Who among us has never heard of the gilded ratio? We speak of a mathematical constant, the number 1.618, produced by a formulation of Euclid and indicated with the lowercase Greek alphabetic character φ (phi). It contains many algebraic and geometric properties that take ever attracted the interest of many scholars, in remote and recent times. The gold ratio is so much present in the physical reality to define the whole universe, it tin can be considered, for good reasons, the mathematical representation of life. Due to this peculiarity, it has been applied in diverse areas and has allowed u.s.a. to create unexpected links between apparently afar disciplines: botany, physics, zoology, architecture, painting and music, also with mystical-esoteric values.

The golden ratio had such a fascination for Greek civilisation that architects and sculptors made it their canon of perfection, beauty and harmony. Later on, in the Renaissance, the Italian mathematician Leonardo Pisano (called Fibonacci) created the famous sequence of numbers related to it that bears his name. In this serial, each number is the result of the sum of the previous 2: 0, 1, 1, ii, three, 5, eight, 13, 21 … to infinity. Then it was that the gilt proportion became very popular among the artists and mathematicians of the time. Information technology represented the real mystical key in the arts and sciences, then much so as to be defined as "divine proportion". At that place were numerous artists who used it in their architectural and pictorial works, i above all the great Leonardo Da Vinci who illustrated it in the famous Vitruvian Man and used information technology in works such equally the Concluding Supper and the Mona Lisa. Even in modern times painters such as Picasso, Seurat, Dali, Mondrian and architects such as Le Corbusier take made all-encompassing use of it.

The mythical and mystical side of the gold ratio is not the prerogative of figurative art, many musicians accept been won past the magic of these mathematical relationships and numerous great composers of the past have used information technology in their works. Nosotros tin find it in the rhythms and musical structures, in the system of accents within movements and in the relationship between the latter. Many examples prove how the proportion of the various parts of a work is often set in the viii/5 ratio, close to the Phi number. It is like shooting fish in a barrel to find those elements in some works by Bach, Haydn, Mozart or Beethoven. But in add-on to the formal canons of musical language, it is in the very atoms of music, the notes, that the golden ratio tin be found incredibly. In the octave, the founding unit of measurement of melody and harmony, we see Fibonacci numbers popping up everywhere.

In the music of the twentieth century the gilt ratio has constitute fertile ground spreading out of all proportion: Debussy, Stockhausen, Bartók, Stravinsky, Manzoni, Ligeti, are but some of the best known names that take voluntarily chosen the employ of these magical proportions. Towards the terminate of the 1900s, a real academy enquiry grouping was born in Paris, the Heart d'Études de Mathématique et Automatique Musicales, with the aim of applying scientific and mathematical cognition to music.

Today Rock music, especially progressive one, has let itself exist conquered by golden proportions. A very meaning case is Genesis' brave song Firth of 5th, which contains solos of 55, 34, 13 confined entirely based on gilt numbers. Not fifty-fifty the most rock ring e'er, Deep Purple, has remained insensitive to the call of the "golden numbers", every bit the famous song Child in Fourth dimension shows. Dream Theater'due south Octavarium album and Tool'southward Lateralus piece are also designed on Fibonacci sequences.

Below you detect a option of musical pieces based on the Fibonacci serial and the golden ratio:

  • Bach –Variazioni Goldberg
  • Mozart –Sonata no. 1 in Practice maggiore K 279 I
  • Beethoven – Sinfonia n. 5 in Do minore I
  • Debussy –12 Preludi (Libro Primo)
  • Satie –Sonneries de la Rose et Croix
  • Bartók – Musica per archi, percussione e celesta,BB 114, SZ 106
  • Stockhausen –Klavierstiicke 9
  • Genesis –Firth of 5th
  • Deep Purple –Child In Time
  • Tool –Lateralus
  • Dream Theater –Octavarium
  • Iannis Xenakis –Metastaeis

Francesca Brocchetta