800/729

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
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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, 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.