800/729

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Interval information
Ratio 800/729
Factorization 25 × 3-6 × 52
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 (log2 nd) 19.1536
Weil height (log2 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.

Notes