Related papers: Pourquoi la gamme a sept notes? Une math{\'e}matiq…
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…
A Pythagorean scale is a mathematical encoding of a musical scale as a finite list of numbers of the form 3^b/2^a. Previous work of the first author discussed the 2-step property as a way to measure which Pythagorean scales are the most…
In the Pythagorean tuning system, the fifth is used to generate a scale of 12 notes per octave. In this paper, we use the octave to generate a scale of 19 notes per tritave; one can play this scale on a traditional piano. In this system,…
The well-known conditions for a simplicial set to be the nerve of a small category generalize with respect to two parameters: the dimension n of the things which compose, and the position i of the thing which is the result of the…
This paper focuses on the modeling of musical melodies as networks. Notes of a melody can be treated as nodes of a network. Connections are created whenever notes are played in sequence. We analyze some main tracks coming from different…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
While recent generative models can produce engaging music, their utility is limited. The variation in the music is often left to chance, resulting in compositions that lack structure. Pieces extending beyond a minute can become incoherent…
A notation system was previously presented which can notate any rational frequency in free Just Intonation. Transposition of music is carried out by multiplying each member of a set of frequencies by a single frequency. Transposition of JI…
The aim of this study is to teach an algorithm how to recognize different types of music. Users will submit songs for analysis. Since the algorithm hasn't heard these songs before, it needs to figure out what makes each song unique. It does…
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…
Both, human appreciation of music and musical genres, transcend time and space. The universality of musical genres and associated musical scales is intimately linked to the physics of sound and the special characteristics of human acoustic…
This paper develops a formal theory of musical scales and their harmonic coverings and introduces orbit covers: coverings obtained by translating a fixed subset across a scale via a group action. Orbit covers generalize familiar…
Repetition is a basic indicator of musical structure. This study introduces new algorithms for identifying musical phrases based on repetition. Phrases combine to form sections yielding a two-level hierarchical structure. Automatically…
This paper presents a novel rule-based approach for generating music by varying existing tunes. We parse each tune to find the Pathway Assembly (PA) [ 1], that is a structure representing all repetitions in the tune. The Sequitur algorithm…
Barraqu\'e's proliferating series give an interesting turn on the concept of classic serialism by creating a new invariant when it comes to constructing the series: rather than the intervals between consecutive notes, what remains unaltered…
The field of music generation using Large Language Models (LLMs) is evolving rapidly, yet existing music notation systems, such as MIDI, ABC Notation, and MusicXML, remain too complex for effective fine-tuning of LLMs. These formats are…
In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and…
Listening habits are strongly influenced by two opposing aspects, the desire for variety and the demand for uniformity in music. In this work we quantify these two notions in terms of musical instrumentation and production technologies that…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
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…