Differential Geometry of Music Perception (Benjamin Himpel, DMV Mathart 2022) скачать в хорошем качестве

Differential Geometry of Music Perception (Benjamin Himpel, DMV Mathart 2022)

In response to the question "Why does music theory sound good to our ears" on Wired.com Tech Support (May 26, 2021) Jacob Collier answers "Music theory doesn't really sound like anything. It sounds like parchment. Music sounds like stuff though, and the truth is no one knows. It's a bit of a mystery." Mathematics allows us to use neuroscientific theories and sychoacoustic discoveries in order to systematically solve the mystery. The ultimate goal is to translate music into measurable entities which can be analysed within a holistic model, and that we can deduce good music based on the manipulation of formal objects. To this end we develop some of the mathematical foundations suitable for describing the way humans perceive music. We show that the space C of musical chords is a stratifold, which is a generalization of a differentiable manifold invented by Matthias Kreck. Its Riemannian metric naturally yields a geodesic distance function suitable for voice-leading. The resulting voice-leading distance satisfies the triangle inequality across different strata of C. Using the rich mathematical structure of C we analyse psychoacoustic quantities like roughness and harmonicity that describe musical qualities of chords. Concepts for the perception of music and musical expectation thereof are introduced and analysed based on the differential-geometry of psychoacoustic paths in C and probability theory. -- Talk by Benjamin Himpel (Hochschule Reutlingen) Find the corresponding paper "Geometry of Music Perception" here: https://www.mdpi.com/2227-7390/10/24/.... -- Talk given at: Minisymposium "Mathematics and Arts" at the annual meeting of the German Mathematical Society, 12. - 16. September 2022 (https://ms-math-computer.science/proj...) Organized by: Milena Damrau and Martin Skrodzki (https://ms-math-computer.science/) Twitter:   / msmathcomp   -- See also: Minisymposium "Mathematics and Arts" at the annual meeting of the German Mathematical Society, 14-17 September 2020 (https://ms-math-computer.science/proj...) Playlist:    • DMV Minisymposium "Mathematics and Arts" 2020   Minisymposium "Mathematics and Arts" at the annual meeting of the German Mathematical Society, 27 September - 1 October 2021 (https://ms-math-computer.science/proj...) Playlist:    • Jigsaw puzzles, bell ringing, and Hamilton...