Related papers: Geometry of Music Perception
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…
We describe here a class of acoustic metamaterials with fractal Hilbert space-filling and coiled geometry with equal tortuosity for noise mitigation. Experiments are performed using a four-microphone impedance tube and benchmarked against…
The melodic consonance of a sequence of tones is explained using the overtone series: the overtones form "flow lines" that link the tones melodically; the strength of these flow lines determines the melodic consonance. This hypothesis…
This is the first half of a two-part paper dealing with the geometry of color perception. Here we analyze in detail the seminal 1974 work by H.L. Resnikoff, who showed that there are only two possible geometric structures and Riemannian…
We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of the perception of the pitch of sounds, especially the sounds known as complex tones that are important for music and speech intelligibility.
Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field…
Real music signals are highly variable, yet they have strong statistical structure. Prior information about the underlying physical mechanisms by which sounds are generated and rules by which complex sound structure is constructed (notes,…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
Automatic melody generation for pop music has been a long-time aspiration for both AI researchers and musicians. However, learning to generate euphonious melody has turned out to be highly challenging due to a number of factors.…
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…
Many people enjoy classical symphonic music. Its diverse instrumentation makes for a rich listening experience. This diversity adds to the conductor's expressive freedom to shape the sound according to their imagination. As a result, the…
The music genre perception expressed through human annotations of artists or albums varies significantly across language-bound cultures. These variations cannot be modeled as mere translations since we also need to account for cultural…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
We propose different methods for alternative representation and visual augmentation of sheet music that help users gain an overview of general structure, repeating patterns, and the similarity of segments. To this end, we explored mapping…
Evaluating generative models remains a fundamental challenge, particularly when the goal is to reflect human preferences. In this paper, we use music generation as a case study to investigate the gap between automatic evaluation metrics and…
The development of models for learning music similarity and feature extraction from audio media files is an increasingly important task for the entertainment industry. This work proposes a novel music classification model based on metric…
This paper addresses the matching of short music audio snippets to the corresponding pixel location in images of sheet music. A system is presented that simultaneously learns to read notes, listens to music and matches the currently played…
We present a new system for simultaneous estimation of keys, chords, and bass notes from music audio. It makes use of a novel chromagram representation of audio that takes perception of loudness into account. Furthermore, it is fully based…
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…