The Math and Philosophy Behind Tool’s Lateralus

By Daniel Miessler on September 25th, 2007: Tagged as Math | Music | Philosophy | Tool

This has been my favorite band since finding Undertow in the 90′s. This just makes me like them even more.

If any of you know any more mathematical connections/relationships, let me know. I’d like to compile a reference.

  • Carl M

    1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …

    OK, this guy is really reaching! 987 (nine hundred eighty-seven) is a number in the sequence. 9-8-7 is not .. nor is it a time signature.

    Perhaps he gives a clue with the words: Over thinking, over analyzing

    And, I’m curious how 6,7,5,8,4,9,13,1,12,2,11,3,10 is a rearrangement of the 13 tracks in a Fibonacci Sequence.

    The human mind is great at seeing patterns (whether or not they are real). Perhaps the syllablic patterns were intentional. The rest is reaching (IMHO).

  • Carl M

    1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …

    OK, this guy is really reaching! 987 (nine hundred eighty-seven) is a number in the sequence. 9-8-7 is not .. nor is it a time signature.

    Perhaps he gives a clue with the words: Over thinking, over analyzing

    And, I’m curious how 6,7,5,8,4,9,13,1,12,2,11,3,10 is a rearrangement of the 13 tracks in a Fibonacci Sequence.

    The human mind is great at seeing patterns (whether or not they are real). Perhaps the syllablic patterns were intentional. The rest is reaching (IMHO).

  • http://slashback.org/ Tim F.

    Someone once told me that you’re supposed to listen to the tracks in a spiral formation starting with 6, then 7, then 5… but it doesn’t make sense — if you go through the track listings that way, you end up with 1, then 12… and 13 is unheard.

    Maybe you’re supposed to listen to 10, 11, and 12 together since it’s considered to be one song in three parts.

    I dunno. Just something I heard.

  • http://slashback.org/ Tim F.

    Someone once told me that you’re supposed to listen to the tracks in a spiral formation starting with 6, then 7, then 5… but it doesn’t make sense — if you go through the track listings that way, you end up with 1, then 12… and 13 is unheard.

    Maybe you’re supposed to listen to 10, 11, and 12 together since it’s considered to be one song in three parts.

    I dunno. Just something I heard.

  • http://slashback.org/ Tim F.

    This Wikipedia link may help explain what I heard. Read the first bullet point there.

  • http://slashback.org/ Tim F.

    This Wikipedia link may help explain what I heard. Read the first bullet point there.

  • Dave

    This sequence is very popular in music and film. All of the Stanley Kubrick are supposed to be using it as well. They call it the “Golden Ratio”. Many artists believe it is the secret to successful art. If you look, there are dances, paintings, music, and movies that all use it. Tool is doing what mathematically aware artists have been doing for a few hundred years, and mother nature since the beginning of time.

    • Darthcalculus@aol.com

      The fibonacci sequence is NOT the Golden Ratio. The Golden Ratio is: ” two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887″ -wikipedia

  • Dave

    This sequence is very popular in music and film. All of the Stanley Kubrick are supposed to be using it as well. They call it the “Golden Ratio”. Many artists believe it is the secret to successful art. If you look, there are dances, paintings, music, and movies that all use it. Tool is doing what mathematically aware artists have been doing for a few hundred years, and mother nature since the beginning of time.

  • Dave

    Actually, looks like the Greeks used it in their architecture. So make that thousands of years.

  • Dave

    Actually, looks like the Greeks used it in their architecture. So make that thousands of years.

  • http://www.stevengharms.com/ Steven G. Harms

    Tool definitely like to work with the Hindu-influenced mystical bend. The work of Alex Gray ( see: Lateralus art work ) is a key visual component. I also heard that Lateralus can be listened to in a way such that it’s complementary to moving energy through the 7 primary chakra centers. The order is:

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

    You can tie this numerical projection to the Qabbalah, to the Fib sequence, to nucleotide ordering, to AI decision trees, to fractals, to construction Golden sections.

    It’s something about φ which reaches deep within the collective unconscious, the noumenal mind (Kantian condition of experience?), or our deep programming.

  • http://www.stevengharms.com Steven G. Harms

    Tool definitely like to work with the Hindu-influenced mystical bend. The work of Alex Gray ( see: Lateralus art work ) is a key visual component. I also heard that Lateralus can be listened to in a way such that it’s complementary to moving energy through the 7 primary chakra centers. The order is:

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

    You can tie this numerical projection to the Qabbalah, to the Fib sequence, to nucleotide ordering, to AI decision trees, to fractals, to construction Golden sections.

