6000000edo: Difference between revisions
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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 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. | ||
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. | 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, or other tuning between 5000000edo and 7000000edo. | ||
== Theory == | == Theory == | ||
Revision as of 13:46, 28 October 2021
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, 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.
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, or other tuning between 5000000edo and 7000000edo.
Theory
6'000'000 factorizes as [math]\displaystyle{ 2^7 \cdot 3 \cdot 5^6 }[/math]. It has 112 divisors, most notable being 128 and 3125.
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.