photo credit: album cover, TOOL
Over the years, I have consistently admired Tool, a progressive metal band. Tool’s song, “Lateralus” (featured on their 3rd studio album, which shares the same name) is undoubtedly one of my favorites, primarily because of their cleverness regarding the song’s lyrical rhythm structure with relation to its meaning.
In this song, Tool’s vocalist, Maynard James Keenan, conveys a message of vulnerably pushing forward: to spiral out into the unknown and to see where it may take you. The phrase ‘spiral out’ is a reoccurring message throughout the concluding lyrics. More notably, what I appreciate most about “Lateralus” is the intentional use of mathematics Tool embedded throughout this track.
Adding to this lyrical exposition of ‘spiraling out,’ the band intentionally incorporates the Fibonacci Sequence into the rhythm structure of the song’s verses. The Fibonacci Sequence is a series of numbers which form a spiral if the sequence continues onward from its starting point. It starts with 1; then the second number is also 1. From this point on, every number is the sum of the previous number.
(and so on…)
So, you have 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…etc.
This mathematical sequence also exists in nature, such as the spiraling pattern of sunflower seeds in a sunflower, as well as the numerical sequence of many different types of flower pedals, leaves and branches, pine cones, pineapples, nautilus shells, snail shells, storm systems – the list goes on indefinitely.
During the verses of the song, the syllables of each word used are also Fibonacci numbers and are rhythmically spaced as such:
Black (1), then (1), white are (2), all I see (3), in my infancy (5).
Red and yellow then came to be (8),
Reaching out to me (5).
Lets me see (3).
As below so above and beyond I imagine (13).
Drawn beyond the lines of reason (8).
Push the envelope (5).
Watch it bend (3).
The 2nd verse is the same, aside from an additional section in the middle which states:
There is (2), so (1), much (1), more and (2), beckons me (3),
To look through to these (5),
Infinite possibilities (8).
In addition to the verses, the time signature during the chorus of the song switches from 9/8 to 8/8 to 7/8, resulting in a 9-8-7. Consequentially, 987 is the 16th number of the Fibonacci sequence as well. This deep level of consideration Tool gives each of their songs, is an undeniable reason this band will infallibly remain one my personal favorites.
Tool’s album, Lateralus, received many accolades, including double platinum recognition, a Grammy for ‘Best Metal Performance,’ and a ‘No. 123’ on Rock & Roll Hall of Fame’s “Definitive 200” list. As a writer, musician, and a fan, I highly recommend this album to anyone who fancies progressive metal.
about the author
Ryan Diehl is a self-taught musician and singer/songwriter from Kansas. So far, he has spent the vast majority of his life tying to write his best song. Sadly, he is also his own worst critic, so it is safe to assume he may never succeed. Nevertheless, he continues to pour his heart and soul onto the keys of his piano in relentless pursuit.