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.

Notes

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.