    It’s something about φ which reaches deep within the collective unconscious, the noumenal mind (Kantian condition of experience?), or our deep programming.

  • M. Kowalski

    6,7,5,8,4,9,13,1,12,2,11,3,10 is not the fibonacci sequence. However if you plot those points on a cartesian axis where point 6 corresponds to point (6,6) etc., and connect these points in the order with spiral like curves. You get something that looks something like the lateralus eye.

    Also something while I don’t think anyone has mentioned is the fact that maynard starts singing 1.618 mins into the song.

  • M. Kowalski

    6,7,5,8,4,9,13,1,12,2,11,3,10 is not the fibonacci sequence. However if you plot those points on a cartesian axis where point 6 corresponds to point (6,6) etc., and connect these points in the order with spiral like curves. You get something that looks something like the lateralus eye.

    Also something while I don’t think anyone has mentioned is the fact that maynard starts singing 1.618 mins into the song.

  • Akshay Wadekar

    In response to the time signature argument, I believe he’s focusing on how many beats per measure assuming that the quarter note gets the beat, so 9/4, 8/4, 7/4, I believe, but I could be mistaken, it is hard to count tool time signatures.

    All very interesting.

  • Akshay Wadekar

    In response to the time signature argument, I believe he’s focusing on how many beats per measure assuming that the quarter note gets the beat, so 9/4, 8/4, 7/4, I believe, but I could be mistaken, it is hard to count tool time signatures.

    All very interesting.

  • Akshay Wadekar

    Also to the comment about Tool’s influence in Hindu culture and so forth, I just noticed that the next track on the album has a very “tabla” sounding drum, I can almost guarantee it is a “tabla”. The track after that, has a resounding “bend” of a drum note that can be attained using a “tabla”.

  • Akshay Wadekar

    Also to the comment about Tool’s influence in Hindu culture and so forth, I just noticed that the next track on the album has a very “tabla” sounding drum, I can almost guarantee it is a “tabla”. The track after that, has a resounding “bend” of a drum note that can be attained using a “tabla”.

  • Akshay Wadekar

    Okay The earlier comment about time signatures should be corrected, the time signatures I believe are 9/8, 8/8, and 7/8, either that or the song is abnormally fast rhythm. Thanks.

  • Akshay Wadekar

    Okay The earlier comment about time signatures should be corrected, the time signatures I believe are 9/8, 8/8, and 7/8, either that or the song is abnormally fast rhythm. Thanks.

  • sammib

    try ordering the cd 1,2,3,5,8,13,4,6,7,9,10,11,12. the first half is the Fib Code but all the songs that are supposed to be grouped are grouped and the flow between each song matches up amazingly. i have found it is the best way to listen to the cd out of all the other orders listed

  • sammib

    try ordering the cd 1,2,3,5,8,13,4,6,7,9,10,11,12. the first half is the Fib Code but all the songs that are supposed to be grouped are grouped and the flow between each song matches up amazingly. i have found it is the best way to listen to the cd out of all the other orders listed

  • Adam Bell

    Anyone notice the 34 bars of 4 at the start of the Lateralus? My guess is that there will be an overall scheme with the climax of the song being at the Golden Section (GS of 55 is 34, 34 is 18 etc.). I also think the separate sections of the song will be a fibonacci number also. I’ll let you know what I find…

  • Adam Bell

    Anyone notice the 34 bars of 4 at the start of the Lateralus? My guess is that there will be an overall scheme with the climax of the song being at the Golden Section (GS of 55 is 34, 34 is 18 etc.). I also think the separate sections of the song will be a fibonacci number also. I’ll let you know what I find…

  • Eli

    Yeah, someone had said that 9-8-7 isn’t a time signature. It’s not, really, but the section of the song is in a repeating pattern of a 9/8 measure, an 8/8 measure, and a 7/8 measure. It repeats every three bars. Written out on sheet music, this is marked as “9 8 7 / 8,” so it does seem pretty plausible that the number 987 is taken into consideration. Maynard is pretty nuts, I wouldn’t put it past him to throw in things like that, that are pretty convoluted and subtle.

  • Eli

    Yeah, someone had said that 9-8-7 isn’t a time signature. It’s not, really, but the section of the song is in a repeating pattern of a 9/8 measure, an 8/8 measure, and a 7/8 measure. It repeats every three bars. Written out on sheet music, this is marked as “9 8 7 / 8,” so it does seem pretty plausible that the number 987 is taken into consideration. Maynard is pretty nuts, I wouldn’t put it past him to throw in things like that, that are pretty convoluted and subtle.

  • Aaron B

    The album in minutes is 78.96666…and so on. Spiral Out, Keep Going. Just like the number.

