402653184edo: Difference between revisions
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402,653,184-EDO is an [[Equal-step tuning|equal-step]] tuning system that allows for finer subdivisions within the standard 128-note [[MIDI]] scale based on [[12edo|12-EDO]], using 32-bit data. | {{niche}} | ||
'''402,653,184-EDO''' is an [[Equal-step tuning|equal-step]] tuning system that allows for finer subdivisions within the standard 128-note [[MIDI]] scale based on [[12edo|12-EDO]], using 32-bit data. | |||
Since 128 notes equal 2^7, this leaves 25 additional bits for further subdivision of the 12-tone equal temperament. By calculating 12 * 2^25, we arrive at a system with 402,653,184 equally spaced divisions of the octave. | Since 128 notes equal 2^7, this leaves 25 additional bits for further subdivision of the 12-tone equal temperament. By calculating 12 * 2^25, we arrive at a system with 402,653,184 equally spaced divisions of the octave. | ||
Revision as of 03:32, 18 March 2025
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402,653,184-EDO is an equal-step tuning system that allows for finer subdivisions within the standard 128-note MIDI scale based on 12-EDO, using 32-bit data.
Since 128 notes equal 2^7, this leaves 25 additional bits for further subdivision of the 12-tone equal temperament. By calculating 12 * 2^25, 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.