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The Fibonacci in Lateralus

Hell yes. Tool’s Lateralus analyzed and put into the context of the Fibonacci sequence. Or vice-versa. It’s always nice to receive confirmation that you’re not the only one who’s completely insane.

24 comments… add one
  • jaced.com September 26, 2007, 1:23 pm

    When the 13 tracks of Lateralus are rearranged with the Fibonacci in mind, the album is smoother, with a seamless transition between each song.

    6, 7, 5, 8, 4, 9, 13, 1, 12, 2, 11, 3, 10

    6. Parabol
    7. Parabola
    5. Schism
    8. Ticks and Leeches
    4. Mantra
    9. Lateralus
    13. Faaip de Oiad
    1. The Grudge
    12. Triad
    2. Eon Blue Apocalypse
    11. Reflection
    3. The Patient
    10. Disposition

    6, 7, 5, 8, 4, 9, 13, 1, 12, 2, 11, 3, 10

    See anything else? Look closely.

    6 + 7 = 13

    5 + 8 = 13

    4 + 9 = 13


    1 + 12 = 13

    2 + 11 = 13

    3 + 10 = 13

  • jaced.com September 26, 2007, 2:24 pm

    I just found this on the Internet. Author currently unknown.

    To me, Tool’s Lateralus is the most amazing piece of music ever composed. I think Tool deliberately wanted to give their fans something truly amazing, but wanted them to find it on their own. “Recognize this as a holy gift…” At first, I thought that the song Lateralus was about tripping acid – discovering true color by seperating the body from the mind. At first listen, I imagined the bending envelope as an intense visual. After becoming more familiar with the track, however, I had reformed my interpretation to something broader: think deeper. Lateralus, perhaps because it is the album’s “title track”, serves as the central clue for a puzzle that a friend of mine had read about somewhere on the internet. “All I know is that there is a different order for the songs – something about two spirals. Oh yeah, and thirteen is in the middle.” After scavenging through endless google search results, I gave up on finding more about this ‘alternate order’. Intent to figure the album out, and very curious about the spirals – I put on the proverbial ‘thinking cap’. I understood how the spirals could have a lot of significance, in that the album’s title track offers the inspiring, “swing on the spiral of our divinity and still be a human……….And following our will and wind we may just go where no one’s been. We’ll ride the spiral to the end and may just go where no one’s been.” In my internet scavenging, I had read one review, written by a drummer, who mentioned that Danny Carey’s drum beat formed a fibonacci sequence during the song Lateralus. A drummer myself, I decided to get out the graph paper and follow Danny. I can’t play like he can, but at least I can hear everything he’s doing, and thus was able to construct the drum tabulature. Sure enough, Danny repeats a Fibonacci sequence through the number 13: 1,1,2,3,5,8,13. After 13, he starts again with 1. Bringing in my Algebra 2 knowledge of the Fibonacci sequence, when the equation for the Fibonacci sequence (which I don’t actually know) is graphed, it forms a sprial whose vertex depends on the number at which the sequence begins. Coincidence? I began to think not. I had already known of Danny’s obsession with sacred geometry and am familiar with Bob Frissell’s book, Nothing in This Book Is True, But It’s Exactly How Things Are , so the significance of what I had stumbled upon had actually begun to settle in. This is where I just had to play with Lateralus. I had doodled a few spirals in the corners of my graph paper, and in doing so made the first important connection to Lateralus. I knew that if the tracks were in fact intended to be heard in a different order, “Parabol” and “Parabola” would have to go together. In drawing my spirals, I had begun with a vertex and ‘spiraled’ outwards. After writing the numbers 1 through 13 linearly, I could immediately see that Parabol and Parabola would have to be the middle of my spiral (in that 13 / 2 = 6.5). I drew a simple arrow between 6 and 7 and then pondered the next pair. At first, I actually drew a spiral connecting pairs of numbers whose sum equaled 13 (the number of songs on the album). This, however, left the last track in the same position and without anything to connect to. At this time, I had used my copy of Lateralus and Cool Edit Pro to take out the silences between tracks and put the songs in the following order: 6,7,5,8,4,9,3,10,2,11,1,12,13. The transition from Parabola into Schism blew my mind, as the plucks, probably dismissed by listeners as a drawn out rant of an ending, perfectly transition into the beginning of Schism. When you count out beats as the strings are plucked, Schism resumes with the same time signature and tempo – mirroring the progression of notes. The transition from Schism into Ticks & Leeches is equally intriguing. Schism ends with strong double-kick bass and tom smacks, and Ticks & Leeches begins with what many would call a ‘tribal’ drum beat. The beat at the very start of Ticks & Leeches is slightly different every subsequent time it is repeated – the measures are two beats longer. Yup – you guessed it – those two beats are ACTUALLY the last two beats of Schism. I can honestly say that I never understood the album’s fourth track, Mantra until reordering the album’s songs. What I had originally heard as whale calls now had begun to resemble the worst imaginable dry heaves – or a stylized choking. Fitting, seeing as how the last line in Ticks & Leeches is “I