So for the longest time, the song length of Lateralus has been bothering me to no end. Honestly, I couldn't understand why such a meticulously constructed song, laden with the Fibonacci sequence in EVERY respect, would have such a random number for it's length...
Then for some reason, tonight I started looking into it in more depth. Decided to see if it might be the total number of seconds (564), but all attempts to try and find any relation with the Fibonacci sequence proved fruitless. Then I decided to do a bit more research on the sequence again, and see if I could possibly find some clues. I stumbled upon a few interesting constructs, including Hosoya's triangle, Diophantine sets, Fermet's spiral, and, most importantly, the Pascal triangle.
Still looking at 564 for some stupid reason, I thought maybe it had something to do with the golden ratio, PHI. Dividing/multiplying by PHI didn't quite give me anything close to any of the Fibonacci numbers. So I started looking at Hosoya's triangle, and thinking it might be within that construct somewhere, but I was never able to find it (or the original 924). Then I looked at the Pascal triangle, and learned that you can actually find the Fibonacci sequence by looking at shallow diagonals within the triangle itself. Well then!
That was intriguing in and of itself... until I looked at the 13th "level" of the Pascal triangle. Whadaya know! We found our 924!
Finally, I can stop wondering where the hell they got that damn number!
... until I looked at the 13th "level" of the Pascal triangle. Whadaya know! We found our 924!
I must say, that is just an excellent sentence to wake up to and read first thing in the mornng. The time spent calculating abstract numbers into that solid concrete line certainly paid off. Makes me want to locate the 13th "level" of the Pascal triangle to have a look myself. Cheers.
__________________ Time is still the infinite jest.
It boggles my mind just how involved they got in every aspect of this damn song. At least now I know I'm not crazy for thinking that number wasn't random... although can't really say I'm not altogether sane, really.
Another rather interesting thing to note is that shading all numbers divisible by n>1 resembles the Sierpinski triangle (a fractal pattern), and 924 is actually at the center of the largest divisible by 3 shaded region of the first 17 levels of the Pascal triangle.
Whoa... I decided to delve into the Fibonacci sequence just a tad bit more with the progression of the song. The first 13 notes actually follow the 1 1 2 3 5 pattern (the 3 sounds like a 16th note, very subtle but it's there). At 13 seconds in is when Danny Carey starts hittin' that bass... real quiet, I had to wear headphones blasted as loud as it could go to hear it. At 21 seconds, not exactly sure what it is, but another aural element is definitely added in. Couldn't catch anything at 34 but I'm thinking that's when things just start getting more prominent. I also think that's when the spiral starts going back, because at 47 it sounds like the bass drum gets louder, at 55 I can hear the bass guitar, at exactly 1 minute, everything starts getting progressively louder within a few seconds of eachother. So at 1 minute, we're back to 5 in the Fib sequence, so 1:03, 1:05, and then starts going back up again at 1:08, and the song "begins" at 1:13.
Fibonacci sequence for the first 73 seconds:
1 1 2 3 5 8 13 13 8 5 3 2 3 5
And at exactly 2:33 in (the 13th Fibonacci number), is when he starts singing "Over thinking, over analyzing..."
Are fibonacci, you mentioned 1, 2, 3, 5, 8, 13, 21, 34, 55, 233.
"So at 1 minute, we're back to 5 in the Fib sequence, so 1:03, 1:05, and then starts going back up again at 1:08, and the song "begins" at 1:13."
So at 1, you ignore the 1 there, but in 233 you take the 2 in account. Also, converting time to fibonacci doesnt quite relate so easily, for instance how do you read 89? Or 377?
/sarcasm
Good finding, it is interesting to find these kind of connections - almost like riddles :)
... until I looked at the 13th "level" of the Pascal triangle. Whadaya know! We found our 924!
I must say, that is just an excellent sentence to wake up to and read first thing in the mornng. The time spent calculating abstract numbers into that solid concrete line certainly paid off. Makes me want to locate the 13th "level" of the Pascal triangle to have a look myself. Cheers.
LMAO!!....yeah, me too..me too
__________________ "WITHOUT A LITTLE EVIL, GOOD WOULD NEVER EXIST"
It boggles my mind just how involved they got in every aspect of this damn song. At least now I know I'm not crazy for thinking that number wasn't random... although can't really say I'm not altogether sane, really.
Another rather interesting thing to note is that shading all numbers divisible by n>1 resembles the Sierpinski triangle (a fractal pattern), and 924 is actually at the center of the largest divisible by 3 shaded region of the first 17 levels of the Pascal triangle.
Whoa... I decided to delve into the Fibonacci sequence just a tad bit more with the progression of the song. The first 13 notes actually follow the 1 1 2 3 5 pattern (the 3 sounds like a 16th note, very subtle but it's there). At 13 seconds in is when Danny Carey starts hittin' that bass... real quiet, I had to wear headphones blasted as loud as it could go to hear it. At 21 seconds, not exactly sure what it is, but another aural element is definitely added in. Couldn't catch anything at 34 but I'm thinking that's when things just start getting more prominent. I also think that's when the spiral starts going back, because at 47 it sounds like the bass drum gets louder, at 55 I can hear the bass guitar, at exactly 1 minute, everything starts getting progressively louder within a few seconds of eachother. So at 1 minute, we're back to 5 in the Fib sequence, so 1:03, 1:05, and then starts going back up again at 1:08, and the song "begins" at 1:13.
