2013 Joint Mathematics Meetings
John H. Chalmers
Artists
Statement
My digital graphics are based on the transformations that harmonic musical scales undergo as the tuning of their constituent triads is varied over the span of the octave. In general, the resolution is 2 cents (there are 1200 cents in an octave), so the computer generates a data set of 360,000 items for each of the scales. From these data various functions such as Rothenberg propriety interval profile, number of interval differences, heteromorphic profiles ( N. Carey) , numbers of ambiguous or contradictory intervals, etc., and combinations thereof are calculated and plotted. The colors of the various regions are selected from a preset palette as each of the regions is computed, so there is an element of visual unpredictability in an otherwise deterministic procedure. Technical details of the computation and music theory are available upon request.