Kirnberger's atom: Difference between revisions

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'''Kirnberger's atom''', is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]]. It is the difference between the [[81/80|syntonic comma]] and a stack of eleven [[32805/32768|schismas]]~~; {{monzo| 161 -84 -12 }} in~~ [[~~monzo~~]] and ~~0.01536093 [[cent]]s in size~~.

'''Kirnberger's atom''' ({{monzo|legned=1| 161 -84 -12 }}), is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]], 0.01536093 [[cent]]s in size. It is the difference between the [[81/80|syntonic comma]] and a stack of eleven [[32805/32768|schismas]], between the [[Pythagorean comma]] and a stack of twelve schismas, or equivalently, between twelve syntonic commas and eleven Pythagorean commas.

[[16384/10935|Kirnberger's fifth]], which is the perfect fifth of [[3/2]] flattened by a [[schisma]], is practically identical to seven steps of [[12edo]], which realizes a rational intonation version of the equal temperament. Kirnberger's atom arises as the tiny interval by which twelve of Kirnberger's fifths exceed seven [[octave]]s, (16384/10935)<sup>12</sup>/2<sup>7</sup>.

== Temperaments ==

Kirnberger's atom is [[tempering out|tempered out]] in such notable edos as {{EDOs| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, and 46032 }}, leading to the [[Very high accuracy temperaments #Atomic|atomic temperament]], in which eleven schismas make up a syntonic comma and twelve schismas make up a [[Pythagorean comma]]; any tuning system ([[41edo]], for example) which the number of divisions of the octave is not multiple of 12 cannot be tempering out ~~the~~ Kirnberger's atom.

Kirnberger's atom is [[tempering out|tempered out]] in such notable edos as {{EDOs| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, and 46032 }}, leading to the [[Very high accuracy temperaments #Atomic|atomic temperament]], in which eleven schismas make up a syntonic comma and twelve schismas make up a [[Pythagorean comma]]; any tuning system ([[41edo]], for example) which the number of divisions of the octave is not multiple of 12 cannot be tempering out Kirnberger's atom.

== Approximation ==

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[[Category:Atomic]]

[[Category:Kirnberger]]

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

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-'''Kirnberger's atom''', is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]]. It is the difference between the [[81/80|syntonic comma]] and a stack of eleven [[32805/32768|schismas]]; {{monzo| 161 -84 -12 }} in [[monzo]] and 0.01536093 [[cent]]s in size.
+'''Kirnberger's atom''' ({{monzo|legned=1| 161 -84 -12 }}), is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]], 0.01536093 [[cent]]s in size. It is the difference between the [[81/80|syntonic comma]] and a stack of eleven [[32805/32768|schismas]], between the [[Pythagorean comma]] and a stack of twelve schismas, or equivalently, between twelve syntonic commas and eleven Pythagorean commas.
 [[16384/10935|Kirnberger's fifth]], which is the perfect fifth of [[3/2]] flattened by a [[schisma]], is practically identical to seven steps of [[12edo]], which realizes a rational intonation version of the equal temperament. Kirnberger's atom arises as the tiny interval by which twelve of Kirnberger's fifths exceed seven [[octave]]s, (16384/10935)<sup>12</sup>/2<sup>7</sup>.
 == Temperaments ==
-Kirnberger's atom is [[tempering out|tempered out]] in such notable edos as {{EDOs| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, and 46032 }}, leading to the [[Very high accuracy temperaments #Atomic|atomic temperament]], in which eleven schismas make up a syntonic comma and twelve schismas make up a [[Pythagorean comma]]; any tuning system ([[41edo]], for example) which the number of divisions of the octave is not multiple of 12 cannot be tempering out the Kirnberger's atom.
+Kirnberger's atom is [[tempering out|tempered out]] in such notable edos as {{EDOs| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, and 46032 }}, leading to the [[Very high accuracy temperaments #Atomic|atomic temperament]], in which eleven schismas make up a syntonic comma and twelve schismas make up a [[Pythagorean comma]]; any tuning system ([[41edo]], for example) which the number of divisions of the octave is not multiple of 12 cannot be tempering out Kirnberger's atom.
 == Approximation ==
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 [[Category:Atomic]]
 [[Category:Kirnberger]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]