相关论文: On the mathematical structure of Tonal Harmony

This chapter considers how string-based methods might be adapted to address music-analytic questions related to the discovery of musical organization, with particular attention devoted to the analysis of tonal harmony. I begin by applying…

This paper provides a new mathematical axiom system for classical harmony, which is a prescriptive rule system for composing music, introduced in the second half of the 18th century. The clearest model of classical harmony is given by the…

The collaboration of mathematics in the two musical systems of Pythagorean sounds and of equal sounds is evident and opportune for generating the elements and managing their relationships. The only essential notion for a rational…

We introduce the notion of Riemannian twistorial structure and we show that it provides new natural constructions of harmonic maps.

Based on Plato's Timaeus, we present some reflections on music, cosmology and mathematics and their mutual influence.The article is dedicated to the composer Walter Zimmermann. The final version of this article will appear in the volume…

Consonance is related to the perception of pleasantness arising from a combination of sounds and has been approached quantitatively using mathematical relations, physics, information theory, and psychoacoustics. Tonal consonance is present…

Using Eulerian and Euler numbers, we establish congruences concerning sums involving harmonic numbers, tangent numbers and Genocchi numbers.

Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real,…

Tame arrangements were informally introduced by Orlik and Terao for the study of Milnor fibers of hyperplane arrangements. After that, tame arrangements have been applied to a lot of researches on arrangements including freeness, master…

Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific…

A new approach to problems of the Uncertainty Principle in Harmonic Analysis, based on the use of Toeplitz operators, has brought progress to some of the classical problems in the area. The goal of this paper is to develop and systematize…

In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion.…

How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We…

We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…

Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…

Monotonic convergence is established for a general class of multiplicative algorithms introduced by Silvey, Titterington and Torsney [Comm. Statist. Theory Methods 14 (1978) 1379--1389] for computing optimal designs. A conjecture of…

We introduce and prove several new formulas for the Euler-Mascheroni Constant. This is done through the introduction of the defined E-Harmonic function, whose properties, in this paper, lead to two novel formulas, alongside a family of…

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.

Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…

Traditional approaches to combination tones based on Helmholtz theory encounter essential interpreting difficulties, which the most known example is the anomalous behaviour of the combination tone 2f1-f2. Without doubt the phenomenon of…