Nadir comma
(Redirected from 1162261467/1048576000)
Jump to navigation
Jump to search
This page is a stub. You can help the Xenharmonic Wiki by expanding it.
| Ratio | 1162261467/1048576000 |
| Factorization | 2-23 × 319 × 5-3 |
| Monzo | [-23 19 -3⟩ |
| Size in cents | 178.20387¢ |
| Name | nadir comma |
| FJS name | [math]\text{A1}_{5,5,5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 60.0801 |
| Weil height (log2 max(n, d)) | 60.2286 |
| Wilson height (sopfr (nd)) | 118 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.56881 bits |
| Comma size | large |
| open this interval in xen-calc | |
1162261467/1048576000, the nadir comma, generates the nadir temperament. It has a melodic shape similar to porcupine or trimean, with a neutral second generator close to 11/10, three of which approximate 4/3. However, the best approximation to the 5th harmonic is both more complex and causes more damage to the other intervals, leaving it unused for actual composition so far. It is the furthest 5-limit temperament on the Syntonic-chromatic equivalence continuum that has patent vals other than 7edo, hence the name nadir. It was named by CompactStar.