TL;DR
This paper explores the phase components of Fourier coefficients of pitch class sets, offering new insights into triads, the Tonnetz, and transitions between different pitch collections.
Contribution
It introduces a novel analysis of phase information in Fourier coefficients, enhancing understanding of musical structures and relationships.
Findings
Phase analysis reveals new relationships between triads.
Continuous gestures between diverse pc-sets are characterized.
Insights into the Tonnetz structure are provided.
Abstract
The import of the magnitude of fourier coefficients of a pitch class set is fairly well known. This paper deals with the angular component of these compelx numbers, the phase. It enables to shed new light on triads, the Tonnetz, and continuous gestures between diverse pc-sets, even those with different cardinalities.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quasicrystal Structures and Properties · Topological and Geometric Data Analysis