800/729
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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
| Interval information |
supersharp comma
(Shannon, [math]\sqrt{nd}[/math])
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.