  • Aaron B

    The album in minutes is 78.96666…and so on. Spiral Out, Keep Going. Just like the number.

  • http://operamail.com/ M Lawrence

    Danny Carey is quoted in an interview saying “987″ was a working title indeed because of it’s 987/8 time signature, and admits to understanding that 987 is indeed the 16th Fibinacci sequence.

  • http://operamail.com M Lawrence

    Danny Carey is quoted in an interview saying “987″ was a working title indeed because of it’s 987/8 time signature, and admits to understanding that 987 is indeed the 16th Fibinacci sequence.

  • g-house

    thats fuckin cool man

  • Jason

    Someone may have already posted this, but the missing section occurs at 3:12……from 9:24…..derivatives 3 & 2, but i don't know if that's significant in the sequence of the song.

  • http://drycereal.blogspot.com Riker

    This is correct; Adam or Danny (I forget which) mentioned in an interview once that before it was named Lateralis, they gave the song a working title of 9-8-7, based on the beat count.
    Also note, much like Aenima and Aenema, the song is not spelled the same way as the album :) Those guys are just full of little tricks like that.

  • Jordan D

    987 is actually the 17th step of the Fibonacci Sequence.

    Great and very interesting video otherwise!

    P.S. @2:36, do you think the band was trying to make an ironic statement over what people would do to this song? Obvious that isn't true, as Maynard puts a ton of time and effort into writing the songs this way, but just thought i'd point that out.

  • Jordan D

    987 is actually the 17th step of the Fibonacci Sequence.

    Great and very interesting video otherwise!

    P.S. @2:36, do you think the band was trying to make an ironic statement over what people would do to this song? Obvious that isn't true, as Maynard puts a ton of time and effort into writing the songs this way, but just thought i'd point that out.

  • yboT

    ah thankyou so much, i have to analyse a song in my music class at school and i really wanted to get some shit on the fibonacci sequence so i could impress my teacher…..also helped me to understand the song thanks alot!

  • cyborg206

    the singing starts at 1:37:something, wich is 1.618 aprox of 2 minutes, so there is the golden ratio again, well the drumming tempo it's already there, and i've been trying to corroborate it, but iI think that every 5 times there are 1.618 seconds again, not completely sure, the time signature during the “verse” is 5/8, again, 2 numbers from the fibonacci sequence, keep overthinking man!!! it's unstoppable, man!! i just realize something else, the strong part ! from the beginning lasts till the 34th compass, another number of the fibonacci sequence! just amazing man, can't believe how cool is this song, i've listened to it almost two hundred times in my ipod's counter, almost 200 man… love the golden ratio

  • Jon

    What he means is at that point in the song, the time signatures change each measure, staring at 9/8, to 8/8, to 7/8, and then repeating itself. Pretty sure members of the band, specifically the drummer, have admitted to that being another reference to the Fibonacci sequence. I might be wrong about that last part though.

  • Jon

    The rearranged track order is something I'm curious about too, even if it is a supposed to be a spiral formation from the center of the track numbers, that isn't a Fibonacci sequence.

  • Jon

    Tracks 10-12 are considered to be the three parts of a single song, they're often played together at concerts, but I don't think that's what he's referring to.

  • Jon

    Trying to graph that eye on a Cartesian plane… not working.

  • Jon

    What he means is at that point in the song, the time signatures change each measure, staring at 9/8, to 8/8, to 7/8, and then repeating itself. Pretty sure members of the band, specifically the drummer, have admitted to that being another reference to the Fibonacci sequence. I might be wrong about that last part though.

  • Jon

    The rearranged track order is something I'm curious about too, even if it is a supposed to be a spiral formation from the center of the track numbers, that isn't a Fibonacci sequence.

  • Jon

    Tracks 10-12 are considered to be the three parts of a single song, they're often played together at concerts, but I don't think that's what he's referring to.

  • Jon

    Trying to graph that eye on a Cartesian plane… not working.

  • Pingback: The ‘James Keenan Maynard’ experience « footprints…

  • Martin Davies

    it starts left to right +1-2+3-4+5 then right to left -7+8-9+10-11+12 it skips 6 because it started with 6 this is also known as the holy gift.

  • Darthcalculus@aol.com

    Actually, the song title Cesaro Summability is a mathematical concept far beyond the fibonacci sequence. Look it up on wikipedia and prepare to have your mind blown. Also, Parabola, of course, is the name given to the shape of the graph f(x) = x^2 (“x to the second power”)… a “U-shape”. I am keeping my eyes open for other songs which reference mathematics.

  • Dr Aterru

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