Related papers: Mathematical Harmony Analysis
A harmonic mapping is a univalent harmonic function of one complex variable. We define a family of harmonic mappings on the unit disk whose images are rotationally symmetric rosettes with $n$ cusps or n nodes, where $n \ge 3$. These…
We present a technique to search for the presence of crucial events in music, based on the analysis of the music volume. Earlier work on this issue was based on the assumption that crucial events correspond to the change of music notes,…
Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…
Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent…
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from…
In this paper we present mathematical and physical models to be used in the analysis of the problem of intonation of musical instruments such as guitars, mandolins and the like, i.e., we study how to improve the tuning on these instruments.…
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,…
Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific…
Sonar systems are frequently used to classify objects at a distance by using the structure of the echoes of acoustic waves as a proxy for the object's shape and composition. Traditional synthetic aperture processing is highly effective in…
Transformer architectures offer significant advantages regarding the generation of symbolic music; their capabilities for incorporating user preferences toward what they generate is being studied under many aspects. This paper studies the…
Melody estimation or melody extraction refers to the extraction of the primary or fundamental dominant frequency in a melody. This sequence of frequencies obtained represents the pitch of the dominant melodic line from recorded music audio…
A combination of three or more tones played together is called a chord. In the chromatic scale, chords which are consonant are of particular interest and can be divided into several groups, two main ones being the major and minor chords.…
This study borrows and extends probabilistic language models from natural language processing to discover the syntactic properties of tonal harmony. Language models come in many shapes and sizes, but their central purpose is always the…
We introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
A test of uniformity on [0,1] is developed for the setting of a single observation recorded with sufficient precision. Although consistency against general alternatives is not attainable with only one draw in the classical large-sample…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
We report an approach to obtaining complex networks with diverse topology, here called syntonets, taking into account the consonances and dissonances between notes as defined by scale temperaments. Though the fundamental frequency is…
Chains are vector-valued signals sampling a curve. They are important to motion signal processing and to many scientific applications including location sensors. We propose a novel measure of smoothness for chains curves by generalizing the…
In this paper, graph theory is used to explore the musical notion of tonal modulation, in theory and application. We define (pivot) modulation graphs based on the common scales used in popular music. Properties and parameters of these…