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.
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 18-edo (or 18-tET) 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 , and Ivor Darreg, who refretted guitars to this system and wrote many pieces using it.
The term "third-tone" is also often used loosely to express one degree, and the basic "step" size, of 19-edo (or 19-tET), which is ratio 1 : ~1.037155044 = exactly 63 3/19 cents.
Any musical interval in the neighborhood of 67 cents (¢). The 28/27 (63¢) is a typical [just] third tone.
The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.