Quoted from Ani Williams - Geometry, Music and Healing:
Leonardo de Pisa (circa 1180-1240 AD), better known as Fibonacci, discovered the uniformity of ancient harmonic wisdom. He realized that the natural branching, flowering, and spiraling forms in nature follow the same uniform laws found in musical scales.
He found this harmonic in nature is equal to a number sequence of 1-1-2-3-5-8-13-21-34-55-89-144 and so on, found by adding each number to the previous one to get the next number.
The Fibonacci series relates to all of the musical intervals, which comprise beautiful chords.
The Fibonacci ratios were also utilized in sacred temple architecture, including the towering Gothic Cathedrals. Guillaume Dufay (c. 1400-1474) from the Netherlands composed music for the dedication of Florence's cathedral of Santa Maria del Fiore in 1436. His musical piece was based on the Fibonacci series of tones, which corresponded to the dimensions of the cathedral's dome. These 'musical temples' were part of the medieval renaissance of sacred geometry, Hermetic mysteries and the flowering of art and music.
Listen to a piece of music that uses the ratios of the first eight Fibonacci numbers, ascending up the scales of E and E minor.
Here's a playlist of some other mathematically-derived musical tones.