4. DESCRIPTION OF "3D MUSIC TETRAHEDRON "

A. History and investigations to find the right shapes

My first idea was to create a world made of scenes in different places (forest, desert, city....) and put a music in each one. But it was too much work. So we decided we will use simple shapes: sphere, cylinder, tube... and will put a music in.

Also, we had to look for the right way to place them in the space so that we will have a central point located at the same distance from each shape (to have a point where all the styles will be heard with the same intensity):

We asked mathematicians and physicists to help us to solve this mathematical problem. Here are in brief the informations we got:

Let’s say that the 6 shapes are 6 points on the screen (A,B,C,D,E,F), and we want a balance point Z. But if the points play sounds (our musics), the straight lines AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF, must have the same length.(1)

The only possibility to have Z at the same distance from the others is to put A,B,C,D,E,F on a sphere and put Z in the center. But the identity (1) is not possible in a 3D world, whose limit is 4 points: in a 3D world the solution to this problem is the tetrahedron.

But still we needed 6 or 7 points to have 6 or 7 groups of music. For that we should need a 5D space, which is obviously impossible to realize.

Now it was clear that we could not find a solution with 6 or 7 shapes. But the idea of the tetrahedron was here. This shape let us have 4 points at the same distance from the middle.

Jason first tryed to put 5 tetrahedrons together, but the conditions were still not there. He finally had the idea to put 20 tetrahedrons together. This assembling enters a sphere, and we have on that sphere 12 points; these points-the vertexes- (which are actually instruments of music) are placed at the same distance from the center.

(See Picture 1)

Each tetrahedron has a band in. We also have 13 more tetrahedrons where we can put 13 bands in.

(Picture 1)

This way we found the solution that allows us to use 20 groups inside 20 tetrahedrons with a meeting point at the center.