Sqrt(2187/2048)

Interval information

Expression	[math]\displaystyle{ \sqrt{2187/2048} }[/math]
Size in cents	56.8425¢
Name	half-apotome semiaugmented unison
Special properties	reduced

sqrt(2187/2048), the half-apotome, or semiaugmented unison, is a radical interval of about 57 cents, in the sqrt(2).sqrt(3) subgroup or dicot (ploidacot) more precisely. It is a quartertone-like interval; differing from the smaller quartertone sqrt(256/243) by half a pythagorean comma. It is reached by +7 hemififths octave reduced, with a fractional monzo of [-11/2 7/2⟩.

In temperaments

The half-apotome can be made equal to many rational intervals, most notably, to 33/32, tempering out the rastma (243/242), or much more accurately to 1323/1280, tempering out the breedsma (2401/2400).

It is most often written in scores by a half-sharp, . However, this does not mean C = D always; D is a lower pitch than C. This antiintuitive notion is due to the fact that the apotome - an augmented unison - is wider than a minor second in Pythagorean tuning, and JI more generally. The equality holds true if and only if the pythagorean comma is tempered out.