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]]; {{ | '''Kirnberger's atom''', is a [[5-limit]] [[unnoticeable 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 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)< | 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)<sup>12</sup> / 2<sup>7</sup> = 2<sup>161</sup> 3<sup>-84</sup> 5<sup>-12</sup>, 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. | == Temperament == | ||
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 #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. | |||
== See also == | |||
* [[Unnoticeable comma]] | |||
[[Category:5-limit]] | [[Category:5-limit]] | ||
[[Category:Unnoticeable comma]] | [[Category:Unnoticeable comma]] | ||
[[Category:Atomic]] | |||