Related papers: Mathematical Harmony Analysis
Audio-to-score alignment is an important pre-processing step for in-depth analysis of classical music. In this paper, we apply novel transposition-invariant audio features to this task. These low-dimensional features represent local pitch…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of the knot and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form which can…
The harmonic numbers are the sequence 1, 1+1/2, 1+1/2+1/3, ... Their asymptotic difference from the sequence of the natural logarithm of the positive integers is Euler's constant gamma. We define a family of natural generalizations of the…
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
Solutions to Laplace's equation are called harmonic functions. Harmonic functions arise in many applications, such as physics and the theory of stochastic processes. Of interest classically are harmonic polynomials, which have a simple…
In this work, we consider the modeling of signals that are almost, but not quite, harmonic, i.e., composed of sinusoids whose frequencies are close to being integer multiples of a common frequency. Typically, in applications, such signals…
This work has a purpose to collect selected facts about the completely monotone (CM) functions that can be found in books and papers devoted to different areas of mathematics. We opted for lesser known ones, and for those which may help…
In this article indicators to describe the "beauty" of noises are proposed. Rhythmic, tonal and harmonic suavity are introduced. They give a characterization of a noise in terms of rhythmic regularity (rhythmic suavity), of auditory…
We classify three-tone and four-tone chords based on subgroups of the symmetric group acting on chords contained within a twelve-tone scale. The actions are inversion, major-minor duality, and augmented-diminished duality. These actions…
Following the ideas of von Helmholtz and Plomp-Levelt, an algorithm for calculating the total dissonance of complex sounds, free from logical inconsistencies and useful for comparing different chords, is proposed. The method is tested by…
Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points where all iterates of this expanding map…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
Centrality describes the importance of nodes in a graph and is modeled by various measures. Its global analogue, called centralization, is a general formula for calculating a graph-level centrality score based on the node-level centrality…
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…
We study the growth rate of harmonic functions in two aspects: gradient estimate and frequency. We obtain the sharp gradient estimate of positive harmonic function in geodesic ball of complete surface with nonnegative curvature. On complete…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
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…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…