6000000edo: Difference between revisions

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The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.

While this system is absurdly large for any human application, from a technical standpoint it is the ~~only one~~ that rightfully bears the name [[Microtonal|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts.

While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[Microtonal|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable. (The factorization of 11769898 is 2 * 7<sup>2</sup> * 83 * 1447.)

This title can be contested by 1000000ed9/8, approx. 5884949edo, if a "tone" is defined to be a just [[9/8]] interval instead of an octave fraction.

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 The '''6 million divisions of the octave,''' or '''literal microtonal system,''' divides the 2/1 into steps of exactly 0.0002 cent, or 200 microcent each.
-While this system is absurdly large for any human application, from a technical standpoint it is the only one that rightfully bears the name [[Microtonal|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts.
+While this system is absurdly large for any human application, from a technical standpoint it is one of the few that rightfully bears the name [[Microtonal|'''microtonal''']], since it divides a tone, which is 1/6th of an octave, into 1'000'000 steps, and the SI prefix "micro-" denotes division of a unit into 1 million parts. If we instead take a tone to be [[9/8]], we get 5884949edo, which has an almost perfectly off [[3/2]] so that its double, 11769898edo, may be reasonable. (The factorization of 11769898 is 2 * 7<sup>2</sup> * 83 * 1447.)
 This title can be contested by 1000000ed9/8, approx. 5884949edo, if a "tone" is defined to be a just [[9/8]] interval instead of an octave fraction.