Richard Guy <rkg@cpsc.ucalgary.ca> writes:

It IS known by some mathematicians. See p.257 of The Book of Numbers. But, lack-a-day, we define it as `the difference between 7 fifths and 4 octaves' whereas it should be `12 and 7'.

According to Margo Schulter's believable-sounding Usenet post (citing Boethius's _De Institutione Musica_ as translated by Calvin Bower in _Fundamentals of Music_), 2^8:3^5 is a limma or diesis or Pythagorean minor semitone, 3^7:2^11 is an apotome, 3^12:2^19 is the Pythagorean comma, 3^6:2^9.5 is a schisma, and 2^4:3^2.5 is a diaschisma. Dan Hoey@AIC.NRL.Navy.Mil