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

The standard theory of musical scales since antiquity has been based on harmony, rather than melody. While recent analyses provide mixed support for a role of melody as well as harmony, we lack a comparative analysis based on cross-cultural…

If scattering amplitudes are ordinary complex numbers (not quaternions) there is a universal algebraic relationship between the six coherent cross sections of any three scatterers (taken singly and pairwise). A violation of this…

The buildup and release of a sense of tension is one of the most essential aspects of the process of listening to music. A veridical computational model of perceived musical tension would be an important ingredient for many music…

Understanding complete musical scores entails integrated reasoning over pitch, rhythm, harmony, and large-scale structure, yet the ability of Large Language Models and Vision--Language Models to interpret full musical notation remains…

Tipping points are moments of change that characterise crucial turning points in a piece of music. This study presents a first step towards quantitatively and systematically describing the musical properties of tipping points. Timing…

Western tonality provides a hierarchy of stability among melodic scale-degrees, from the maximally stable tonic to unstable chromatic notes. Tonal stability has been linked to emotion, yet systematic investigations of the associations…

We define a 3-algebra with structure constants being symmetric in the first two indices. We also introduce an invariant anti-symmetric tensor into this 3-algebra and call it a symplectic 3-algebra. The general N=5 superconformal…

We study pairs and m--tuples of compositions of a positive integer n with parts restricted to a subset P of positive integers. We obtain some exact enumeration results for the number of tuples of such compositions having the same number of…

We present a melody based classification of musical styles by exploiting the pitch and energy based characteristics derived from the audio signal. Three prominent musical styles were chosen which have improvisation as integral part with…

We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…

We present a model for spectral theory of families of selfadjoint operators, and their corresponding unitary one-parameter groups (acting in Hilbert space.) The models allow for a scale of complexity, indexed by the natural numbers…

The trichotomy between regular, semiregular, and strongly irregular boundary points for $p$-harmonic functions is obtained for unbounded open sets in complete metric spaces with a doubling measure supporting a $p$-Poincar\'e inequality,…

The aim is to explore new opportunities of the pitch organization of the musical scale. Specifically, a numerical comparison of the different musical temperaments among themselves in the degree of approximation of the Pythagorean scale is…

We introduce the notion of multi-patterns, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach in encoding musical phrases lies in the fact that it becomes possible to compose multi-patterns in order to…

Pitch and meter are two fundamental music features for symbolic music generation tasks, where researchers usually choose different encoding methods depending on specific goals. However, the advantages and drawbacks of different encoding…

We study various boundary and inner regularity questions for $p(\cdot)$-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for $p(\cdot)$-harmonic…

We present a semiclassical approach to n-point spectral correlation functions of quantum systems whose classical dynamics is chaotic, for arbitrary n. The basic ingredients are sets of periodic orbits that have nearly the same action and…

For $l,n \in \mathbb{N}$ we define tonal partition algebra $P^l_n$ over $\mathbb{Z}[\delta]$. We construct modules $\{ \Delta_{\underline{\mu}} \}_{\underline{\mu}}$ for $P^l_n$ over $\mathbb{Z}[\delta]$, and hence over any integral domain…

Let T be a finite subset of the complex unit circle S^1, and define f: S^1 -> S^1 by f(z) = z^d. Let CH(T) denote the convex hull of T. If card(T) = N > 2, then CH(T) defines a polygon with N sides. The N-gon CH(T) is called a…

The term melodic template or skeleton refers to a basic melody which is subject to variation during a music performance. In many oral music tradition, these templates are implicitly passed throughout generations without ever being…