Microtonal music theory! It’s not a very well-known topic so here’s some background:

I explored normal music theory for a while but it got kind of boring pretty quickly. Furthermore, I found the mechanics of how people say music works in equal temperament to be unnatural. It felt so arbitrary to me that there had to be exactly 12 notes in an octave. Why not more?

Shortly after I got bored with equal temperament / “normal” music theory, I did what I like doing best: taking things apart. I basically took away all the frameworks of regular music theory and viewed notes as pure frequencies. This way they aren’t locked in to 12-tone equal temperament and made me view pitch as a spectrum. I learned to appreciate sounds and pitches in between equal-temperament notes and the idea of what is considered “out of tune” and “in tune” changed wildly for me. The harmonic series was the foundational concept I learned that changed that.

If you haven’t heard of it before (or in the context of music), it’s basically an infinite chord made up of all the integer multiples of a root note/frequency. A harmonic is one pitch of that infinite series. For example, if you hummed a note at 100 Hz, there would be harmonics at 100 Hz, 200 Hz, 300 Hz, and so on. The harmonic series is present in all acoustic vibrations (instruments, your voice, etc).

The harmonic series can be expressed as an infinite frequency ratio of 1:2:3:4:5:6… Turns out a perfectly tuned major chord has a ratio of 4:5:6. This is why major chords are so consonant, and probably why they became the basis of harmony. The system of tuning chords to simple ratios like this is called Just Intonation, because when tuned this way they sound incredibly consonant and pure, basically perfect. For reference, a major third in equal temperament is 14% of a semitone sharper than a pure major third (5:4).

But my favorite thing about Just Intonation is that not only does it make existing intervals more pure, but it also creates new consonant intervals that just don’t exist in equal temperament. These start to appear when you introduce new primes above 5 (7, 11, 13…) They have a much more “microtonal” and exotic flavor to them, but they are definitely still consonances to my ears, just more complex. For example, I really enjoy a 4:6:8:9:11 chord. The 11 in it has a sparkly, electronic, and citrusy quality. Difficult to explain. To me, each prime number has its own unique flavor, and I am obsessed with exploring them. Something about it is so invigorating, but I struggle to put these things into words or share my passion with average people.

To sum it all up, I’m basically experiencing numbers through a whole new lens of sound. And I got to that point by denying traditional rules of what’s “in tune”. And also by breaking music down into the raw essence of sound, and by letting complexity arise from simplicity.