Related papers: Knots, Music and DNA
Music has always been central to human culture, reflecting and shaping traditions, emotions, and societal changes. Technological advancements have transformed how music is created and consumed, influencing tastes and the music itself. In…
Notes in a musical piece are building blocks employed in non-random ways to create melodies. It is the "interaction" among a limited amount of notes that allows constructing the variety of musical compositions that have been written in…
This is an expository article on diagrammatic representations of knots and links in various settings via braids.
In this paper we propose the Music Note Ontology, an ontology for modelling music notes and their realisation. The ontology addresses the relation between a note represented in a symbolic representation system, and its realisation, i.e. a…
Data science offers a powerful tool to understand objects in multiple sciences. In this paper we utilize concept of data science, most notably topological data analysis, to extend our understanding of knot theory. This approach provides a…
Out of the scope of the usual positions of computing in the field of music and musicology, one notices the emergence of human-computer systems that do exist by breaking off. Though these singular systems take effect in the usual fields of…
Bonded knots arise naturally in topological protein modeling, where intramolecular interactions such as disulfide bridges stabilize folded configurations. These structures extend classical knot theory by incorporating embedded graphs, and…
In this article, a framework for defining and analysing a family of graphs or networks from symbolic music information is discussed. Such graphs concern different types of elements, such as pitches, chords and rhythms, and the relations…
Historically originated as a sub-field of topology, knot theory is an active area of mathematical investigation that has strong connections with a diverse set of scientific fields such as algebra, biology, and statistical mechanics. A…
This application-oriented study concerns computational musicology, which makes use of grammar systems. We define multi-generative rule-synchronized scattered-context grammar systems (without erasing rules) and demonstrates how to…
Musical mode is one of the most critical element that establishes the framework of pitch organization and determines the harmonic relationships. Previous works often use the simplistic and rigid alignment method, and overlook the diversity…
In physics, timbre is a complex phenomenon, like color. Musical timbres are given by the superposition of sinusoidal signals, corresponding to longitudinal acoustic waves. Colors are produced by the superposition of transverse…
Multimodal learning has driven innovation across various industries, particularly in the field of music. By enabling more intuitive interaction experiences and enhancing immersion, it not only lowers the entry barriers to the music but also…
We consider ribbon n-knots for n\geq 2. For such knots we define a set of moves on ribbon disks, and show that any two ribbon disks for isotopic knots are related by a finite sequence of such moves and ambient isotopies. Using this we are…
Knots and links which are closed 3-braids are a very special class. Like 2-bridge knots and links, they are simple enough to admit a complete classification. At the same time they are rich enough to serve as a source of examples on which,…
We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The algebras conjecturally give the relative…
Music and dance have always co-existed as pillars of human activities, contributing immensely to the cultural, social, and entertainment functions in virtually all societies. Notwithstanding the gradual systematization of music and dance…
In this report, I will start by first giving a brief introduction on knots to build some intuition before beginning the more rigorous review in the Literature Review section. There, I will define knot equivalence, the Jones polynomial…
Music similarity is an essential aspect of music retrieval, recommendation systems, and music analysis. Moreover, similarity is of vital interest for music experts, as it allows studying analogies and influences among composers and…
These notes were prepared to supplement the talk that I gave on Feb 19, 2004, at the First East Asian School of Knots and Related Topics, Seoul, South Korea. In this article I review aspects of the interconnections between braids, knots and…