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.

'''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 2^7, 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 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 [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^-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.

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.

[[Category:Equal divisions of the octave]]

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-{{niche}}
+{{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.
+'''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 2^7, 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<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.
-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.
+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]]