Language Log post on AtD orthographic phonetics

[robinlandseadel at comcast.net]

Found this:

"The 'syntonic comma', also known as the 'comma of Didymus", is the difference between the major third created by four intervals of a perfect fifth (e.g. C,G,D,A,E) and the just interval of a major third, corresponding to the ratio 5/4. In decimal terms, 5/4 is obviously 1.25. A fifth in just intonation is the ratio 3/2. (3/2)4 = 81/16, which is two octaves (64/16) plus an interval 81/64, or 1.265625. The "syntonic comma" is (81/64)/(5/4) = 1.0125, which is about a quarter of a semitone. (An equally-tempered third -- 24/12 , or about 1.259921 -- roughly splits the difference.)

The ancients saw the syntonic comma as one of several troubling flaws in the design of the universe, another being the irrationality of the diagonal of a unit square. Though for some of the Pythagoreans, such things hinted at hidden messages..."




 -------------- Original message ----------------------
From: Prokopis Prokopidis <prokopis at ilsp.gr>
> The syntonic phonetics of Pynchon's pitchuhv
> <http://itre.cis.upenn.edu/~myl/languagelog/archives/004023.html#more>
>