The Piano Explained From The Thought Of Pythagoras

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The piano explained from the thought of Pythagoras


The philosopher and mathematician Pythagoras, founded the school which gave an important boost to the development of mathematics in ancient Greece.

Pythagoras are attributed to having transformed mathematics with a liberal teaching through the abstract formulation of their results, regardless of the material context in which some of them were already known. For example, the famous theorem of Pythagoras, which establishes the relationship between the sides of a triangle (square of the hypotenuse is equal to the sum of the squares of the categories).

Pythagoras declared that there was a mathematical relationship between tones that sounded harmonically and so he realized that music could be measured by means of whole numbers.

We know that the sounds produced when touching a rope depend on the length, thickness and tension. We understand that these variables affect the sound of the strings.

Pythagoras discovered, is that by dividing the rope into 2 he was able to produce pleasant sounds to the ear; That was a great confirmation of his theory, numbers and beauty were one.

Arje is a philosophical concept of ancient Greece, means the beginning of the universe or the creation of all things.

"Things are numbers and everything is mathematizable and reducible to numbers".

According to Pythagoras, everything has its figure, and to this in turn, it corresponds to a number, according to its form; if there are no numbers then things would not exist either.

Knowing the Arje of Pythagoras and how it works we will relate it to a well -known and used instrument, the piano. What is the relationship of piano and the pythagoras arje?


To start the piano is a musical instrument, classified as a string and percussion instrument. It has a resonance box with a keyboard, in which the steel ropes with hammers covered with felt are touched, producing harmonic sounds.

A piano has 7 white keys and 5 black keys with a total of 12 keys per eighth (eight -degree interval between two notes of musical scale). Most modern pianos have 7 octaves.

White keys are classic notes and black keys correspond to modified notes.

The tones are distributed by octaves, on the left are the tones of the Fa Pentagram and on the right side are the tones of the sunshot.

Considering the definition of Pythagoras’ arje "things are numbers and everything is mathematizable and reducible to numbers", it is determined that the piano in a thing and its keys are also things are also things.

For the above, if we represent the piano and the black and black keys for a number and we turn it into the musical notes we know now, they would be like this:


Arje number



0; zero

Set of musical notes

Key 1 (white)



Key 2 (white)



Key 3 (white)



Key 4 (white)



5 (white) key



Key 6 (white)



Key 7 (white)



Key 8 (black)



Key 9 (black)


My b#

10 (black) key



Key 11 (black)



Key 12 (black)



Therefore, we complete the 12 keys in an eighth in the piano with their respective musical note.

The musical composition is the art that aims to create harmonies, works; It consists of the combination of musical elements and their components; In other words, the musical composition is the process of creating a new musical piece.

With the use of the keys, a musical composition can be formed, the notes of each key are placed in the FA and Sun Pentagram to give a better mobilization to the sound.

The formation of the notes (sounds determined by a vibration whose frequency is constant) and pentagrams (site where the musical notes and signs are written) are related to mathematics, since the sums, subtraction, multiplications and divisions for their Formations.

For example, the Pythagorean tuning: it is a musical scale built on intervals of the tuning per fifth, at a rate of 3/2 (three media), therefore, the pythagorean repetitions of the note do would be the following: 1, 2, 2, 4, 8, 16, 32, 64, 128, 256, among others.

For Pythagoreans, music had a moralist and medicinal value; This is why Pythagoras asked to start music for music, using certain melodies and rhythms; Thanks to which he cured the character features and the desires of man.


  • The piano is a musical instrument and according to the definition of the Arje de Pythagoras it is something that has its figure.
  • The piano keys are also things that have a figure and therefore correspond to them a number.
  • The octaves represent the set of keys and their representations in numbers of the pythagoras arje.
  • Sun and FA pentagrams are a better help for the location of notes and musical composition.
  • Therefore all these pentagrams formations are a small modification for the existence of numbers and keys.
  • Musical compositions are the formations of musical notes that are at the same time numbers, that is, without the notes there would be no musical compositions.
  • Mathematics helps numbers to be part of musical compositions and pentagrams formations.
  • The piano is not only related to the pythagoras arje in terms of form and numbers but also because of its mathematical relationship between tones that sounded harmonically and thus realized that music could be mathematically measured and reducible to numbers.
  • With this I conclude that the piano has not only been linked to the Arje de Pythagoras, but with its multiple compositions and structures has become an object that shows the realism of the pythagoras arje with respect to the beginning of life.

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