23 minutes ago
If you know much about Ben's Third Quartet, you know it works its way measure by measure through a 53-note microtonal scale. The finale of the Seventh is built on a similar plan, but the structural tone row consists of 176 pitches - all different, 176 pitches within one octave, heard in the viola on each successive downbeat. Many other notes are heard in the other instruments whose harmonies link each note to the next, and Tim tells me that altogether there are more than 1200 discrete pitches in the movement - more than one per cent, five times as many as most people can perceive.
Tim demonstrated how the players are supposed to proceed from the opening C to the subsequent D7bv-, a pitch ratio of 896/891. The violist is tasked to move upward from this C and come back down on a pitch 9.7 cents higher - just under one tenth of a half-step - than she started on. At the downbeat of the next measure, the violist lands on Dbb--, pitch ratio 2048/2025 - another ten cents higher. And so on for another 175 measures until the viola ends up traversing the octave and ends at C again. A good half of Tim's paper was spent talking us through the performance challenges of the first two measures.