Equilibrate [13edo Microtonal Ambient Music]

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This track is a relatively simple exploration into the weird world of 13 equal temperament, taking the regular 12 tones and adding in another one, while squishing each interval down slightly. Melodically, it can function similarly to 12edo as long as small steps are used, with a slightly flat semitone and a fairly accurate 10/9 (and thus 9/5) that feels like a flat version of the whole tone (and its inversion, the minor seventh) of 12edo. 13edo also has a convincing, albeit flat 5/4 major third (and thus also a sharp 8/5 minor sixth that is enharmonic with 13/8). However, that's where the similarities end.

Yep, 13edo has no fourth or fifth, making for bizarre melodies involving larger intervals and chord progressions. Its closest approximation to the fifth (3/2) and fourth (4/3) are out by 36.5 cents, more than a third of a semitone, making them almost entirely unrecognizable. Interestingly enough, that doesn't stop us using diatonic chords.

Often in jazz (and styles borrowing from jazz), chords will be played with many extensions, including the seventh, ninth, eleventh, thirteenth and so on. The fifth can sometimes be dropped entirely, as the root is reinforced more than enough by the extensions to make a complete feeling chord without it. This technique is easily applicable to make familiar sounding chords here, as 13edo has a very accurate minor seventh and viable major ninth, not to mention the many bonus chord extensions available including the 11th and 13th harmonics (11/8 and 13/8) as well as 11/10, 13/10 and 13/9, tempered with other intervals to make chord progressions surprisingly interesting and consonant while also feeling a bit warped. It seems to be that many composers, myself included, take the default major chord to be 4:5:9 in 13edo, a major add9 chord with the fifth dropped out, rather than the usual 4:5:6 in 12edo. This seems to work quite well, using the 'fifth of the fifth' to emulate the power the fifth creates.

13edo definitely has an inharmonic sound to it a lot of the time due to the absence of the many simpler frequency ratios, and lends itself well to more shimmery inharmonic timbres such as the steel pans I used here, but can also work with strongly harmonic timbres (like the bassline) if used carefully. Instagram: www.instagram.com/xotlamusic/