相关论文: Musical intervals under 12-note equal temperament:…

For example, in the chromatic circle, the twelve tones are represented by twelve points on a circle, and in Tonnetz, the relationships among harmonies are represented by a triangular lattice. Recently, we have shown that several…

The impossibility of a transposable 12 semitone tuning of the octave arises from the mathematical fact that $2 \times 2^{7/12} \neq 3$ i.e., the second harmonic of the fifth can not exactly match the third harmonic of the fundamental. This…

By Northcott's Theorem there are only finitely many algebraic points in affine $n$-space of fixed degree over a given number field and of height at most $X$. For large $X$ the asymptotics of these cardinalities have been investigated by…

We introduce the {\em pair-cut cone $PCUT_n$} of metrics on sets with $n\ge 3$ elements, that correspond to linear combinations with non-negative coefficients of the cut-metrics resulting from cuts that are pairs. Given a metric, we fully…

This paper unifies several generalizations of coherent rings in one notion. Namely, we introduce $n$-$\mathscr{X}$-coherent rings, where $\mathscr{X}$ is a class of modules and $n$ is a positive integer, as those rings for which the…

Information valuable words are the strings with the significant deviation of real frequency from the expected one. The expected frequency is determined through the maximum entropy principle of the reconstructed (extended) frequency…

The new formulas, which determine sign and amplitude of utilitarian emotions, are proposed on the basis of the information theory of emotions. In area of perception of musical chords the force of emotions depends on the relative pitch of…

We characterize $n$-rectifiable metric measure spaces as those spaces that admit a countable Borel decomposition so that each piece has positive and finite $n$-densities and one of the following: is an $n$-dimensional Lipschitz…

We study two-flavor neutrino oscillations in a homogeneous and isotropic ensemble under the influence of neutrino-neutrino interactions. For any density there exist forms of collective oscillations that show self-maintained coherence. They…

We continue the study of positive geometries underlying the {\it Grassmannian string integrals}, which are a class of "stringy canonical forms", or stringy integrals, over the positive Grassmannian mod torus action, $G_+(k,n)/T$. The…

We consider a \textit{PT}-symmetric cubic oscillator with an imaginary double well. We prove the existence of an infinite number of level crossings with a definite selection rule. Decreasing the positive parameter $\hbar$ from large values,…

Relations among various musical concepts are investigated through a new concept, musical icosahedron that is the regular icosahedron each of whose vertices has one of 12 tones. First, we found that there exist four musical icosahedra that…

In this paper we show how quantum corrections, although perturbatively small, may play an important role in the analysis of the existence of some classical models. This, in fact, appears to be the case of static, uniform--density models of…

Relying upon the division-algebra classification of Clifford algebras and spinors, a classification of generalized supersymmetries (or, with a slight abuse of language,"generalized supertranslations") is provided. In each given space-time…

Schanuel has pointed out that there are mathematically interesting categories whose relationship to the ring of integers is analogous to the relationship between the category of finite sets and the semi-ring of non-negative integers. Such…

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…

Melodic similarity measurement is of key importance in music information retrieval. In this paper, we use geometric matching techniques to measure the similarity between two melodies. We represent music as sets of points or sets of…

We define a new congruence relation on the set of integers, leading to a group similar to the multiplicative group of integers modulo $n$. It makes use of a symmetry almost omnipresent in modular multiplications and halves the number of…

We present an audio-to-analysis pipeline that produces composer-level information-theoretic profiles : reflecting compositional vocabulary as it emerges from aggregated performances : from raw recordings, built on a transcription layer…

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…