Inversional Projections Network: symmetrical properties of the chromatic system and equivalences by multiplication M5 and M7 (Orfeu, 2017)
This work is a second reflection onthe Inversional Projections Network, aconcept presented previously in our article “Inversional Projections Network, Relationship between Tonnetze of DifferentTricords” (ALBUQUERQUE, SALLES: 2017).We return here to our study of the schemeof harmonic organization developed tosupply a model that could relate sets of different species and different cardinalities,a demand apparently not contemplatedby traditional neo-Riemannian proposals.We built our system based on the concomitants between sets implicit in differentTonnetze, generated from inversions ofall possibilities of tricords, revealing important symmetrical properties inherentto the chromatic universe in its full extension. We worked supported by the extensive discussion promoted by theorists dedicated to the development of specializedanalytical tools for the study of the post--tonal repertoire, focusing in particular onthe consortium between parameters derived from musical set theory and neo-Riemannian theory.
Keywords: Inversional projections network; Symmetry; Musical set theory; Neo-Riemannian theory; Post-tonal music