Tool, Fibonacci, and You: An Extended Discussion
So I’m listening to a recent @therealjacksepticeye video and he mentions Tool’s use of the Fibonacci Sequence in their song Lateralus. As a long time Tool fan myself, as well as someone who loves looking into this kind of shit, I was pretty happy, to say the least. However, this isn’t the band’s only use of the sequence. Given that I’m sure some of his fans are at least somewhat interested in learning more, I thought I’d make a little post, going into more detail. (Grab a drink, this’ll be a long one.)
Now before I get too ahead of myself, allow me to give a brief explanation of what the Fibonacci sequence is:
“The Fibonacci sequence is a sequence of numbers in which each successive number in the sequence is obtained by adding the two previous numbers in the sequence. The sequence is named after the Italian mathematician Fibonacci. The sequence starts with zero and one, and proceeds forth as 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. The Fibonacci sequence is widely used in applications pertaining to mathematics, science, computers, art and nature. The Fibonacci sequence is also known as the Fibonacci series or Fibonacci numbers.“
(Source: https://www.techopedia.com/definition/15823/fibonacci-sequence)
Now you might be wondering “What the hell does this have to do with some metal band?”. As Sean mentioned in his video, the lyrics do make up a Fibonacci sequence. The song in question can be found here: https://www.youtube.com/watch?v=_tcW-j7KFgY
Here are the full lyrics, along with the syllable count of each line:
[8] red and yellow then came to be
[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
Now that is neat in and of itself. However, Sean DIDN’T mention that this song isn’t the only instance of the sequence being used by Tool, and, seeing as Lateralus is also the name of the album that this song is on, I think the sequence in the song might have been a clue of sorts.
*Quick note here: To my knowledge, Tool hasn’t confirmed if the following was intentional. Because of this, some fans have spoken out against it.
But then again... Maynard James Keenan, lead singer for Tool (as well as A Perfect Circle and Puscifer) has been known to be a bit of a troll to both fans and the press. Seriously, Google “maynard james keenan troll“. You’ll find plenty of examples.
What do I mean? The answer lies within the whole album. Not the fact that there are 13 tracks (though 13 is a Fibonacci number), but in the order of the tracks. Here’s the official listing:
10. Disposition 11. Reflection 12. Triad 13. Faaip De Oiad
Now here’s the interesting part: Fans have put together an alternate order that has come to be known as “The Holy Gift.” In order to hear this, you need to rearrange the tracks so that they are in the following order:
I found an article that does a good job explaining the math behind it, so I’ll just quote them here:
“So the final track order is 6, 7, 5, 8, 4, 9, 13, 1, 12, 2, 11, 3, 10, or [6,7] [5,8] [4,9] [13] [1,12] [2,11] [3,10], which is a “triad” of pairs divided by a split – or “schism” – in the middle. This, also, is not all.
2 of these tracks namely, Mantra and Eon Blue Apocalypse are non-lyrical, almost non-musical tracks. So that leaves us with 11 actual tracks. Now, to create a split, or a schism, 11/2 = 5.5
Taking the mean, in whole numbers 11/2 = 5. The fifth track of the album is called, yeah, Schism. Now here are the first few lines of Schism:
“I know the pieces fit ’cause I watched them fall away.
Mildewed and smoldering. Fundamental differing.
Pure intention juxtaposed will set two lovers souls in motion
Disintegrating as it goes testing our communication”
(Source: https://unbumf.com/tool-fibonacci-secret-album-holy-gift/)
I’ve been listening to The Holy Gift as I worked on this post, and I actually do like it better. Don’t get me wrong, Lateralus played in it’s “official” order is great, and you should check it out if you’ve never listened to it. But the reorder seems to flow better, IMO. They just seem to transition from track to track more smoothly.
The Holy Gift can be listened to in it’s entirety, thanks to Youtuber hiabovetheclouds . https://youtu.be/COTrB7N7EOA
I hope you enjoyed this little essay of sorts. If you’d like to learn more, below are some links that talk about this further.
Btw, for anyone that’s curious where the name “The Holy Gift” came from...
“So the "secret" of "The Holy Gift" is supposedly organizing the songs in a pair of spirals with number 13 in the middle. The first pair of the sequence is "Parabol," + "Parabola," tracks No. 6 and 7 (13/2 = 6.5), the latter of which features a line saying "Recognize this as a holy gift."
(Source: https://www.ultimate-guitar.com/news/general_music_news/so_tool_have_a_secret_album_called_the_holy_gift_heres_what_it_sounds_like.html)
The Fibonacci in Lateralus: https://youtu.be/wS7CZIJVxFY
Fibonacci Sequence in “Lateralus” : http://www.ecojazz.com/2012/10/31/fibonacci-sequence-in-lateralus/
How Tool Used Math to Create "Lateralus" : https://www.youtube.com/watch?v=uOHkeH2VaE0
Music From The Fibonacci Sequence : https://www.youtube.com/watch?v=IGJeGOw8TzQ
The Mind-Blowing Mathematics of Sunflowers: https://www.youtube.com/watch?v=z9d1mxgZ0ag
The magic of Fibonacci numbers: https://www.youtube.com/watch?v=SjSHVDfXHQ4
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