Kirnberger's atom
Factorization | 2^{161} × 3^{-84} × 5^{-12} |
Monzo | [161 -84 -12⟩ |
Size in cents | 0.015360929¢ |
Name | Kirnberger's atom |
FJS name | [math]\text{19d12}_{5,5,5,5,5,5,5,5,5,5,5,5}[/math] |
Special properties | reduced, reduced subharmonic |
Tenney height (log_{2} n⋅d) | 322 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.3983 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
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} / 2^{7} = 2^{161} 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.