相关论文: Unified Music Theories for General Equal-Temperame…

A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…

The classical number system encodes magnitude using a single scalar value whose sign positive or negative has remained conceptually unchanged for centuries. This work introduces Multisign Algebra, a mathematical generalization of the sign…

Modern keyboards allow a musician to play multiple instruments at the same time by assigning zones -- fixed pitch ranges of the keyboard -- to different instruments. In this paper, we aim to further extend this idea and examine the…

An algebraic formalism for quantum decoherence in systems with continuous evolution spectrum is introduced. A certain subalgebra, dense in the characteristic algebra of the system, is defined in such a way that Riemann-Lebesgue theorem can…

This paper deals with the algebraic structure of the sequence of harmonics when combined with equal temperaments. Fractals and the golden ratio appear surprisingly on the way. The sequence of physical harmonics is an increasingly enumerable…

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 discuss the problem of the separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to…

This paper proposes appropriate sound and complete proof systems for algebraic structures over metric spaces by combining the development of Quantitative Equational Theories (QET) with the Enriched Lawvere Theories. We extend QETs to Metric…

String theory suggests the existence of gravitational-strength scalar fields ("dilaton" and "moduli") whose couplings to matter violate the equivalence principle. This provides a new motivation for high-precision clock experiments, as well…

We analyze the concept of virtuosity as a collective attribute in music and its relationship with the entropy based on an experiment that compares two sets of digital signals played by composer-performer electric guitarists. Based on an…

A Pythagorean scale is a mathematical encoding of a musical scale as a finite list of numbers of the form 3^b/2^a. Previous work of the first author discussed the 2-step property as a way to measure which Pythagorean scales are the most…

It is common for most people to think of science and art as disparate, or at most only vaguely related fields. In physics, one of the biggest successes of thermodynamics is its explanation of order arising from disordered phases of matter…

In a recent article, arXiv:2605.12414, it is stated that a certain scale transformation has been "systematically overlooked" in discussions of the tensionless string. Here we point out that this kind of symmetry is treated in numerous…

We present a new system for simultaneous estimation of keys, chords, and bass notes from music audio. It makes use of a novel chromagram representation of audio that takes perception of loudness into account. Furthermore, it is fully based…

An unorthodox unified theory is developed to describe external and internal attributes and symmetries of fundamental fermions, quarks and leptons. Basic ingredients of the theory are an algebra which consists of all the…

We revisit the existence, background independence and uniqueness of closed, open and open-closed bosonic- and topological string field theory, using the machinery of homotopy algebra. In a theory of classical open- and closed strings, the…

The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…

The well-known conditions for a simplicial set to be the nerve of a small category generalize with respect to two parameters: the dimension n of the things which compose, and the position i of the thing which is the result of the…

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…

In recent years, thanks to advances in automatic music transcription (AMT), several large-scale datasets of automatically transcribed piano solo music have been released. While these datasets undoubtedly offer extensive material for…