Niobium comma

This page presents a novelty topic. It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

Interval information

Factorization	2-875 × 3492 × 541
Monzo	[-875 492 41⟩
Size in cents	0.7226942¢
Name	niobium comma
FJS name	[math]\displaystyle{ - }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	1750
Weil height (log2 max(n, d))	1750
Wilson height (sopfr(nd))	3431
Comma size	unnoticeable
Open this interval in xen-calc

The niobium comma or alternately 41-atom (monzo: [-875 492 41⟩) is an unnoticeable 5-limit comma measuring about 0.7 cents. Tempering it out results in the rank-2 niobium temperament.

Temperaments

The niobium comma can be regarded as the 41st-octave counterpart of Kirnberger's atom. Just as Kirnberger's atom splits the octave into 12 equal parts, and its generator is the difference between the just and 12 tone tempered fifth, the niobium comma splits the octave into 41 parts, and the reduced generator is a tiny interval that stands for the difference between the most just and the 41edo-inherited fifth of temperaments supporting it.