Tuning Systems: Temperament and Just Intonation

Every synth defaults to 12-TET, so most live coders never hear how much tuning shapes a set: a sustained drone in just intonation locks into beatless purity that no equal-tempered pad can match, while a gamelan-flavored pattern in pelog simply cannot be played on the default grid. This module builds toward one whole task — a comparative tuning demo where the same chord progression is rendered in 12-TET, just intonation, a historical temperament, an alternative equal temperament, and a non-Western scale, with the differences quantified in cents. That deliverable is exactly what you need before committing to a tuning for a drone set, an ambient release, or a microtonal collaboration.

The arc starts supported: first drill the cent as a logarithmic measure until converting ratios to cents is automatic, then A/B a tempered fifth against a natural 3:2 fifth on sustained tones and hear the ~2-cent gap. From there, build the Pythagorean stack of fifths by hand and discover the comma that refuses to close — which motivates meantone and well temperaments as historical fixes with distinct key colors. Only then move to the sequencer: SuperCollider’s Pbind pitch hierarchy (stepsPerOctave and scale) is the JIT how-to for re-rendering the progression in 19-TET and pelog without rewriting any pitch logic.

The required atoms gate the capstone directly: without the cents unit there is no quantification; without the temperament atoms there is nothing to compare; without the Pbind tuning chain there is no re-render. The supporting atoms — the harmonic series, the 2:1 octave, the chromatic semitone grid — refresh the acoustic ground these systems are all negotiating with, deepening the demo without being needed to complete it.