Kirnberger's atom: Difference between revisions

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'''Kirnberger's atom''', is a [[5-limit]] [[unnoticeable comma]]. It is the difference between [[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 fifth, which is flattened the perfect fifth of [[3/2]] by a schisma is practically identical to seven steps of [[12edo]], which realizes a rational intonation version of the equal temperament. Twelve of Kirnberger's fifths of 16384/10935 exceed seven octaves by the tiny interval of (16384/10935)12 / 27 = 2161 3-84 5-12, Kirnberger's atom.

Kirnberger's fifth, which is flattened the perfect fifth of [[3/2]] by a schisma is practically identical to seven steps of [[12edo]], which realizes a rational intonation version of the equal temperament. Twelve of Kirnberger's fifths of 16384/10935 exceed seven octaves by the tiny interval of (16384/10935)12 / 27 = 2161 3-84 5-12, Kirnberger's atom.

Kirnberger's atom is tempered out in such notable EDOs as 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|temperament]] in which eleven schismas make up a syntonic comma and twelve schismas make up a [[531441/524288|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.

[[Category:Comma]]

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 '''Kirnberger's atom''', is a [[5-limit]] [[unnoticeable comma]]. It is the difference between [[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 fifth, which is flattened the perfect fifth of [[3/2]] by a schisma is practically identical to seven steps of [[12edo]], which realizes a rational intonation version of the equal temperament. Twelve of Kirnberger's fifths of 16384/10935 exceed seven octaves by the tiny interval of (16384/10935)<font style="vertical-align: super;">12</font> / 2<font style="vertical-align: super;">7</font> = 2<font style="vertical-align: super;">161</font> 3<font style="vertical-align: super;">-84</font> 5<font style="vertical-align: super;">-12</font>, Kirnberger's atom.
+Kirnberger's fifth, which is flattened the perfect fifth of [[3/2]] by a schisma is practically identical to seven steps of [[12edo]], which realizes a rational intonation version of the equal temperament. Twelve of Kirnberger's fifths of 16384/10935 exceed seven octaves by the tiny interval of (16384/10935)<font style="vertical-align: super;font-size: 0.8em;">12</font> / 2<font style="vertical-align: super;font-size: 0.8em;">7</font> = 2<font style="vertical-align: super;font-size: 0.8em;">161</font> 3<font style="vertical-align: super;font-size: 0.8em;">-84</font> 5<font style="vertical-align: super;font-size: 0.8em;">-12</font>, Kirnberger's atom.
 Kirnberger's atom is tempered out in such notable EDOs as 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|temperament]] in which eleven schismas make up a syntonic comma and twelve schismas make up a [[531441/524288|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.
 [[Category:Comma]]