Fibonacci sequence for the first 73 seconds:
1 1 2 3 5 8 13 13 8 5 3 2 3 5
And at exactly 2:33 in (the 13th Fibonacci number), is when he starts singing "Over thinking, over analyzing..."
Dear GOD! This shit is like crack!
Wow dude, you really don't have a life do you?
Hence the entire moral of the story to quit over-thinking and over-analyzing. It's like sweet irony to my ears no matter how pathetic it makes you.
__________________ "WITHOUT A LITTLE EVIL, GOOD WOULD NEVER EXIST"
It was all done late at night while procrastinating from my homework. Don't have a life? Since when does a college student have a life anyway?
I dunno, I find your insinuation rather insulting. Since when does exploring a topic of interest constitute being "pathetic"? I got some personal satisfaction out of it, and I feel all the better for it.
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.
According to my cheap calculator, 97/60 is 1.61666666666666666666. Nowhere near 1.618.
Quote:
The time signatures of the chorus change from 9/8 to 8/8 to 7/8; as drummer Danny Carey says, "It was originally titled 9-8-7. For the time signatures. Then it turned out that 987 was the 17th number of the Fibonacci sequence. So that was cool."[3]
Obviously high speedings with Lamborghini has mixed Danny's thoughts and does not understand the TRUE MEANING of MJK's lyrics: its much more significant than just plain 'cool'.
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.
Yeah, I had stopped once I got to 1:13 as I just ended up getting back to homework. However, I theoretically could've just kept going with it, just stopped trying to find a pattern. At that point there are three 8 second sections, ending at 1:37 where Keenan's vocals come in (though for some reason it's 1:38 for me).
Meh, for the most part I'm done with this. Anyone else want to continue then by all means, I just don't see a point when more people are interested in derailing a thread than contributing.
Brohsan, don't give up. I've read some posts here, and, surprisingly, they all end up either unreplied or derailed. But some begin neatly.
Anyway, your level of analysis surprised me too. It's like you were looking at your TV from 1 inch away, looking on the red-green-blue points, trying to figure out the images.
I'm not insulting oyu or making fool out of you. It all just means you are fascinated. And Lateralus IMO is well-worth fascination.
Maybe you will help me figuring that out:
2-3-3-5-3-3-5-5-3-5-5-3-3-3-5-3-3-5-5-3-5-5
It's Adam's picking from Jambi - Damn my eyes if they should compromise our fulcrum (...) then I might as well be gone - here it kicks in. AFAIK no one could link it to anything what makes sense. All prime numbers, and sounds pretty cool.
Another beautiful sequence is:
|0-00-0-00-0-00-0-00-0-|0-00-0-00-0-00-0-00-0-|
That's Danny's kick drum pattern from Merkaba. Makes perfectly 11/8, but sounds like disturbed 5/8 or 5/16 at first glance. Maybe I'm a moron, but it's hard for me to listen to Tool song if I cannot feel/predict the rhythm (drummer's customs?) so first time listening to Merkaba or Schism was like brainfu.. for me. Then come the hard moments of figuring out all the measure changes etc. But I feel GREAT, and listen with huge satisfaction to their songs once I got the rhythm part deciphered. Maynard's work comes next.
Right In Two is in 11/8 too.
BUT... Intension is nearly whole made in 7/8 with a few (2 or 3?) moments when one measure of 2/4 is inserted (or it's intended to make 11/8 together at these points).
Try this! I've got the best opportunity toanalyze it while taking a 4-hour coach travel to my family. ALLWAYS i do it with headphones on and Tool playing. Once I played Parabol/Parabola 7 times one by one with closed eyes. It was probably the most amazing trip. I felt like traveling in time and space. Being eternal.
OK, I'm crazy, I give up.
__________________ "music has infinite potential of positivity for mankind"Lord Worm www.last.fm/user/michalkob
I know what's minor scale, I play some guitar sometimes you know.
Another thing is: These are not fret numbers, but how many times a string was picked.
You know: tada-tadada-tadada-tadadadada- :D And it's all played on single muted note.
Why do you blast off with dumbass? If it's a local custom i can try and accomodate :)
I agree they are overused. Just like four chords of With Or Without You by U2.
Cheers from Poland.
__________________ "music has infinite potential of positivity for mankind"Lord Worm www.last.fm/user/michalkob
Rivek > IE... Here's why. Rivek is pompous and pretentious and it's hilarious because he's right 99.9% of the time. IE is pompous and pretentious and it's annoying because he could be a special olympics alternate.
if you don't get why people are fucking with him, you're in the same boat.
We are blind to the deep and meaningful conversations on this website, so to you guys we appear as ignorant outsiders who miss the point in everything you post?
Rivek > IE... Here's why. Rivek is pompous and pretentious and it's hilarious because he's right 99.9% of the time. IE is pompous and pretentious and it's annoying because he could be a special olympics alternate.
And you were denied entry because you're just too damn fuckin' stupid and retarded to be considered.
__________________ "WITHOUT A LITTLE EVIL, GOOD WOULD NEVER EXIST"
