Greetings! This summer, I’m going to explore microtonality and extended Just Intonation in multiple ways to expand understanding and accessibility of it to give musicians another level of intention and control in their composing, performance, and producing.
To explain how everything works, I need to discuss how sound works.
Sounds are typically a chaotic looking waveform such as the one on the left. However, all sounds can be decomposed into a sum of sine waves with different frequencies and amplitudes.
The frequency profile of all the sine waves is always the same. That is, the musical pitch/frequency (Hz) the sound is heard at is the frequency of the first sine wave, or the fundamental frequency. The next sine wave is twice the frequency of the fundamental, the next three times, and so on indefinitely. As the frequency gets higher, the volume/amplitude gets lower exponentially approaching zero. This mathematically geometric profile of frequencies is called the Harmonic Series.
The graphic above represents a sine wave as it would be seen on an oscillating string, much like a guitar. The extended Harmonic Series, using C2 as a fundamental, looks like this.
The red numbers are cents out of tune. This is a measurement that is on instrument tuners, used by musicians. Zero cents means that you are perfectly in tune. 50 or -50 cents means you are playing perfectly in between your intended note and the one above it. Negative means you’re flat, positive means you’re sharp. The important thing to note is that the current system of twelve geometrically equally spaced notes to be in tune with is limiting.
Performers often tune to the harmonic series, because that’s what we hear and what will sound more “in tune”. This practice is called intonation and commonly doesn’t go much farther than trusting one’s ear and routinely playing a note “flatter”. For practicality and playability, the 12 note system approximates the first few harmonics very closely allowing our ear to recognize the intention.
Microtonality is using notes outside of the common 12 to better approximate the intended harmony (Just Intonation), access new harmonies (extended Just Intonation), or simply create unfamiliar sounds. I should make clear there’s an assertion here that all harmony derives from the harmonic series. This is not true for all musicians, but is often what is relied upon.
I am going to use the Lumatone Isomorphic Keyboard to interact with these unfamiliar harmonies and compose with them depending on the harmonic series.
My initial intentions are going to be to try 24, 31, and 53, notes per octave, as opposed to the standard 12. This will serve to familiarize myself with the instrument and “stretch my ears” to these unfamiliar harmonies to eventually use them fluently in my compositions. Currently, my compositions are tuned to harmonic series intervals after post composing.
This has unveiled to me a lot about the intentions of the mechanisms taught to us in Western Music Theory classes, though current methods of notating for preservation can be tedious to write, cumbersome to read, and can be sparse enough to not fully understand months later without tracing steps.
To study these intended harmonic operations, I’m going to code a MIDI analyzer in Python. This program will translate the MIDI into matrices of Harmonic series relations for better processing. And to avoid some tedium, the program will tune the broad strokes if the MIDI isn’t tuned as intended.
The knowledge gained from analyses of harmonic patterns will influence my playing and composing. At some point, my composing will experiment with writing in terms of linear transformations of the harmonic matrices. In short, the matrices may hint at a better aid to notation than my current attempts.
Another goal is to be able to use this system for autotune. This will have the most impact in the industry for it can be enjoyed by producers of all levels of microtonal knowledge. I will mix and master MIDI compositions in Ableton.
Within Ableton, I will tune my music with Melodyne autotune for a proof of concept. The MIDI profile generated from my program will be plugged into Melodyne.
The end goal is that this can be done with live sound and vocals. We already use autotune, why not give the musicians more control over what is “in tune”?
Sincerely,
Peter Fasano
HSF House Blogs 