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.

Mathematics or Music,this is question?!

Music, the Guide © Wayne Roberts.

Acrylic on two canvas panels,

overall dimensions 180cm (h) x 240cm (w)

When we hear a piece of music or composed them, in many case don't know or attention to special recipes or mathematical patterns that exist in them;

ok, it is normal, but do you know any person who applies this rule in contrary patterns? (Wants to convert natural or mathematical patterns to music),

One of them is Daniel Cummerow, according to his recipe each of notes in musical scale assumed to one digit in 1-8,
Suppose that 1 = do, 2 = re, 3 = mi, 4 = fa, 5 = sol, 6 = la, 7 = ti, 8 = do* (one octave higher),

Then he tried composed a pi tune. (Pi is the number you get when you divide a circle's circumference by its diameter.)

So he composed this piece:
mi, do, fa, do, sol, sol, re, la, sol, mi, sol, do*, do*, ti, ti, mi, re, mi, do*, fa, la, re, la, fa, mi, mi, do*, mi, re, ti, ti, sol, rest, re do*, do*, fa, do, do, ti, do, la, la.

You can play this piece in any rhythm or harmony and dynamic that you like!


Of course there is many of this pieces in nature,
Can you hear them?