Related papers: Modes in modern music from a topological viewpoint
Music generated by deep learning methods often suffers from a lack of coherence and long-term organization. Yet, multi-scale hierarchical structure is a distinctive feature of music signals. To leverage this information, we propose a…
Automatic music transcription converts audio recordings into symbolic representations, facilitating music analysis, retrieval, and generation. A musical note is characterized by pitch, onset, and offset in an audio domain, whereas it is…
Every art form ultimately aims to invoke an emotional response over the audience, and music is no different. While the precise perception of music is a highly subjective topic, there is an agreement in the "feeling" of a piece of music in…
After a quick exposition of Mazzola's quantum modulation model for the so-called triadic interpretation of the major scale within the equal temperament, we study the model for the tetradic interpretation of the same scale. It is known that…
The band-unfolding method is widely used to calculate the effective band structures of a disordered system from its supercell model. The unfolded band structures show the crystallographic symmetry of the underlying structure, where the…
Music, enchanting and poetic, permeates every corner of human civilization. Although music is not unfamiliar to people, our understanding of its essence remains limited, and there is still no universally accepted scientific description.…
We propose a simple phenomenological model describing composite crystals, constructed from two parallel sets of periodic inter-penetrating chains. In the harmonic approximation and neglecting thermal fluctuations we find the eigenmodes of…
Visualizing spatial correlations in 3D ensembles is challenging due to the vast amounts of information that need to be conveyed. Memory and time constraints make it unfeasible to pre-compute and store the correlations between all pairs of…
We classify three-tone and four-tone chords based on subgroups of the symmetric group acting on chords contained within a twelve-tone scale. The actions are inversion, major-minor duality, and augmented-diminished duality. These actions…
We introduce the classical theory of the interplay between group theory and topology into the context of operads and explore some applications to homotopy theory. We first propose a notion of a group operad and then develop a theory of…
The comparison principle for scalar second order parabolic PDEs on functions $u(t,x)$ admits a topological interpretation: pairs of solutions, $u^1(t,\cdot)$ and $u^2(t,\cdot)$, evolve so as to not increase the intersection number of their…
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…
We establish counting formulas and bijections for deformations of the braid arrangement. Precisely, we consider real hyperplane arrangements such that all the hyperplanes are of the form $x\_i-x\_j=s$ for some integer $s$. Classical…
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…
Sonification offers a non-visual way to understand data, with pitch-based encodings being the most common. Yet, how well people perceive slope and acceleration-key features of data trends-remains poorly understood. Drawing on people's…
In the age of music streaming platforms, the task of automatically tagging music audio has garnered significant attention, driving researchers to devise methods aimed at enhancing performance metrics on standard datasets. Most recent…
Given a category with a bifunctor and natural isomorphisms for associativity, commutativity and left and right identity we do not assume that extra constraining diagrams hold. We introduce groupoids of coupling trees to describe a version…
Musical genre's classification has been a relevant research topic. The association between music and genres is fundamental for the media industry, which manages musical recommendation systems, and for music streaming services, which may…
In many musical traditions, the melody line is of primary significance in a piece. Human listeners can readily distinguish melodies from accompaniment; however, making this distinction given only the written score -- i.e. without listening…
The music genre perception expressed through human annotations of artists or albums varies significantly across language-bound cultures. These variations cannot be modeled as mere translations since we also need to account for cultural…