6000000edo: Difference between revisions

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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.

~~== Theory ==~~

If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes. In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' [[mean free path]]'s width.

If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes.

Remarkably, it has a perfect fifth that differs from just by 1 part in 231, which ultimately derives from [[80000edo]]. In a twist of irony, it provides good approximations for the 2.3.17.19 [[subgroup]], which is typically associated with [[12edo]].

~~In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' [[mean free path]]'s width.~~

Remarkably, it has a perfect fifth that differs from just by 1 part in 231, which ultimately derives from [[80000edo]].

In a twist of irony, it provides good approximations for the 2.3.17.19 [[subgroup]], which is typically associated with [[12edo]].

=== Prime harmonics ===

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 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.
-== Theory ==
+If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes. In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' [[mean free path]]'s width.
-If the starting note is Middle C, one step of this tuning would have a beating period of 33086 seconds, or more than 9 hours. At 20 kHz, the extreme end of human range, the period of the wahwah caused by two similar frequencies is still more than 7 minutes.
+Remarkably, it has a perfect fifth that differs from just by 1 part in 231, which ultimately derives from [[80000edo]]. In a twist of irony, it provides good approximations for the 2.3.17.19 [[subgroup]], which is typically associated with [[12edo]].
-In order to hypothetically make any use of this system, humans would have to hear sounds as high pitched as 140 MHz. At this point, it is already just 36 air molecules' [[mean free path]]'s width.
-Remarkably, it has a perfect fifth that differs from just by 1 part in 231, which ultimately derives from [[80000edo]].
-In a twist of irony, it provides good approximations for the 2.3.17.19 [[subgroup]], which is typically associated with [[12edo]].
 === Prime harmonics ===