Below you will find pages that utilize the taxonomy term “Mathematics”
April 12, 2024
Tonality structure in music
Project: 3D Visualization of Tonal Harmony from MIDI Events
Quick start examples
MIDIport ▶ |
FluidSynth ▶ |
Windows ▶
The systematic recording of thoughts on musical harmony led to the placement of the twelve musical tones on a constructible three-dimensional surface of an umbilic torus. To this visualized link of mathematics and music I gave the personal name Cholidean harmony structure.
May 14, 2014
The polyhedron with the minimum of vertices, which considers itself a doughnut
Looping breathing-and-separation animation of the Császár torus
Photo of paper Császár polyhedron
Animated Császár polyhedron
Paper cut unfold of a Császár polyhedron
The article is about Császár polyhedron.
(Its dual is the Szilassi polyhedron).
Tutorial
I was never able to construct Szilassi by myself, but there it follows how i constructed Császár polyhedron.
Algebraic start
The Euler characteristic X of a torus is zero.
So our torus has V-E+F=0, where V=vertices, E=edges and F=faces.