Magic Chart!

Hey! in this picture you can see musical harmony and match it with geometry!

Here,You can play with intervals , same notes,scales, modes, geometrical shape that caused by different sequences,....

In first you see chart created by half steps, major 7ths, perfect fourths and perfect fifths


(I):
1-find and join same notes ,(you can write them as any scale or your favor sequence inside the chart,too)
2- attention to result shapes and find new relation between them


(II):
1- what is your favor scale ?
2- find its notes on chart,then write numbers behind them
3- try to create a shape by following numbers,

(III):
how appears a mode on chart ?if you move mode's chart,which mode or harmony caused?


Modes and The resulting scale degrees are :
C Ionian - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8/1 ( C D E F G A B C)
D Dorian- 1 - 2 - b3 - 4 - 5 - 6 - b7 - 8/1 (D E F G A B C D)
E Phrygian-1 - b2 - b3 - 4 - 5 - b7 - 8/1 ( E F G A B C D E)
F Lydian-1 - 2 - 3 - #4 - 5 - 6 - 7 - 8/1 (F G A B C D E F )
G Mixolydian-1 - 2 - 3 - 4 - 5 - 6 - b7 - 8/1 (G A B C D E F G)
A Aeolian-1 - 2 - b3 - 4 - 5 - b7 - 8/1 (A B C D E F G A )
B Locrian-1- b2- b3 - 4- b5 - b6 - b7 - 8/1 (B C D E F G A B)


discover new games and try to find its harmony!

The Relationship between Music-Astronomy-Math

Hypatia - one of the first women to study math, astronomy and philosophy

Handwrites & old Papers say that Plato said: the strongest of all life’s influences is music!

The Harmony of the World, 1619,The Keller's book describes that suggestion with mathematic and astronomy;

The new technology couldn't ignore them yet; what you can say about relationship between music in sky and mathematics and world harmony?

According to Plato we can 5 science of mathematics:
(I)Arithmetic, (II) 3-dimensional geometry, (III) plane geometry, (IV) Astronomy, (V) Music;
Perhaps music and astronomy can't match in our mind with other items;

For describing this section you can find a lot of information that most of them try to say that the world made of signals and music is too! Or , but of them can match with mathematics and so on;

About astronomy, the first reference is Pythagoras or Plato's Republic;

And actually when you read them you can not analyze them to only sections and because their subject that consist in music, philosophy, mathematics, geometry and astronomy are mixed peacefully and very nice!

Harmonics

Mathematics exists in many case of our life , and many happening have mathematical reasons; we can distinct different parts sound by it , and our feel (dissonance and consonance) depend on it and…

When two different musical instrument for example piano and violin are playing the same note, everybody can tell which of them is playing now; but how our brain can process them and what is real reason?is there any mathematic theory for this case?

The answer is hidden under a concept that named Harmonics. Harmonics caused many different sections in music; most of what follows, was discovered by Herman Helmholtz in 19th century;
In physics, Harmonics are at proportional frequencies, and at inversely proportional amplitudes.
The other word we can describe it by the lowest frequency that called Fundamental; the other tones are called Overtones; if the overtones have frequencies that are whole number multiples (x2, x3, x4,…, x14) of the Fundamental frequency, they are called harmonics.

If you play a "A" (440hz) with full harmonics , you won't only hear the 440hz tone.because it also has 880hz tone at half the volume (first harmonic) , a 1320hz tone at a third the volume (second harmonic), a 1760hz tone at a quarter of the volume (third harmonic) , and so on.these tones follows until the frequencies get too high or the volume gets too low to be heard...

The next posts of this article will discuss on other parts of harmonics and its results.

Harmony & Geometry

About previous discussions and describing the relationship between music and geometry,

must say about harmony and how showing it in a circle,

For example you want say a chord, try to connect your notes for that chord together, on circle;

You can find many of attractive things on music by this way, for example, related chords! When you draw two related chords in one circle, you can see they have symmetries by a line in circle,

or an equilateral triangle make augmented triads,

Isosceles triangle can make diminished chords and Sus, what is difference between Major & minor…

Cmaj(C-G-E):

Cmi(C-G-D#) :

You can expanse this role for other chords as froths, fifths…Try and discover new rules!

(C7)

( Cmi7)

(CMaj7)

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?

As a bird

"Anything that one wants to do really and one loves doing, one must do every day. It should be as easy to the artist and as natural as flying is to a bird. And you can't imagine a bird saying, 'Well, I’m tired today. I’m not going to fly."

Yehudi Menuhin