3rd-tone, third-tone, 1/3-tone

• 1. Used in a general sense, approximately 1/3 of a whole tone.

  One of the most famous instances of the application of the idea of 1/3-tones in music-theory is in the calculation of the 'relaxed chromatic genus' of the ancient Greek theorist Aristoxenus.

  
  

• 2. Calculated as the 18th root of 2, or 2^(1/18), an irrational proportion with the approximate ratio of 1 : 1.039259226032, and an interval size of exactly 66 ²/₃ cents.

  It is the size of one degree, and thus the basic "step" size, in the 18edo (or 18tET) scale, also called the "third-tone scale" or system.

  Two of the most famous advocates of this system were Ferrucio Busoni, in his Sketch for a New Aesthetic of Music [1907], and Ivor Darreg, who refretted guitars to this system and wrote many pieces using it.

  
  

• 3. The term "third-tone" is also often used loosely to express one degree, and the basic "step" size, of 19edo (or 19tET), which is ratio 1 : ~1.037155044 = exactly 63 ³/₁₉ cents.

  
  [from Joe Monzo, JustMusic: A New Harmony]

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  Any musical interval in the neighborhood of 67 cents (¢).

  The 28/27 (63¢) is a typical [just] third tone.

  [from John Chalmers, Divisions of the Tetrachord]

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updated:

2002.09.14 - added info on 19edo and a few new links
2000.01.13

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