From Circle to Hyperspheres

Episode I :
When Tonnetze go 4D

Chapters

0 Intro
1 Newton Circle
2 Planar Tonnetze
3 Torus and traditional 3D Spaces
4 Combining 2x 2D Spaces
5 Planet 4D Pitch and Chordal Space
6 Traditional Chordal Spaces in 2D
7 Ideograms in 3 parametric dimensions
8 The Hypersphere of Chords
9 The Hypersphere of Anysets

This Panel shows some chosen geometrical models representing the 12 tone equal tempered system that I’ve either re-colorized, reconstructed in 3D, or self-created from scratch in 3D or 4D during my PhD.
The examples are ordered by geometrical complexity. We start with the simplest circle and end up with a true 4D model that resides on a hypersphere.
The pedagogic purpose of this visualization is not to list or prefer any particular existing model but to illustrate the one I have created.
We will progressively familiarize the
spectator to the concepts of hyper-symmetry and four dimensional spaces.

Premiered at IRCAM Paris , 2011

Embeded Youtube Playlist :

From Circle to Hyperspheres Chap00 /

From Circle to Hyperspheres, when Tonnetze go 4D.
Scenario here : (updated 2013/02)
https://www.dropbox.com/s/u0dneo1tofn0a5c/Scenario%20for%20MCM%20Movie.pdf

Intro :
Only the title of the movie

2013 :
The Saga contents now two episodes
The First one was premiered in Paris ...Ircam Centre Pompidou , June 2011
The Second one was premiered in Montreal, McGill University , June 2013[+] Show More