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 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. 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 {{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|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.

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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;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 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. 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 {{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|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.