hope you choke.” After this transition, none of those following it really seemed to make much sense. I certainly didn’t like that Disposition and Reflection had been seperated – as they sound quite good when played sequentially on the album. This was the only real roadblock in my disciphering of the Holy Gift. Then I had remembered what my friend had told me – 13 was in the middle. At the time, probably just wanting to believe that there was more to this cd, I had equated this to the positioning of the song “Intermission” on the previous release, Ænema. For the song to be in the ‘middle’ of the album it would have to be the seventh track in sequence, here having six tracks on either side of it. So I inserted Faaip de Oiad after Lateralus, and almost peed my pants when I discovered that (ever-so-faintly) the fading tone of the last note of Lateralus could be heard in beginning of Faaip de Oiad, and how the distortion of the guitars at the tail end of Lateralus resembled, and later transitioned seamlessly into, the static at the beginning of Faaip de Oiad. The lyrics of Lateralus justify this break in the spiral, almost instructing: “spiral out, keep going, spiral out, keep going.” I went back to Lateralus to find the next clue. In Danny Carey’s amazingly competent Fibonacci sequence, he had stopped at 13 and gone back to 1. This is what I chose to do to finish the sequence. A second spiral was now constructed, and the order for the Holy Gift now became 6,7,5,8,4,9,13,1,12,2,11,3,10. Already many of you are probably fascinated at what I have revealed to you, but I can not even begin to tell you what this new order has opened up for me. The beauty of Lateralus is very, very fragile and has to be viewed with a very open mind. It can also be different when looked at from different points of view. Aside from the fact that the new order of the songs places them in an order where they flow together nicely – often ending and resuming on the same notes or within the same progression, and some times – in the case of Lateralus into Faaip de Oiad and The Grudge into Triad – even overlapping (though admittadly sound much better when actually electronically overlapped, this is kind of cheating. Consider this a hint, however, if you plan on doing this yourself), the two spirals help to tell a story that every Tool fan should hear. In the interest of not boring the only casually intrigued, I will try to keep this very brief. I would also recommend familiarizing yourselves with Frissell’s book (yeah – the one I mentioned earlier). I consider Parabol and Parabola to be quite expository. Maynard wants us to know that no matter what happens, we must all know that this is not our only existance. Our very minds and the contents of our subconscious are intended to be immortal, and if we accept this into our lives (be it because of personal or religious reasons), it will be so. As such, pain is an illusion. At first, I called it “The Lateralus Prophecy” (for reasons you will soon understand), but I have since decided to call the ‘reordered’ version of Lateralus “The Holy Gift”. As Maynard says, “Recognize this as a holy gift and celebrate this chance to be alive and breathing,” I take the word “this” to mean much more than just his simple cautioning. Since Parabola is the second track of the Holy Gift, it can be considered at the beginning (esp. considering the context of it’s duality with Parabol), and as such, I interpret Maynard’s words as more than just clever lyrics in a song. They are a plead for his listeners to listen to everything he has to say and truly celebrate the chance of immortality offered throughout. I would be lying if I said that each song has a specific translation. On the contrary, Tool’s music is designed to make you think, not say something specific. It must be treated like great literature – much is hidden contextually. I will elude to Geometric-Drumming’s previous post, where he explains the time signatures of Schism: “It represents the title…it’s arranged in 12/8 time which is SPLIT into 5/8 and 7/8 – which only really FITS as you PUT THE PIECES BACK TOGETHER.” Where Geometric-Drumming claims Schism as his favorite Tool song, I have heard some fans say that it was a retched pick for the album’s only single – but I think it was brilliant. Not to downplay the interpretations of those who have posted before me (in fact, I agree with much of what %BlueSoulRobot% has to say), but I think that to the casual listener who knows nothing of Tool, it can be a powerful invitation. Think about it – a lot of dingbats with MTV and a radio would walk around with the words “I know the pieces fit” in their heads. I wonder how many of them took the time to put the pieces back together to (re)discover what is trying to be communicated. I welcome any feedback. I would love to share interpretations of the songs via email – just too lengthy to post here. I would like to offer the following advice: DO NOT use MP3s to digitally reorder Lateralus. A lot of VERY IMPORTANT information is encoded on the actual cd. Ever notice how everyone who has lost or broken that cd has IMMEDIATELY gone out and bought a new copy? I know I have. It’s because there are things encoded on the factory pressing of the cd that are lost in the mp3 compression process and any direct copy onto a cd-r. If you want to do it, do it right – I can’t stress how important this is. Use the cda tracks as you put it together and maintain all audio fidelity using professional mixing software.

