Nadir comma
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Ratio | 1162261467/1048576000 |
Factorization | 2^{-23} × 3^{19} × 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 (log_{2} nd) | 60.0801 |
Weil height (log_{2} max(n, d)) | 60.2286 |
Wilson height (sopfr (nd)) | 118 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.2107 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.