Related papers: Modulation Graphs in Popular Music
After briefly revising the concepts of consonance/dissonance, a respective mathematic-computational model is described, based on Helmholtz's consonance theory and also considering the partials intensity. It is then applied to characterize…
Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…
The determinants of modular Collatz graphs and the modular Conway amusical permutation graph are determined, and some interesting number theoretic properties are described.
This study argues that electronic tones routinely used in contemporary popular music - including 808-style bass and power chords - are structurally and perceptually equivalent to multiphonics in contemporary classical music. Using listening…
Tablature notation is widely used in popular music to transcribe and share guitar musical content. As a complement to standard score notation, tablatures transcribe performance gesture information including finger positions and a variety of…
We apply geometric group theory to study and interpret known concepts from Western music. We show that chords, the circle of fifths, scales and certain aspects of the first species of counterpoint are encoded in the Cayley graph of the…
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general…
Tonal structure is in part conveyed by statistical regularities between musical events, and research has shown that computational models reflect tonal structure in music by capturing these regularities in schematic constructs like pitch…
In this work, we propose a symbolic music generation model with the song structure graph analysis network. We construct a graph that uses information such as note sequence and instrument as node features, while the correlation between note…
In Music Information Retrieval (MIR), modeling and transforming the tone of musical instruments, particularly electric guitars, has gained increasing attention due to the richness of the instrument tone and the flexibility of expression.…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
Understanding the structural and cognitive underpinnings of musical compositions remains a key challenge in music theory and computational musicology. While traditional methods focus on harmony and rhythm, cognitive models such as the…
In this paper, we describe some recent spectral Moore theorems related to determining the maximum order of a connected graph of given valency and second eigenvalue. We show how these spectral Moore theorems have applications in Alon-Boppana…
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from…
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…
Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum modularity of a partition. We consider the…
Popular music is a key cultural expression that has captured listeners' attention for ages. Many of the structural regularities underlying musical discourse are yet to be discovered and, accordingly, their historical evolution remains…
Melody estimation or melody extraction refers to the extraction of the primary or fundamental dominant frequency in a melody. This sequence of frequencies obtained represents the pitch of the dominant melodic line from recorded music audio…
This paper investigates the relations between modular graph forms, which are generalizations of the modular graph functions that were introduced in earlier papers motivated by the structure of the low energy expansion of genus-one Type II…
In signal processing, exploring complex systems through network representations has become an area of growing interest. This study introduces the modularity graph, a new graph-based feature, to highlight the relationship across the graph…