Niobium comma
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| This page presents a novelty topic. It features ideas which are less likely to find practical applications in xenharmonic music. It may contain numbers that are impractically large, exceedingly complex, or chosen arbitrarily. Novelty topics are often developed by a single person or a small group. As such, this page may also feature idiosyncratic terms, notations, or conceptual frameworks. |
| Factorization | 2-875 × 3492 × 541 |
| Monzo | [-875 492 41⟩ |
| Size in cents | 0.72269423¢ |
| Name | niobium comma |
| FJS name | [math]-[/math] |
| Special properties | reduced, reduced harmonic |
| Tenney height (log2 nd) | 1750 |
| Weil height (log2 max(n, d)) | 1750 |
| Wilson height (sopfr(nd)) | 3431 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.2047 bits |
| 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.