'll learn about them deeply. But terms like those are part of the standard language of western music theory, and we're going to build on that.

Writing music in terms of intervals and pitches gives us the power to automatically transform the music's sound by choosing how we tune the intervals. You can write a song once and then contort it a hundred different ways. Some people enjoy that a lot. It's a cheap way to make something familiar into something fresh.

Intervals also come in different dimensional spaces. Standard western music theory uses a 2-dimensional interval space, but you can compose in 3D interval space, 4D, and so on. In this way, intervals act as stepping stones, helping you to write with high dimensional musical concepts. As we work with higher dimensional interval spaces, we'll also learn to work with frequency ratios that have larger prime factors. This is the real power of microtonal music theory. If you can bear to learn some new notation, then soon it will be yours.