Kirnberger's atom: Difference between revisions
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'''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 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)<sup>12</sup> / 2<sup>7</sup> = 2<sup>161</sup> 3<sup>-84</sup> 5<sup>-12</sup>, 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)<sup>12</sup> / 2<sup>7</sup> = 2<sup>161</sup> 3<sup>-84</sup> 5<sup>-12</sup>, Kirnberger's atom. | ||
== Temperament == | == Temperament == | ||
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[[Category:Atomic]] | [[Category:Atomic]] | ||
[[Category:Kirnberger]] | |||
Revision as of 11:27, 3 January 2024
| Interval information |
reduced subharmonic
Kirnberger's atom, is a 5-limit unnoticeable comma. It is the difference between the syntonic comma and a stack of eleven schismas; [161 -84 -12⟩ in monzo and 0.01536093 cents 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)12 / 27 = 2161 3-84 5-12, Kirnberger's atom.
Temperament
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 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.