
About
Just Intonation
A musical harmony is 'just' when its two pitches vibrate in a simple whole-number ratio — 2:1 for an octave, 3:2 for a fifth, 5:4 for a major third. These proportions occur naturally in the overtone series of any vibrating string or column of air, and they are perceived as unusually pure and resonant: in Just Intonation, the harmonics of different notes reinforce each other rather than clash, producing a quality of stillness and depth that equal temperament cannot replicate.
The idea is ancient — Pythagoras described it in the sixth century BCE — and central to the classical music of India, where melody is built directly on the natural resonances of a drone. Western music largely abandoned pure tuning with the adoption of equal temperament, which divides the octave into twelve mathematically equal semitones, enabling free modulation at the cost of slightly mistuning every interval. Michael Harrison's work reclaims Just Intonation as a compositional foundation, building tuning systems in which the precise proportions between pitches determine not only harmony but structure, duration, and form.
Resources
The interactive Tuning Lattice is a tool for visualizing and hearing Just Intonation.
Tunings by Michael Harrison



Lattice diagrams created by Elliot Cole using tuninglattice.com.