Scale & Geometry

For describing relation between mathematics & music ,If I say ancient theories ,I guess there are many disagreements to describe that they are just theories without applicability;

Therefore I prefer to describe application theories then I'll say ancient theories;

We know music composed of harmony, melody and rhythm;
at first,For making a piece you must select scale,
If you take all 12 notes (the chromatic scale) and arrange them around a circle you produce a clock -like image; that is important for describing this topic.

Then try to connect each note of scale together for making musical scale,
so, you have a seven-angles;

Move one of these angels, what happened?
Seven-angles turned around circle's center and makes a new scale!
Repeat this pattern for making any scale, you can't make mistake with this pattern,

Many concepts in music can display as shapes and angles,
Think!

But why we have 12 tones in octave?
It has mathematical reason, too.