Septimal quarter tone
A septimal quarter-tone (in music) is an interval with the ratio of 36:35 ( play (help·info)), which is the difference between the septimal minor third ( play (help·info)) and the Just minor third ( play (help·info)), or about 48.77 cents wide. The name derives from the interval being the 7-limit approximation of a quarter tone. The septimal quarter-tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a given tuning system, the distinction between the two different types of minor thirds is lost. The septimal quarter-tone may be derived from the harmonic series as the interval between the thirty-fifth and thirty-sixth harmonics.
Composer Ben Johnston uses a small seven ("") as an accidental to indicate a note is lowered 49 cents, or an upside-down seven ("") to indicate a note is raised 49 cents. The Maneri-Sims notation system designed for 72-et uses the accidentals and for a quarter-tone (36:35 or 48.77 cents) up and down.
The septimal quarter-tone is tempered out by twelve-tone equal temperament, but not in any of 19-TET, 22-TET, 24-TET, or 31-TET. 22-TET and 24-TET offer a very close match to the septimal quarter-tone.
- Douglas Keislar; Easley Blackwood; John Eaton; Lou Harrison; Ben Johnston; Joel Mandelbaum; William Schottstaedt. p.193. "Six American Composers on Nonstandard Tunnings", Perspectives of New Music, Vol. 29, No. 1. (Winter, 1991), pp. 176-211.
- "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", John Fonville, p.113, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106-137.