Nadir comma

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Interval information
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{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.