800/729
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Ratio | 800/729 |
Factorization | 2^{5} × 3^{-6} × 5^{2} |
Monzo | [5 -6 2⟩ |
Size in cents | 160.89742¢ |
Names | diptolemaic major second, supersharp comma |
Color name | sayoyo 2nd, syy2 |
FJS name | [math]\text{M2}^{5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 19.1536 |
Weil height (log_{2} max(n, d)) | 19.2877 |
Wilson height (sopfr (nd)) | 38 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.22847 bits |
Comma size | large |
open this interval in xen-calc |
The diptolemaic major second is a 5-limit interval measuring about 161 ¢. It is the difference between 27/20 and 40/27, as well as 9/8 lowered by two syntonic commas.
Temperaments
If used as a comma to be tempered out, this interval may be called the supersharp comma, and tempering it out leads to the rank-2 supersharp temperament, which splits the octave into two 27/20~40/27 semioctaves and generally tempers 3/2 very sharp (sharper than 3\5).
Etymology
The name supersharp has been around no later than 2010^{[1]}, coming from the fact that a very sharp fifth is a generator for the temperament.
Tristan Bay proposes the name la brea in August 2024 in reference to the taric mos scale pattern that can be formed from tempering it out.