What the Golden Ratio Sounds Like
Tool’s song “Lateralus” from the album of the same name features the Fibonacci sequence symbolically in the verses of the song. The syllables in the first verse count 1, 1, 2, 3, 5, 8, 5, 13, 13, 8, 5, 3. The missing section (2, 1, 1, 2, 3, 5, 8) is later filled in during the second verse. The time signatures of the chorus change from 9/8 to 8/8 to 7/8; as drummer Danny Carey says, “It was originally titled 9-8-7. For the time signatures. Then it turned out that 987 was the 16th number of the Fibonacci sequence. So that was cool.”
Click here for: A Tribute to Tool’s Lateralus album & Its Sacred Geometry
Fibonacci intervals (counting in semitones) in Bartók’s Sonata for Two Pianos and Percussion, 3rd mov. (1937).
Ernő Lendvaï analyzes Béla Bartók’s works as being based on two opposing systems, that of the golden ratio and the acoustic scale. In the third movement of Bartok’s Music for Strings, Percussion and Celesta, the opening xylophone passage uses Fibonacci rhythm as such: 1:1:2:3:5:8:5:3:2:1:1.
The Fibonacci numbers are also apparent in the organisation of the sections in the music of Debussy’s Image, Reflections in Water, in which the sequence of keys is marked out by the intervals 34, 21, 13 and 8.
Polish composer Krzysztof Meyer structured the values in his Trio for clarinet, cello and piano according to the Fibonacci sequence.
American musician BT also recorded a song titled “Fibonacci Sequence”. The narrator in the song goes through all the numbers of the sequence from 1 to 21 (0 is not mentioned). The track appeared on a limited edition version of his 1999 album Movement in Still Life, and is also featured on the second disc of the Global Underground 013: Ibiza compilation mixed by Sasha.