Countercentisma
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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 | 2-1 × 3-3300 × 52700 × 11-300 |
| Monzo | [-1 -3300 2700 0 -300⟩ |
| Size in cents | 0.14186985¢ |
| Name | countercentisma |
| Special properties | reduced |
| Tenney height (log2 nd) | 12538.4 |
| Weil height (log2 max(n, d)) | 12538.4 |
| Wilson height (sopfr(nd)) | 26702 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.1984 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
The countercentisma is an 11-limit unnoticeable comma which is the difference between 300 4-cent commas and the octave. Tempering out this comma results in the countercentismic temperament in the full 11-limit or the countercentic temperament in the 2.3.5.11 subgroup, which are both extreme microtemperaments that make the 4-cent comma (which is 4.0004729 cents) exactly 4 cents or 1 step of 300edo. The comma was named by CompactStar in 2024 because it is analogous to the centisma also named by him, which equates 17/12 to exactly 603 cents and 289/288 (the semitonisma or septendecimal 6-cents comma) to exactly 6 cents.