Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited




    Syntonic Comma

    • The syntonic comma is the most important of the musical commas for the notation of musical intervals. While the Pythagorean comma aids in the construction and analysis of tuning systems, the Syntonic comma defines the way thirds are notated in chords.

    • The syntonic comma is defined as the difference between a Pythagorean major third (made from the difference twixt 4 just 3/2 perfect fifths up and 3 octaves) and a 5/4 major third:

      [from Brian McLaren]

      . . . . . . . . . . . . . . . . . . . . . . . . . . .

      The ratio 81/80, in JustMusic prime-factor notation designated as 345-1, with an interval size of approximately 0.22 Semitones [= 21.506+ cents].

      It is the difference between the Pythagorean or 3-Limit "major 3rd" of approximately 4.08 Semitones [= 81/64 = 34 = 407.82+ cents] and the 5-limit so-called "just" "major 3rd" of approximately 3.86 Semitones [= 5/4 = 51 = 386.3137+ cents]. Also known as the Comma of Didymus, who was the first theorist to specify the use of 5/4 in music theory; frequently referred to simply as comma.

      [from Joe Monzo, JustMusic: A New Harmony]

      . . . . . . . . . . . . . . . . . . . . . . . . . . .

      A small interval whose ratio is 81/80 (20.5 cents [¢]).

      It is the difference between the Ditone and the ratio 5/4, the Major Third of Just Intonation.

      Also called the Comma of Didymos (latinized as Didymus).

      [from John Chalmers, Divisions of the Tetrachord]


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  • For many more diagrams and explanations of historical tunings, see my book.
  • If you don't understand my theory or the terms I've used, start here

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