> > The Syntonic Comma is the amount short of an > >octave that you get when you tune 3 pure contiguous 3rds. That 21.5 cents > >(theoretical) difference, gap or shortfall is called the Comma. > > I must disagree. > A pure M3 is 386 cents wide. Three of these span a distance of 1158 cents. > An octave is 1200 cents wide. The difference between three Just > contiguous thirds and an octave is a diesis, and it is approx. 41 cents. > A syntonic comma is the difference between four just fifths and two Just > octaves. See Jorgensen, "Tuning", pg 777 > > Ed Foote RPT The difference between four just fifths, (702*4) and 2 octaves (1200*2) is the Pythagorean third, or 408 cents. It is the difference between this and the just third (386) or 21.5 cents that is the syntonic comma, sometimes called the comma of Didymus. Also the difference of three just thirds less than the octave is the "lesser diesis". The difference between 4 minor 3rds (over) the octave is the "greater diesis". 41.1 and 62.6 cents respectively. _New Groves_ "Temperaments" p 661. ---ric
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