相关论文: Modulation Graphs in Popular Music

Understanding music popularity is important not only for the artists who create and perform music but also for the music-related industry. It has not been studied well how music popularity can be defined, what its characteristics are, and…

The melodic consonance of a sequence of tones is explained using the overtone series: the overtones form "flow lines" that link the tones melodically; the strength of these flow lines determines the melodic consonance. This hypothesis…

Let G be a simple graph of order n. The domination polynomial of a graph is the generating function of its dominating sets. We study the domination polynomials of generalized friendship graphs. We also consider book graphs formed by joining…

Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we…

We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are…

Transformational musical theory has so far mainly focused on the study of groups acting on musical chords, one of the most famous example being the action of the dihedral group D24 on the set of major and minor chords. Comparatively less…

We make some general observations about partial orders on quotient spaces, and explore their use in music theory, in two different contexts. In the first, we show that many of the most familiar chord and scale types in Western music appear…

This paper surveys a comprehensive, although not exhaustive, sampling of graph polynomials with the goal of providing a brief overview of a variety of techniques defining a graph polynomial and then for decoding the combinatorial…

In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…

In this paper we present a mathematical way of defining musical modes, we derive a formula for the total number of modes and define the musicality of a mode as the total number of harmonic chords whithin the mode. We also give an algorithm…

Of all the characteristics of a violin, those that concern its shape are probably the most important ones, as the violin maker has complete control over them. Contemporary violin making, however, is still based more on tradition than…

Metric graphs are often introduced based on combinatorics, upon "associating" each edge of a graph with an interval; or else, casually "gluing" a collection of intervals at their endpoints in a network-like fashion. Here we propose an…

Motivated by studies of oscillator networks, we study the spectrum of the join of several normal matrices with constant row sums. We apply our results to compute the characteristic polynomial of the join of several regular graphs. We then…

We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…

The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.

We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several…

Symbolic music analysis tasks are often performed by models originally developed for Natural Language Processing, such as Transformers. Such models require the input data to be represented as sequences, which is achieved through a process…

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…

A generalization of the classical statistics ``maj'' and ``inv'' (the major index and number of inversions) on words is introduced, parameterized by arbitrary graphs on the underlying alphabet. The question of characterizing those graphs…

The goal of these lectures is to present an informal but precise introduction to a body of concepts and methods of interest in number theory and string theory revolving around modular forms and their generalizations. Modular invariance lies…