Related papers: Group theory approach to combination tones
After briefly revising the concepts of consonance/dissonance, a respective mathematic-computational model is described, based on Helmholtz's consonance theory and also considering the partials intensity. It is then applied to characterize…
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…
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,…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
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…
The transduction process that occurs in the inner ear of the auditory system is a complex mechanism which requires a non-linear dynamical description. In addition to this, the stochastic phenomena that naturally arise in the inner ear…
The origins of consonance in human music has long been contested, and today there are three primary hypotheses: aversion to roughness, preference for harmonicity, and learned preferences from cultural exposure. While the evidence is…
Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely…
The dichotic method of hearing sound adapts in the region of musical harmony. The algorithm of the separation of the being dissonant voices into several separate groups is proposed. For an increase in the pleasantness of chords the…
This is a survey. The main subject of this survey is the homotopical or homological nature of certain structures which appear in classical problems about groups, Lie rings and group rings. It is well known that the (generalized) dimension…
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…
The degraded performance and group unfairness caused by confounding sensitive attributes in rumor detection remains relatively unexplored. To address this, we propose a two-step framework. Initially, it identifies confounding sensitive…
In this paper I want to suggest a new solution to the problem of musical tuning. On one hand, I see it as a generalization of Just Intonation (JI) to inharmonic timbers, on another, as a unification of spectral interference and harmonicity…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
Since the seminal work by H.L.F. Helmholtz in 1863, to understand the basic principles of hearing has been a great, but still unresolved, challenge for physicists. Some time ago, it has been pointed out (Egu\'{\i}luz et al., Phys. Rev.…
We consider a combinatorial problem occurring naturally in a group theoretical setting and provide a constructive solution in a special case. More precisely, in 1999 the author established a logarithmic bound for the derived length of the…
Even though chord roots constitute a fundamental concept in music theory, existing models do not explain and determine them to full satisfaction. We present a new method which takes sequential context into account to resolve ambiguities and…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We aim to explain whether a stress memory task has a significant impact on tonal coarticulation. We contribute a novel approach to analyse tonal coarticulation in phonetics, where several f0 contours are compared with respect to their…
In the production of modern music, the musical characteristics of the guitar or keyboard amplifier play an integral role in the creative process. This article explores the physics of music with an emphasis on the role of distortion in the…