3072edo: Difference between revisions

Line 1:

~~'''3072EDO'''~~ is the [[~~EDO~~|~~equal division of the octave~~]] ~~into 3072 parts of exact 0.390625 cents each~~, ~~which is to say~~ 2~~(~~1/~~3072)<~~/~~sup> as a frequency ratio~~. ~~Its adjacent~~ step is known as '''Octamu''' (eighth MIDI-resolution unit, 8mu, 28 = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and 5 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.

~~==Intervals==~~

==Theory==

3072EDO is consistent to the [[11-limit]], tempering out |37 25 -33> (whoosh) and |161 -84 -12> ([[Kirnberger's atom|atom]]) in the 5-limit; 250047/250000, |-2 -25 1 14>, and |-53 -1 9 12> in the 7-limit; 9801/9800, 151263/151250, 184549376/184528125, and 73525096183/73466403840 in the 11-limit.

3072edo is consistent to the [[11-limit]], tempering out {{monzo|37 25 -33}} (whoosh) and {{monzo|161 -84 -12}} ([[Kirnberger's atom|atom]]) in the 5-limit; 250047/250000, {{monzo|-2 -25 1 14}}, and {{monzo|-53 -1 9 12}}; in the 7-limit; 9801/9800, 151263/151250, 184549376/184528125, and 73525096183/73466403840 in the 11-limit.

=== Significance in digital audio software ===

3072edo's step is known as '''Octamu''' (eighth MIDI-resolution unit, 8mu, 28 = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and 5 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.

==See also==

*[[Equal-step tuning|Equal multiplications]] of MIDI-resolution units

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''3072EDO''' is the [[EDO|equal division of the octave]] into 3072 parts of exact 0.390625 cents each, which is to say 2<sup>(1/3072)</sup> as a frequency ratio. Its adjacent step is known as '''Octamu''' (eighth MIDI-resolution unit, 8mu, 2<sup>8</sup> = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or &minus;) showing the direction of the pitch-bend up or down, and 5 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.
+{{EDO intro|3072}}
-==Intervals==
+==Theory==
-EDO is consistent to the [[11-limit]], tempering out |37 25 -33&gt; (whoosh) and |161 -84 -12&gt; ([[Kirnberger's atom|atom]]) in the 5-limit; 250047/250000, |-2 -25 1 14&gt;, and |-53 -1 9 12&gt; in the 7-limit; 9801/9800, 151263/151250, 184549376/184528125, and 73525096183/73466403840 in the 11-limit.
+edo is consistent to the [[11-limit]], tempering out {{monzo|37 25 -33}} (whoosh) and {{monzo|161 -84 -12}} ([[Kirnberger's atom|atom]]) in the 5-limit; 250047/250000, {{monzo|-2 -25 1 14}}, and {{monzo|-53 -1 9 12}}; in the 7-limit; 9801/9800, 151263/151250, 184549376/184528125, and 73525096183/73466403840 in the 11-limit.
+=== Significance in digital audio software ===
+edo's step is known as '''Octamu''' (eighth MIDI-resolution unit, 8mu, 2<sup>8</sup> = 256 equal divisions of the [[12edo]] semitone). The internal data structure of the 8mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or &minus;) showing the direction of the pitch-bend up or down, and 5 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.
 ==See also==
 *[[Equal-step tuning|Equal multiplications]] of MIDI-resolution units