Why music should use 31 tones per octave -- and how to get started

Almost all music in the world uses a system called Twelve Tone Equal Temperament (12ET), which divides the octave into 12 equally sized pieces. Thirty-One Tone Equal Temperament (31ET) would be preferable, as various people have tried to explain to the world's reluctant musicians. 12ET represents a historical compromise between harmonic justice, key-changing convenience, and mechanical feasibility. 31ET offers greater harmonic justice: it allows musicians to come closer to the harmonic "truth" that motivated 12ET in the first place. Changing key in 31ET is no more difficult than doing so in 12ET, and the variety of harmonic structures 31ET offers is immensely greater. 31ET has been available for a long time for stringed instruments. With the recent advent of two-dimensional grid controllers, keyboardists can now use it too.

The first section, Harmonic Justice, explains the origins of 12ET, and why 31ET outdoes it. The argument relies largely on simple audio comparisons -- no mathematical understanding is required. (Numbers will appear, but most of them can be safely ignored.) After justifying the switch, the second second, Getting Started, offers suggestions I think will be helpful for musicians trying out this new environment: appropriate hardware and software, how to hack a conventional synth so that it works in 31ET, and how to translate the music you already know in 12ET into the 31ET system.

Someday I mgiht address the second argument in favor of 31ET, that it offers a variety of melodic and harmonic possibilities vastly wider than 12ET, is one I can only begin to make. It's a space I only started exploring a couple years ago, and doing a thorough job would occupy several lifetimes. If I write something along those lines, it will appear in the last section, Music Theory for 31ET.

Read the full document at msu.edu


04 September 2011

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