402653184edo

This page presents a primarily software-related tuning. This tuning is more notable for use in software rather than for its musical properties.

402,653,184edo is an equal-step tuning system that allows for finer subdivisions within the standard 128-note MIDI scale based on 12edo, using 32-bit data.

Since 128 notes equal 2⁷, this leaves 25 additional bits for further subdivision of the 12-tone equal temperament. By calculating 12 × 2²⁵, we arrive at a system with 402,653,184 equally spaced divisions of the octave.

It could be applied through the 7.25 pitch attribute introduced in MIDI 2.0.

The step size is about 2.98 × 10^-6 cents, meaning that intervals rounded to this system have a precision of 1.49 × 10^-6 cents. At 20000 Hz, the phase precision is approximately 16 hours.