Posted by: 181first | Category: Music | Saturday 19th of June 2010 12:42:10 PM | Privacy: PUBLIC
In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. The golden ratio is an irrational mathematical constant, approximately 1.6180339887.
At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties http://en.wikipedia.org/wiki/Fibonacci_number http://en.wikipedia.org/wiki/Golden_ratio
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.
Counting between pauses, the syllables in Maynard James Keenan's vocals during the verses form the first few Fibonacci numbers, ascending and descending:
(1) Black,
(1) then,
(2) white are,
(3) all I see,
(5) in my infancy,
(8) red and yellow then came to be,
(5) reaching out to me,
(3) lets me see.
(2) There is,
(1) so,
(1) much,
(2) more and
(3) beckons me,
(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.
(5) Push the envelope.
(3) Watch it bend.
The Fibonacci sequence shares a relationship with spirals, which are mentioned several times later in the lyrics.
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.
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."
...and the ENTIRE the album too.
Anyway, all this got one unknown fan to write up a big long post somewhere and to speculate that the actual order of the songs on the album Lateralus needed to be rearranged so as to reveal the "true" message of the album. Basically, the idea is this: Lateralus has 13 tracks (a Fibonacci number, BTW) so you place that track at the center of your new track order. The surrounding tracks are all grouped into pairs that sum the number 13 and spiraling in toward 13, then outward from it. Here's the suggested track arrangement with the two "spirals" in bold:
6, 7, 5, 8, 4, 9, 13, 1, 12, 2, 11, 3, 10
The unknown fan calls this arrangement The Holy Gift