相关论文: Modulation Graphs in Popular Music

Statistical modeling of popular music presents a unique challenge due to the complexity of song structures, which cannot be easily analyzed using conventional statistical tools. However, recent advances in data science have shown that…

The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…

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…

After our book---Mathematics and Music: Composition, Perception, and Performance, 2nd edition, CRC Press, 2020---was published, we found a striking example of the importance of the Tonnetz for analyzing the harmonic structure of The…

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…

Musical chords, harmonies or melodies in Just Intonation have note frequencies which are described by a base frequency multiplied by rational numbers. For any local section, these notes can be converted to some base frequency multiplied by…

To date, calculating the frequencies of musical notes requires one to know the frequency of some reference note. In this study, first-order ordinary differential equations are used to arrive at a mathematical model to determine tonal…

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…

This paper presents an approach to model melodies (and music pieces in general) as networks. Notes of a melody can be seen as nodes of a network that are connected whenever these are played in sequence. This creates a directed graph. By…

The musical realm is a promising area in which to expect to find nontrivial topological structures. This paper describes several kinds of metrics on musical data, and explores the implications of these metrics in two ways: via techniques of…

Consonance is related to the perception of pleasantness arising from a combination of sounds and has been approached quantitatively using mathematical relations, physics, information theory, and psychoacoustics. Tonal consonance is present…

Melody reduction, as an abstract representation of musical compositions, serves not only as a tool for music analysis but also as an intermediate representation for structured music generation. Prior computational theories, such as the…

Chord diagrams are used by guitar players to show where and how to play a chord on the fretboard. They are useful to beginners learning chords or for sharing the hand positions required to play a song.However, the diagrams presented on…

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…

A directed graph, called an M-graph, is attached to every melody. Our chief concern in this paper is to investigate (1) how the positivity of the slope of the M-graph is related to singability of the melody, (2) when the M-graph has a…

In this paper, we analyze web-downloaded data on people sharing their music library. By attributing to each music group usual music genres (Rock, Pop...), and analysing correlations between music groups of different genres with…

Motifs often recur in musical works in altered forms, preserving aspects of their identity while undergoing local variation. This paper investigates how such motivic transformations occur within their musical context in symbolic music. To…

How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We…

We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…

The aim of this paper is twofold: on one side we review the classical concept of musical mode from the viewpoint of modern music, reading it as a superimposition of a base-chord (seventh chord) and a tension-chord (triad). We associate to…