    There’s a Fibonacci in Maynard’s lyrics, specifically the syllables:

    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]

    there is [2]

    so [1]

    much [1]

    more and [2]

    beckons me [3]

    to look through to these [5]

    infinite possibilities [8]

    as below so above and beyond I imagine [13]

    drawn outside the lines of reason [8]

    push the envelope [5]

    watch it bend [3]

    I suppose it’s not actually a true Fibonacci, since it does reverse itself.

    the Fibonacci Sequence. It’s basically a string of numbers that when you add a number to the number before it, you get the next number. Starting with the numbers 0 and 1. 0+1=1, so the set now looks like this; 0 1 1. You take the 1 and add the previous number (1) and you get 2. The sequence looks like this; 0 1 1 2. Now you take the 2 and add the previous number and get 3. Now you have 0 1 1 2 3. When you add the 3 and the 2 you get 5. 0 1 2 3 5. 5+3=8. 0 1 1 2 3 5 8. The process continues.

  • jaced.com September 27, 2007, 11:24 am

    I just counted out the opening groove to Lateralus. It was pointed out in the demo, but I needed to analyze it for myself. It’s correct.

    The opening groove can be dictated as three bars, consisting of a bar of 9/8, followed by a bar of 8/8, followed by a bar of 7/8.

    9, 8, 7.


    The Fibonacci Sequence:

    0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, …

  • jaced.com September 27, 2007, 1:48 pm

    Ha. I just noticed the 34 bar intro in the beginning, before the opening groove. 34 is the tenth number in the Fib. Sick.

  • jaced.com October 28, 2007, 10:44 am

    Had a convo with a buddy the other night and started thinking about this again. I woke up today noticing something about the Lateralus Fibonacci sequence.

    Again, it’s:

    6, 7, 5, 8, 4, 9, 13, 1, 12, 2, 11, 3, 10

    Now, an interesting pattern can bee seen if we examine the differences between the adjacent numbers:

    6, 7 = 1
    7, 5 = 2
    5, 8 = 3
    8, 4 = 4
    4, 9 = 5

    Then we have:

    9, 13 = 4. Swinging us back for a moment as we hit the epicenter of the spiral.

    It’s implied that we’re missing 6, the first perfect number. Anyhow, starting again with 13 in the sequence and spiraling out:

    13, 1 = 12
    1, 12 = 11
    12, 2 = 10
    2, 11 = 9
    11, 3 = 8
    3, 10 = 7

    There’s probably more going on in the center of the sequence than I’ve wrapped my brain around. I also have a pressing suspicion that the the significance of 6 is gonna slam me across the head one of these days. The first glaring metaphor that jumps out is the idea that, with 6 representing perfection, the spiral must continue eternally in pursuit of perfection. An existence of the number 6 would complete the sequence, putting a lid on it. But that simply can’t happen, right? Infinity has no limits.

    I know the pieces fit…

  • jaced.com October 29, 2007, 5:10 pm


    =view large image for screen=
    =view large image for print= (scale to paper)

    Been thinking about this one a lot the last few days. Had a dream the other night exposing another layer, and today I finally wrapped my brain around the visual part of the Lateralus Fibonacci Sequence, which I’m starting to call, affectionately, the Lateracci Mix. Or the Fiboralus. Take your pick. Or, in the spirit of the piece itself, come up with your own. Call it what you want. Think outside the box. Be your own person.

    To recap, there are 13 tracks on Lateralus. It’s been found through analysis that when these tracks are “arranged in the Fibonacci Sequence”, the album’s true beauty becomes evident. The transitions between the tracks on this Lateracci Mix are startlingly seamless; any Tool fan who listens to the album in this order will get the kind of chills one gets when she solves a riddle. And the best part is that she didn’t even realize was a riddle in the first place. It’s one of the coolest feelings the Universe has to offer.

