source file: m1589.txt Date: Sat, 21 Nov 1998 13:02:38 -0500 Subject: Persistant dispersal chain tunings From: Daniel Wolf At one stage in the development of his metricity parameter Klarenz Barlo needed a quasi-random chain of numbers to contrast with the highest metricity value. He needed a chain so that it could be used to generate ostinati that would be sustained through changes of metre, thereby requiring as many members as there would be attacks in each member. The series should also be quasi-random in that it maintained a equal distribution throughout the measure. This meant that the first two terms would each be distributed in the two halves of the available range, the first three terms in each third of the range, the first four in each fourth, etc.. Curiously, Barlowe needed a chain of eighteen members, but = he was unaware of contemporary research among Ramsey theorists who found tha= t the largest such chain could have only seventeen members. Not being able = to find a chain of more than twelve members at the time, Barlough was forced= to utilize other means to determine metricity in his 'autobus' pieces. = The composer and mathematician David Feldman has posted a complete list o= f these chains, each term of which is notated as a range between two fractional values. These are available at http://www.math.unh.edu/~dvf Although Barhloch orginally intended these series for generating metrical= attacks, anyone working with frequency ratios will soon recognize somethi= ng vaguely familiar - i.e. ratios well-distributed within an octave. Taking one of the longer chains at random, and then assigning a freshman sum rat= io to each term, one can construct collections of pitches which grow in surprising ways while maintaining their distribution within the octave. I= n particular, I have worked with a tuning parameter whose extreme values ar= e derived on one hand from the harmonic series and on the other hand from such a chain. While all of the materials used are just, the resultant collections are often tonally ambiguous, but that's okay since I remain -= - as always -- ambiguous about tonality. = Daniel Wolf =