Evidence for linear transposition in Australian western desert vocal music

Abstract

Frequency analysis of a solo performance of one songline demonstrated a remarkable perfection and stability in frequency-production by the performer. This performance quality enabled us to carry out a detailed numerical analysis of the frequency transposition that occurred in this song. The average deviation of the actual transposition from a logarithmic model is larger by a factor of 40 than from a linear model. However, there are also considerable deviations from a linear equidistant model. Considering the nonequidistant tonal space of the songline, the best explanation is given by assuming a linear, non-equidistant transposition, comparable to the change from one mode to another (except that the interval system is based on frequency differences). These results challenge the widely accepted view that, in music, transpositions are generally based on frequency ratios.