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stefanovagnini

1,61803398874989484820... Music on The Golden Ratio and the Fibonacci sequence

Aggiornamento: 17 ott 2020

The DMX therapy alternates an Acousmatic Electronic composition to each of the 30 Goldberg Variations. Thes original compositions are called Golden Ratio.


The music will be uploaded on a personal device (smart phone, mp3 player...) and enjoyed from headphones (the audience has to keep headphones during the whole therapy).

There are different reasons to use headphones:

  1. to keep the attention focused on the voice during the counting;

  2. to encourage the ears to look for the sound of the harpsichord;

  3. to avoid any kind of verbal communication;

  4. to enjoy the binaural beats and their effect on the brain waves (delta, gamma, theta...).

Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618. It is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment.

The origin of this number can be traced back to Euclid, who mentions it as the “extreme and mean ratio” in the Elements.


The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it:

  • the 2 is found by adding the two numbers before it (1+1),

  • the 3 is found by adding the two numbers before it (1+2),

  • the 5 is (2+3),

  • and so on!


And here is a surprise:

When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio "φ" which is approximately 1,618034...

In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation.


Plants can grow new cells in spirals, such as the pattern of seeds, galaxies, the all universe likes to apply this irrational number to expansions and contractions.

The spiral happens naturally because each new cell is formed after a turn.



I changed the musical scale frequencies with the Fibonacci's sequence to create an unknown but extremely natural sound material. The lower out of earing range sounds are generated by binaural activity.


And I had another surprise:

In the frequency sequence 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377...

the frequency 55 is a perfect pitched A of the equal temperament,

233 is a perfect B flat, 987 a perfect B and 4181 a perfect C!

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