    Once again, the Lateracci Mix is:

    6, 7, 5, 8, 4, 9, 13, 1, 12, 2, 11, 3, 10

    Okay, cool. But really, do you get it? I have yet to see anybody draw it out, so I volunteered. Works like this:

    There are two spirals. One spirals in, the other spirals out in the opposite direction. Like our yin and yang, our yes and no, our good and evil, our black and white, our left and right, our up and down, our on and off, our here and there, our then and now, and our me and you, it’s all about balance. And balance is what sacred geometry is all about.

    Back to our numbers. First, we take the 13 tracks in chronological order:

    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

    Now, we start from the center of the sequence, which is 7. The trick is to pair it up with its neighbor, the perfect number 6. Starting with this pair of numbers, 6 and 7, we create a spiral outward, crossing off track numbers with each segment of the spiral, essentially defining the first half of the Lateracci Mix.

    This first spiral (out) is represented in red, spiraling out from 6 to 9:

    6, 7, 5, 8, 4, 9

    The second spiral (in) is represented in blue, spiraling in from 13 to 10:

    13, 1, 12, 2, 11, 3, 10

    And there we have it.

    6, 7, 5, 8, 4, 9, 13, 1, 12, 2, 11, 3, 10

    I hope you enjoyed tripping out on this one as much as me. Spiral out, keep going. Do something creative and share it. Some of us are listening.



  • Chris December 11, 2007, 11:54 am

    whoa, I had kindof heard about this but could never really wrap my brain about it. Thanks for mappin it out like this, it’s truly amazing.

  • cak daddy February 13, 2009, 7:26 pm

    i’m still not understanding how 6 7 5 8 4 9 has anything to do with fibonacci… hell, i don’t see the second half of the numbers making much sense either… explain those in simple, sober terms for me..

  • jaced.com February 17, 2009, 4:35 pm

    @ cak daddy:

    Again, here’s a visual:


    There are two spirals, a red one and a blue one. Start from the center of the red spiral, and spiral out. It crosses off the song tracks in order:

    6, 7, 5, 8, 4, 9

    Now take the outer blue spiral, and spiral from the outside-in:

    13, 1, 12, 2, 11, 3, 10

    Put the two together, set up an iTunes playlist, and, look Mom! No seams.

    6, 7, 5, 8, 4, 9, 13, 1, 12, 2, 11, 3, 10

  • Stefano July 9, 2009, 11:41 am

    it’s WRONG…. the second spiral isn’t like that, Why?:
    on oficial Lateralus back cover tracks 10, 11 and 12 are joined together seperatly from the others, and not only that, when you listen to the album these tracks are kind of strange if you separate them ’cause the beginnings and the starts MUST match on these 3 tracks.

    second part of the tracklist must be:


    if you start from the center the spiral goes:

    and track 12 finishes with a silence of 2:13 (i’ll let you think about that)

    i salute you

  • jaced.com July 9, 2009, 12:09 pm


    What about Track 13? =see large graphic=

  • david meulenbeld August 18, 2009, 6:13 am

    wow it fits

  • Brent September 14, 2009, 3:34 am

    I agree with Stefano. The second half only fits perfectly like this: 1,2,3,10,11,12 and like he said there’s a 2:13 silence at the end of the cd now symbolizing the vastness of the spiral into infinity. I’m not sure yet how to reconcile the last spiral. When it’s set up the continuity of the first proposed Lateracci mix is lost or changed now…But if you listen closely you’ll see that eon blue apocalypse now flows seamlessly into the patient and so on. And I don’t believe triad can be anywhere but the end of the cd…I’m pretty sure this is how it was intended but beyond that I think the real intention was to make us think outside the box a little and work to decipher this “holy gift” in whatever way suits us most. I’m convinced this cd was meant as a tool for introspective reflection

  • stefano September 14, 2009, 9:43 am

    Brent: Amen.

    Jaced.com: track 13 goes on the exact same place. I mean, after “Lateralis”, and before “The Grudge”. Like this:

    6, 7, 5, 8, 4, 9, 13, 1, 2, 3, 10, 11, 12.

  • Brent September 16, 2009, 9:14 am

    Also it says earlier: “it’s [Maynard’s lyrics in Lateralus] not a perfect fibonacci because it reverses itself”…but I want to point out that the “fibonacci” it does make is a parabola.

  • Daniel January 21, 2010, 10:16 am

    Hey guys!

    Considering it’s lyrics “I have come curiously close to the end”, Reflection (track 11), must be close to the end, and the way Disposition, Reflection and Triad fit together just makes it hard to put them in any other order. The very word triad also indicates that the three are supposed to go together.

