Speaker
Description
The concept of the well-formed scale has been a classic paradigm within mathematical music theory for more than three decades. This keynote address traces its subsequent structural and theoretical developments since our inaugural conference in 2007.
By indexing the seven pitches of the diatonic scale both by fifths and by step intervals, one obtains a permutation of the integers from 0 to 6. The fundamental impetus for this entire line of inquiry lies in the fact that this permutation constitutes a multiplication by 4 modulo 7, which is an automorphism of the cyclic group Z7. From this structural kernel, a comprehensive network of mathematical models has evolved, illuminating how pitches organize themselves and give rise to musical meaning.
Drawing upon Jacques Handschin's evocative concept of the "Tongesellschaft" (tone-society), this lecture invites us to re-evaluate historical frameworks of tonal organization through the lens of algebraic models. The trajectory spans from the medieval gamut and the interpretive conventions governing sixteenth-century partbooks to the ultimate consolidation of common-practice harmonic tonality.