Seqüência de Fibonacci e Phi na música: Tool - Lateralus

deixarei a explicação original em inglês, pra não perder detalhes

“Lateralus”, incorporates the Fibonacci sequence. For example, the syllables of the lyrics follow the Fibonacci pattern, and the time signature of the chorus rotates between 9/8, 8/8, and 7/8 time, referring to the 17th Fibonacci number, 987. The theme of the song describes the desire of humans to explore and to expand for more knowledge and a deeper understanding of everything. The lyric “spiral out”, which is sung repeatedly throughout the song, refers to this desire and also to the Fibonacci spiral, which is formed by creating and arranging squares for each number in the sequence’s 1,1,2,3,5,8,… pattern, and drawing a curve that connects to two corners of each square. This forms a never-ending and infinitely-expanding spiral.

Counting between pauses, the syllables in Maynard James Keenan’s vocals during the verses form the first few Fibonacci numbers, ascending and descending:

(1) Black,

(1) then,

(2) white are,

(3) all I see,

(5) in my infancy,

(8) red and yellow then came to be,

(5) reaching out to me,

(3) lets me see.

(2) There is,

(1) so,

(1) much,

(2) more and

(3) beckons me,

(5) to look through to these,

(8) infinite possibilities.

(13) As below so above and beyond I imagine,

(8) drawn outside the lines of reason.

(5) Push the envelope.

(3) Watch it bend.

The Fibonacci sequence shares a relationship with spirals, which are mentioned several times later in the lyrics.

Additionally, Keenan begins singing at 1:37 into the song. 1 minute 37 seconds, or 97 seconds, is approximately 1.618 of a full minute. This happens to be the golden ratio, which is closely related to the Fibonacci sequence.

Não é o único trabalho elaborado da banda, todo o álbum Lateralus tem coisas assim “escondidas”. Sou suspeito pra falar porque sou fã, mas quem quiser conhecer vale a pena: toolband.com

via proofmathisbeautiful e constantflux