Exploring Perde-Space: 3-D Tonnetz Visualization for Makam Music

Abstract

This paper introduces a similarity and weight metric designed to assess the distance between pitches and melodic fragments within the framework of Turkish Makam Music. Our approach hinges on adapting the Riemannian Tonnetz to represent pitch-based elements, termed “perde” (pitch), or “çes ̧ni” (tetrachordal material for melodic fragments), within a three-dimensional vector space tailored specifically for Turkish Makam Music. We demonstrate the efficacy of this space as a reliable approximation for gauging similarity between musical objects and estimating the cost associated with traversing the music network using different distance metrics namely Euclidean, Minkowski, Manhattan and Cosine, thereby facilitating the construction of a weighted version thereof. Taking weighted relationships into consideration, this metric enables the computation of the cost associated with potential paths between musical objects and furnishes a new predictive tool for supervised learning models. Following the exposition of the geometric model and calculation methodology, we undertake a comparative analysis with results derived from a sample annotated by expert practitioners, revealing a notably high degree of correlation between our algorithm utilizing cosine distance and expert ratings, Spearman’s rho = 0.828 with p-value < .001.