800/729

Interval information

Ratio	800/729
Factorization	25 × 3-6 × 52
Monzo	[5 -6 2⟩
Size in cents	160.8974¢
Names	diptolemaic major second, supersharp comma
Color name	sayoyo 2nd, syy2
FJS name	[math]\displaystyle{ \text{M2}^{5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	19.1536
Weil norm (log2 max(n, d))	19.2877
Wilson norm (sopfr(nd))	38
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 (by more than 20¢). This means that five generators from the Zarlino generator sequence starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit extension adds 50/49 to the comma list, taking advantage of the existing semioctave.

Etymology

The name supersharp has been around no later than 2010, 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.