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Concept

Music and mathematics

Related publications (14)

Data-Driven Music Theory: Curating and Investigating Large Corpora of Digitally Encoded Music Analyses

Johannes Hentschel

This dissertation on data-driven music theory is centered around curatorial practices concerning the creation, publication, and evaluation of large, expert-annotated symbolic datasets. With its primary interest in the harmony of European tonal music from i ...

EPFL2024

Computational modeling of interval distributions in tonal space reveals paradigmatic stylistic changes in Western music history

Martin Alois Rohrmeier, Fabian Claude Moss, Robert Lieck

Diachronic stylistic changes in music are to a large extent affected by composers' different choices, for example regarding the usage of tones, intervals, and harmonies. Analyzing the tonal content of pieces of music and observing them over time is thus in ...

Springernature2024

Fishing for complements with chord, scale, and rhythm nets

Daniel Harasim

The aim of this paper is to argue that complementation is an operation similarly fundamental to music theory as transposition and inversion. We focus on studying the chromatic complement mapping that translates diatonic seventh chords into 8-note scales wh ...

TAYLOR & FRANCIS LTD2023

midiVERTO: A Web Application to Visualize Tonality in Real Time

Fabian Claude Moss, Daniel Harasim

This paper presents a web application for visualizing the tonality of a piece of music-the organization of its chords and scales-at a high level of abstraction and with coordinated playback. The application applies the discrete Fourier transform to the pit ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Hearing functional harmony in jazz: A perceptual study on music-theoretical accounts of extended tonality

Martin Alois Rohrmeier, Steffen Alexander Herff, Daniel Harasim, Gabriele Cecchetti, Christoph Finkensiep

Functional harmony is an integral part of many repertoires in the Western musical practices, including both diatonic and extended tonality. In the latter context, music-theoretical accounts suggest that the three octatonic equivalence classes (OECs) consis ...

SAGE PUBLICATIONS LTD2022

Phantom Curves: Scientific Discovery through Interactive Music Visualization

Fabian Claude Moss, Daniel Harasim

We introduce phantom curves, a novel music-theoretical concept based on the discrete Fourier transform (DFT), and document the creative process that led to their discovery. In particular, we emphasize the importance of interactive web applications for musi ...

ACM2022

Axiomatic scale theory

Martin Alois Rohrmeier, Daniel Harasim

Scales are a fundamental concept of musical practice around the world. They commonly exhibit symmetry properties that are formally studied using cyclic groups in the field of mathematical scale theory. This paper proposes an axiomatic framework for mathema ...

TAYLOR & FRANCIS LTD2020

The Tonal Diffusion Model

Martin Alois Rohrmeier, Fabian Claude Moss, Robert Lieck

Pitch-class distributions are of central relevance in music information retrieval, computational musicology and various other fields, such as music perception and cognition. However, despite their structure being closely related to the cognitively and musi ...

2020

The pleasantness of sensory dissonance is mediated by musical style and expertise

Martin Alois Rohrmeier, Fabian Claude Moss, Markus Franz Josef Neuwirth

Western musical styles use a large variety of chords and vertical sonorities. Based on objective acoustical properties, chords can be situated on a dissonant-consonant continuum. While this might to some extent converge with the unpleasant-pleasant continu ...

Nature Research2019

Transitions of Tonality: A Model-Based Corpus Study

Fabian Claude Moss

Tonality has been the cornerstone of Western music-theoretical discourse for centuries. This study addresses the subject, using traditional music analysis, data-driven corpus methods, and computational models, concentrating on historical changes of tonalit ...

EPFL2019

Statistical characteristics of tonal harmony: A corpus study of Beethoven’s string quartets

Martin Alois Rohrmeier, Markus Franz Josef Neuwirth, Fabian Claude Moss, Daniel Harasim

Tonal harmony is one of the central organization systems of Western music. This article characterizes the statistical foundations of tonal harmony based on the computational analysis of expert annotations in a large corpus. Using resampling methods, this s ...

2019

Octave-spanning dissipative Kerr soliton frequency combs in Si3N4 microresonators

Tobias Kippenberg, Junqiu Liu, Maxim Karpov, Martin Hubert Peter Pfeiffer, Hairun Guo, Erwan Guillaume Albert Lucas, Michail Zervas

Octave-spanning, self-referenced frequency combs are applied in diverse fields ranging from precision metrology to astrophysical spectrometer calibration. The octave-spanning optical bandwidth is typically generated through non-linear spectral broadening o ...

Optical Soc Amer2017

Hydraulic transients in straight and coil pipe rigs

Anton Schleiss, Pedro Filipe De Almeida Manso, David Ferràs Segura

Transient pressure waves in real pipe systems are affected by several phenomena not accounted for in the classic waterhammer theory. Damping mechanisms are differently manifested according to the material, configuration and existing features of pipe system ...

2015

Optimized Kaiser-Bessel Window Functions for Computed Tomography

Michaël Unser, Cédric René Jean Vonesch, John Paul Ward, Masih Nilchian

Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform indepe ...

Ieee-Inst Electrical Electronics Engineers Inc2015