Related papers: Algebraic Structures in Microtonal Music
The high computational complexity of the multiple signal classification (MUSIC) algorithm is mainly caused by the subspace decomposition and spectrum search, especially for frequent real-time applications or massive sensors. In this paper,…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
We consider composition and division algebras over the real numbers: We note two r\^oles for the group $G_{2}$: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are…
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 propose an analytic framework to study the nonperturbative solutions of Witten's open string field theory. The method is based on the Moyal star formulation where the kinetic term can be split into two parts. The first one describes the…
2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a…
Foundation models have revolutionized music information retrieval, but questions remain about their ability to generalize across diverse musical traditions. This paper presents a comprehensive evaluation of five state-of-the-art audio…
Very short computer programs, sometimes consisting of as few as three arithmetic operations in an infinite loop, can generate data that sounds like music when output as raw PCM audio. The space of such programs was recently explored by…
Categorization is crucial for content description in archiving of music signals. On many occasions, human brain fails to classify the instruments properly just by listening to their sounds which is evident from the human response data…
The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…
We use Google's MusicVAE, a Variational Auto-Encoder with a 512-dimensional latent space to represent a few bars of music, and organize the latent dimensions according to their relevance in describing music. We find that, on average, most…
This works introduces several notions of subharmonicity for real-valued functions of one quaternionic variable. These notions are related to the theory of slice regular quaternionic functions introduced by Gentili and Struppa in 2006. The…
Much like most of cognition research, music cognition is an interdisciplinary field, which attempts to apply methods of cognitive science (neurological, computational and experimental) to understand the perception and process of composition…
This paper addresses the matching of short music audio snippets to the corresponding pixel location in images of sheet music. A system is presented that simultaneously learns to read notes, listens to music and matches the currently played…
Music Information Retrieval (MIR) is a collaborative scientific study that help to build innovative information research themes, novel frameworks, and developing connected delivery mechanisms in addition to making the world's massive…
Music genre classification is one example of content-based analysis of music signals. Traditionally, human-engineered features were used to automatize this task and 61% accuracy has been achieved in the 10-genre classification. However,…
In this paper we study certain quaternion algebras and symbol algebras which split.
Computer musicians refer to mesostructures as the intermediate levels of articulation between the microstructure of waveshapes and the macrostructure of musical forms. Examples of mesostructures include melody, arpeggios, syncopation,…
String structures in degree four are associated with cancellation of anomalies of string theory in ten dimensions. Fivebrane structures in degree eight have recently been shown to be associated with cancellation of anomalies associated to…