    This is where I think the lyrics of The Grudge could be somewhat helpful: “Saturn ascends, choose one or ten”

    Saturn, being the sixth planet in our solar system, symbolises track 6, Parabol. The question is what to make of “choose one or ten”, but I’m not set up for figuring that out right now, so I’m leaving it to you guys.

    Then there’s this line: “Let the oceans take and transmutate this cold and fated anchor”. The Grudge itself, being the first song, or the “anchor”, of the album, is supposed to be transmutated into something else. The question is to what. Another anchor, perhaps for the second spiral, or something different? As I said, I’ll leave it to you for now, but I’m back as soon as I figure something out.

  • Blake January 6, 2011, 12:40 am

    What if you think of tracks 10 11 and 12 as one song? It’s clear they shouldn’t be separated, not to mention, “Eon Blue Apocalypse” and “The Patient” have a small overlap. If you don’t believe me, open up “The Patient” in iTunes, crank up the volume, and listen to the first second. You hear the last little bit of “Eon Blue Apocalypse” fading out. Also, at the end of “Reflection” (again, if you crank the volume) you can hear something that sounds like water, and it flows through to the opening to “Triad.” This really is supported by the back of the album, they have a little line drawn between 10 11 and 12.

    I don’t know if the 1 2 3 10 11 12 is quite perfect, but it’s definitely closer than splitting these tracks, that clearly belong together, up.

    I’ll post back if I come up with anything interesting.

  • jaced.com May 8, 2013, 1:31 pm

    *UPDATE: No need to manually set things up in iTunes. Somebody’s already taken the time to post this “Fibonacci mix” of Lateralus on YouTube:

  • Hugo June 6, 2013, 5:33 pm

    Interesting thread,
    but I’m convinced after several listens to both that this ‘Holy Gift’ order doesn’t flow nearly as well as the Fibonacci-sequence-then-the-remainder
    i.e. 1,2,3,5,8,13,4,5,6,7,9,10,11,12

  • Donnie July 18, 2013, 4:35 pm

    6,7,5,8,4,9,3,10,2,11,1,12 (13) 13, isn’t there, but everything adds up to it. That’s why it’s a song featuring a raving lunatic. Write from 1 to 13, in a straight line, left to right (lateral). From 6 to 7 draw an arch above, under draw an arch from 7 to 5, from 5, draw an arch above to 8. Get it…lateral US. The songs arrange to tell the story of life from birth to death…except the after life (13) isn’t included.

  • Matt D December 27, 2013, 4:04 pm

    So, I have been listening to Tool for years and hands down Lateralus is my favorite album. As I was reading through this information I couldn’t help but start to draw some information upon itself.

    The argument for th 6,7,5,8,4,9, 13,1,12,2, 11, 3, 10
    Vs. just putting the last six in order 123 10 11 12 – – –
    This is where I focused my efforts and I think I stumbled upon something significant.

    I’m at work so I cannot expand, but this weekend should I find myself needing to do so, I will explain how I arrive at my understanding of the “Holy Gift” if you will. I dabbled with some number crunching and noticed that more intricate examination points to 13 and ultimately to 21 – which is the next number in the sequence.

    I look forward to putting this down in a bit. I hope people still check in.

  • Johnny December 29, 2013, 10:05 pm

    I don’t feel this sequence is perfect yet. I think that there is a fundamental flaw in this theory that has led me on a search of my own thought the vast reaches of ancient civilizations. There is much more to this puzzlebox than just fibonacci’s golden spiral. The word god is imprinted on the brain of the second to last image in the the cover montage. Now take the name of the track 13 Faaip de Oiad, translated as voice of god/word of god… Now we go back to ancient text. In the beginning there was a word and that word was God. In whatever order is deciphered 13 needs to be the beginning.

    I have also worked a couple other sequences using the Fibonacci golden ratio of 1:1.61 and the 137.5 degrees base for the way flowers grow. Look up sunflowers and rose patterns with fibonacci sequence to understand this. That sequence using 13 first gives us. 13, 8, 3, 11, 6, 1, 9, 4, 12, 7, 2, 10, 5. They lyrically tell a pretty sweet story but always fit with the music.

    Back to the drawing board….

  • Chuck June 30, 2016, 8:28 pm

    I’ve only recently come across “the holy gift”. A fair bit of discourse about the placement of track 13 “the word of god” and some want that song at the beginning of the sequence…However, god comes from within. As the album cover clearly illustrates…It would make spiritual sense to place it within the center of being or the center of the sequence…

  • Chuck June 30, 2016, 8:52 pm

    I’ve also noticed a number of references/allusions in the lyrics to The Scarlet Letter by Hawthorn…might just be a coincidence…

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