Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited

minor 3rd, minor third, m3


    An interval in the range of 300 cents (¢). Common minor thirds in Just Intonation are 6/5 (315¢), 19/16 (298¢) and the Pythagorean 32/27 (294¢).

    This interval is also called the "trihemitone" and "augmented second" in certain contexts.

    [from John Chalmers, Divisions of the Tetrachord]

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

    Some more precise values for the above are:

  • 6/5 = ~315.641287 (close to 315 5/8, closer to 315 9/14) cents.
  • 19/16 = ~297.5130161 (close to 297 1/2, closer to 297 20/39) cents.
  • 32/27 = ~294.1349974 (close to 294 1/7, closer to 294 5/37) cents.

    • The 7-limit ratio 7/6 is also known as the "subminor 3rd". It is ~266.8709056 (close to 266 7/8, or almost exactly 266 27/31) cents.

    Another type of "subminor 3rd" is the 5-limit ratio 75/64, which is ~274.5824286 (close to 274 7/12, almost exactly 274 53/91) cents.

    Successively closer small-integer rational approximations to the 12-EDO "minor 3rd" are: 

    
 ratio    ~cents

 13/11  289.2097194
 19/16  297.5130161
 25/21  301.8465204
 44/37  299.9739036 (less than 1/38 cent narrower than 2(3/12))

    [from Joe Monzo, JustMusic: A New Harmony]

Updated: 2001.11.6

(to download a zip file of the entire Dictionary, click here)

  • 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

    • I welcome feedback about this webpage:
    corrections, improvements, good links.
    Let me know if you don't understand something.

    return to the Microtonal Dictionary index
    return to my home page
    return to the Sonic Arts home page