Microtonal Music Composition
[WIP]
Microtonal music is music that uses intervals that are smaller than a traditional half step. In a nutshell, Microtonal music is made with sounds between the notes on a standard keyboard. For my MU2300 final project, I created one original song and made a cover of another song, both of which did not use the standard 12edo tuning.
Introduction
For starters, traditional Western music breaks down the octave into 12 equally spaced intervals. This tuning method is called twelve-tone equal temperament or 12TET, 12ET, or 12edo (equally divided octave). We call these twelve notes C, C♯/D♭, D, D♯/E♭, E, F, F♯/G♭, G, G♯/A♭, A, A♯/B♭, and B. The interval spanning two notes is called a whole step or a whole tone, and the interval spanning one note is called a half-step or a semitone. We use sharps (♯) and flats (♭) to denote differences of a half step. A traditional Western Major scale follows the interval pattern whole-whole-half-whole-whole-whole-half. For example, a C major scale is the pattern C, D, E, F, G, A, B, C.
22edo
Now, instead of breaking the octave into twelve equally spaced notes per octave, let’s break it into 22 equally spaced notes per octave.
Let's make new accidentals as well. "Up" and "down" can mean shifting the base note up or down by one step, respectively; "sharp" and "flat" can mean shifting up the base note up or down by one step, respectively. Then, we can combine these to make "sharp up", "sharp down", "flat up", and "flat down", which shift the base note by +4, +2, -2, and -4 steps, respectively.
| Symbol | Steps Up/Down |
|---|---|
| ♭↓ | -4 |
| ♭ | -3 |
| ♭↑ | -2 |
| ↓ | -1 |
| ♮ | 0 |
| ↑ | 1 |
| ♯↓ | 2 |
| ♯ | 3 |
| ♯↑ | 4 |
Now, the scale has these 22 notes: C, D♭/C↑, C♯↓/Db↑, C♯/D↓, D, E♭/D↑, D♯↓/Eb↑ D♯/E↓, E, F, G♭/F↑, F♯↓/G♭↑, F♯/G↓, G, A♭/G↑, G♯↓/A♭↑, G♯/A↓, A, B♭/A↑, A♯↓/B♭↑, A♯/B↓, and B.
Now that we have our note names, we can start composing music! Here's an etude I made in A↓ (A-down) minor.
Let’s split the semitone into 100 equally spaced steps, which we’ll call cents. Two notes a cent apart have a frequency ratio of 2^(1/1200):1, and there are 1200 cents in an octave.
Recall that music is fundamentally based on ratios of the harmonic series (1, 1/2, 1/3, 1/4, etc.) and that an octave has the frequency ratio of 2:1, a perfect fifth has a ratio of 3:2, and a perfect fourth has a ratio of 4:3. This method of tuning an instrument based on fundamental frequencies is called just intonation, or JI.
12edo splits the octave into twelve equal, irrational ratios of 12root2:1. A fifth (C to G) in 12edo has the ratio of 2^(7/12):1; this ratio is about 2 cents flat of the ratio 3:2. The harmonic seventh (C to B♭) has a ratio of 2^(5/6):1 in 12edo, which is 31 cents sharp of its just intonation counterpart, 7:4.