Inversional Projections Network: symmetrical properties of the chromatic system and equivalences by multiplication M5 and M7
DOI:
https://doi.org/10.5965/2525530402012017121Keywords:
Inversional projections network, Symmetry, Musical set theory, Neo-Riemannian theory, Post-tonal musicAbstract
This work is a second reflection on
the Inversional Projections Network, a
concept presented previously in our article “Inversional Projections Network, Relationship between Tonnetze of Different
Tricords” (ALBUQUERQUE, SALLES: 2017).
We return here to our study of the scheme
of harmonic organization developed to
supply a model that could relate sets of different species and different cardinalities,
a demand apparently not contemplated
by traditional neo-Riemannian proposals.
We built our system based on the concomitants between sets implicit in different
Tonnetze, generated from inversions of
all possibilities of tricords, revealing important symmetrical properties inherent
to the chromatic universe in its full extension. We worked supported by the extensive discussion promoted by theorists dedicated to the development of specialized
analytical tools for the study of the post-
-tonal repertoire, focusing in particular on
the consortium between parameters derived from musical set theory and neo-Riemannian theory.
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