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Chart by Elliot Cole

Tuning the Ear

Tuning the Ear is an ear-training book that develops listening skills through the practice of just intonation, approaching tuning as both a perceptual experience and a concrete musical system grounded in ratio-based harmonic relationships. Through guided exercises, analytical examples, and clear conceptual frameworks, the book trains readers to hear beating, resultant tones, and interval color while engaging directly with the practical realities of 7-limit just intonation—including ratio thinking, commas, and modal organization. By integrating listening, calculation, and creative application, Tuning the Ear presents just intonation as a living practice in which theory and ear inform one another, offering performers, composers, and curious listeners a practical path toward deeper musical awareness.

Tuning the Ear Excerpt

Tools

Alex Van Gils – JIAVG

Elliot Cole – the Tuning Lattice

Elliot Cole – the Tuning Lattice Tuner

Elliot Cole – the Tuning Lattice Overtone Calculator

Robin Hayward – Hayward Tuning Vine

Tom Mudd – Just Intonation Toolkit

Thomas Nicholson (in collaboration with Marc Sabat and Rafał Rawicki) – Harmonic Space Calculator

Alexander Garsden– Erv’s Spiral

Difference Tone Demonstrations

Coming Soon!

Addendums

On Page 3, Partch's gamut is incorrectly listed as 53-tones. It is supposed to say 43 tones-per-octave. This typo was copied to the footnote as well, my apologies.

© 2026 by Alec Goldfarb

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