46032edo: Difference between revisions

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'''46032EDO''' is the [[EDO|equal division of the octave]] into 46032 parts of exactly 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.

In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo| 161 -84 -12 }} as well as {{monzo| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 ~~FLUs~~, and the Pythagorean comma, 531441/524228, to 900 ~~FLUs~~. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 ~~FLUs~~, which is the measure in ~~FLUs~~ of the schisma, 32805/32768.

When used as an [[interval size unit]], 46032edo's step size is called a '''flu''' (from ''FLU'', "five-limit unit"), in terms of which the [[cent]] is approximately 38.36 flus. The FLU is useful when crafting irregular or [[circulating temperament]]s with twelve notes to the octave with an eye to its [[5-limit]] approximations.

== Theory ==

In the 5-limit, the 46032 division tempers out [[Kirnberger's atom]], {{monzo| 161 -84 -12 }} as well as {{monzo| 454 427 -487 }}. It maps the [[syntonic comma]], 81/80, to 825 flus, and the [[Pythagorean comma]], 531441/524228, to 900 flus. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 flus, which is the measure in flus of the schisma, 32805/32768.

46032edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size.

[[~~Category:Equal divisions of the octave|#####~~]] ~~~~

=== Prime harmonics ===

== External links ==

* [http://tonalsoft.com/enc/f/flu.aspx flu] on [[Tonalsoft Encyclopedia]]

[[Category:Atomic]]

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 {{Infobox ET}}
-'''46032EDO''' is the [[EDO|equal division of the octave]] into 46032 parts of exactly 0.02606882 cents each. This creates the unit known as the '''FLU''' (five-limit unit), in terms of which the cent is precisely 38.36 FLUs. The FLU is useful when crafting irregular or circulating temperaments with twelve notes to the octave with an eye to its 5-limit approximations.
+{{ED intro}}
-In the 5-limit the 46032 division tempers out [[Kirnberger's atom]], {{monzo| 161 -84 -12 }} as well as {{monzo| 454 427 -487 }}. It maps the syntonic comma, 81/80, to 825 FLUs, and the Pythagorean comma, 531441/524228, to 900 FLUs. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 FLUs, which is the measure in FLUs of the schisma, 32805/32768.
+When used as an [[interval size unit]], 46032edo's step size is called a '''flu''' (from ''FLU'', "five-limit unit"), in terms of which the [[cent]] is approximately 38.36 flus. The FLU is useful when crafting irregular or [[circulating temperament]]s with twelve notes to the octave with an eye to its [[5-limit]] approximations.
+== Theory ==
+In the 5-limit, the 46032 division tempers out [[Kirnberger's atom]], {{monzo| 161 -84 -12 }} as well as {{monzo| 454 427 -487 }}. It maps the [[syntonic comma]], 81/80, to 825 flus, and the [[Pythagorean comma]], 531441/524228, to 900 flus. Both of these are composite numbers divisible by 3 and 5, which is convenient for the purpose of twelve-note tempering, and 825/11 = 900/12 = 75 flus, which is the measure in flus of the schisma, 32805/32768.
 edo marks the [[optimal patent val]] for [[Very high accuracy temperaments #Atomic|atomic]] in the 5-limit. The size of the atom, however, does exceed half of the edostep's size.
-[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
+=== Prime harmonics ===
+{{Harmonics in equal|46032}}
+== External links ==
+* [http://tonalsoft.com/enc/f/flu.aspx flu] on [[Tonalsoft Encyclopedia]]
 [[Category:Atomic]]