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Harmonies: twelve audible music-theory visualizations by Luke Steuber
01
Circle of Fifths
Twelve keys around a ring, each a perfect fifth from the last. The anchor of the whole suite.
Circle of Fifths
02
Circle of Fifths · Keys
The same ring drawn as piano keys, lighting up as the chord moves.
Circle of Fifths · Keys
03
Circle of Thirds
The symmetric divisions of the octave: major and minor thirds as their own rings.
Circle of Thirds
04
Two Circles
Morph between the chromatic circle and the circle of fifths and watch the same twelve notes rearrange.
Two Circles
05
Tonnetz
The lattice of triads. Every triangle is a chord; the P, L and R moves slide you between them.
Tonnetz
06
Euclidean Rhythms
Spread k beats as evenly as possible across n steps and the world's folk rhythms fall out.
Euclidean Rhythms
07
The Spiral That Won't Close
Stack twelve pure fifths and they overshoot the octave by 23.46 cents: the Pythagorean comma.
The Spiral That Won't Close
08
Lissajous
Frequency ratios you can see as well as hear: figures of ratio, with a harmonograph mode.
Lissajous
09
Clapping Music
Steve Reich's twelve against twelve: two rings drifting through every alignment, then back home.
Clapping Music
10
Polyrhythm
Wheels within wheels: two tempos turning at once, meeting only at the downbeat.
Polyrhythm
11
Just Intonation
The pure lattice: whole-number ratios, the untempered Tonnetz that never quite closes.
Just Intonation
12
Orbifold
The shape of chords themselves: Tymoczko's twisted space where voice-leadings live.
Orbifold