Fractional Set Theory (April 3, 2008) -- a work in progress...

"Fractional set theory" is a term coined by composer Nolan Stolz during the introduction to the premiere of his brass trio Merritt, performed by the Yale Brass Trio at The Hartt School March 14, 2008.

Merritt uses [0, 3] [0, 2] [0, 1] and [0, 2.5] (the 2.5 being the interval between a major second and a minor third, creating a quarter-tone) Further rendering of the pitch material, Stolz generates the intervals of [0, .5] and [0, 1.5].

Stolz's Kaena Point (for violin, viola, 'cello and piano) uses microtones such as the 1/6 tone (about 31 cents flat), simulating just intonation, in this case, the natural 7th harmonic. For example, the notes C and B-flat (but 1/6 tone flatter) would be represented as [0 , 9.69] or simplified to [0, 2.31] The lowered minor seventh interval inverts into a raised major second. In the case of just intonation, the lowered minor seventh interval is in a 7:4 ratio, which when calculated into "cents" (100 cents being a "half-step"), is approximately 31 cents flatter than what the equal tempered minor seventh is.