402653184edo: Difference between revisions
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| text = '''This page presents a primarily software-related tuning.''' | |||
Since 128 notes equal 2 | This tuning is more notable for use in [[software]] rather than for its musical properties. | ||
| icon = Information icon.svg | |||
| icon size = 40px | |||
}} | |||
'''402,653,184edo''' is an [[equal-step tuning|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 2<sup>7</sup>, this leaves 25 additional bits for further subdivision of the 12-tone equal temperament. By calculating 12 × 2<sup>25</sup>, we arrive at a system with 402,653,184 equally spaced divisions of the octave. | |||
It could be applied through the [https://amei.or.jp/midistandardcommittee/MIDI2.0/MIDI2.0-DOCS/M2-104-UM_v1-0_UMP_and_MIDI_2-0_Protocol_Specification.pdf#page=34 7.25 pitch attribute] introduced in MIDI 2.0. | It could be applied through the [https://amei.or.jp/midistandardcommittee/MIDI2.0/MIDI2.0-DOCS/M2-104-UM_v1-0_UMP_and_MIDI_2-0_Protocol_Specification.pdf#page=34 7.25 pitch attribute] introduced in MIDI 2.0. | ||
The step size is about 2.98 × 10 | The step size is about 2.98 × 10<sup>-6</sup> cents, meaning that intervals rounded to this system have a precision of 1.49 × 10<sup>-6</sup> cents. At 20000 Hz, the phase precision is approximately 16 hours. | ||
[[Category:Equal divisions of the octave]] | |||
Latest revision as of 22:36, 10 August 2025
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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.