Pythagoras

Pythagoras (c. 570-c. 495 BCE) was a Greek Mathematician and Philosopher who founded the Philosophy of Pythagoreanism.
He is known as the ‘Father of Mathematics’, the ‘Father of Geometry’, and the ‘Father of ‘Father of Music’. His teachings influenced Socrates, Plato and Aristotle.

Pythagoras' Theorem states the relationship between the three sides of a right angled triangle.
‘The square of the Hypotenuse, is equal to the sum of the squares of the other two sides.’
Also written as: ‘a’ squared + ‘b’ squared = ‘c’ squared’.

Pythagoras said that the highest goal of music is to connect the soul to its Divine Nature.
He was an accomplished Lyre player.
He developed the idea of octave scales and began exploring the science of music.
He was the first person to prescribe music as a medicine.

Pythagorean Hammers:

He discovered the intervals in music by listening to the sounds produced by four hammers of different sizes as they struck red hot iron on an anvil. When they struck simultaneously, they produced consonance and dissonance. He conjectured that the different tones were produced by the ratio of the size of the hammers to the anvils.

The Monochord:

He invented a musical instrument called the monochord to demonstrate harmonies of pairs of strings with different integer length ratios.
A string exactly half the length of another, will play a pitch exactly one octave higher.
If the string is divided into thirds, the pitch is raised by an octave and a fifth.

Pythagorean Theorum of Music:

There are 12 notes in an octave.
If the length of a string is cut in half, the pitch would be equal in tone, but at twice the frequency: an octave.

Pythagorean Scale:

Starts with a note (frequency), when doubled, it is the same note one octave higher.
It is any scale which can be constructed by only using pure fifths (3:2) and octaves (2:1).
Pythagoras was able to describe the basis of virtually any musical scale, including the pentatonic, the Western, the Chromatic and the Arabic scales.
In Greek music, the scale was used to tune tetrachords, composed into scales spanning an octave.
There is also a 12-tone Pythagorean temperament.