3072edo: Difference between revisions
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==Theory== | ==Theory== | ||
3072edo is consistent to the [[11-limit]] and it is an extremely accurate 5-limit tuning, 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. | 3072edo is consistent to the [[11-limit]] and it is an extremely accurate 5-limit tuning, 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. | ||
Although consistent to the 11-limit, it makes more sense to actually see 3072edo as a 2.3.5.7.13 subgroup tuning, due to lower relative error. There it tempers out 140625/140608 and 1990656/1990625. In higher limits, it is not as impressive, with only [[53/32]] being 17% off and 2.3.5.67.71 subgroup having less than 4% error. | |||
=== Significance in digital audio software === | === Significance in digital audio software === | ||
3072edo'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 −) 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. | 3072edo'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 −) 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. | ||