Monday, January 31
Maynard James Keenan and Fibonacci Sequences
In this interview, Tool / A Perfect Circle frontman Maynard James Keenan discusses the philosophy of art and the greek number of Phi = (SQRT5 + 1)/2 which is embedded within his songwriting, Lateralus in particular.
"MK: "I use the archetype stories of North American aboriginals and the themes or colours which appear over and over again in the oral stories handed down through generations. Black, white, red, and yellow play very heavily in aboriginal stories of creation."
Maynard now mentions the Spiral Sequence of Life, the Golden Rectangle, the Fibonacci Sequence and the Phi Ratio. For further information on these aspects of Tool's songs and ideas, there are several websites to consider for reference:
http://library.thinkquest.org/27890/theSeries1.html
http://library.thinkquest.org/27890/applications6.html
The mathmetician credited for discovering the sequence is Leonardo Fibonacci in 1202 (a.d.). Each number in the sequence is generated by adding the previous two, which produces a string of numbers like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987. To arrive at each number of the series, you simply add the two numbers that came before it. And so each number of the series is the sum of the two numbers preceding it. In nature, you see many patterns which displays numbers from this sequence e.g. pineapples, flowers, conk shells, pine cones (hmmm...), etc. What I get from the sequence is the relation of a ratio (Phi) which has fixed spatial constraints on biological organisms. And so you see the pattern repeat itself again and again because of these spatial constraints.
If you look at the syllable of the opening lyrics in 'Lateralus', you can see evidence of the Fibonacci sequence 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.)
The drummer of Tool, Danny Carey is very much interested in numerology, geometry, etc. His drum patterns are chosen very carefully to reflect some of the patterns he finds in the Fibonacci sequence and elsewhere. This has led me to consider to what degree there may be underlying patterns in nature, shape, and number, which resonate with us in musical notation. And that it is partially due to this pattern recognition which has had such a huge impact on Tools' fans.
The band is also very interested in what is called threedimensional sound. For some time, Maynard and I talked about Synesthesiathe perceptual sensation produced when a stimulus experienced by one sense is experienced in another, as when the hearing of a certain sound induces the visualization of a certain colour or geometric shape. I recalled listening to 'Schism' and noting how the metre of Maynard's lyrical cadence was offset from the bass and drums in certain parts as to invoke a type of sharpsidedness. I do not actually 'see' a geometric shape before me. But I do get a sense of what he meant. This ephemeral capacity to 'see' sound is about as close as I've gotten to a synesthetic experience. "
From Wikipedia:
Some time after Lateralus was released a minor flurry of interpretive activity arose around the album. In particular, Carey told an interviewer about Keenan's remark that the time signatures of the main riff in "Lateralus" (987) also represented a step in the Fibonacci sequence (the sixteenth step, as it turns out). This led some Tool fans to suggest that the tracks on Lateralus can be listened to in spirallike orders: 6,7,5,8,4,9,3,10,2,11,1,12,13 ("The Lateralus Prophecy") or 6,7,5,8,4,9,13,1,12,2,11,3,10 ("The Holy Gift"). Both arrangements produce different storylines for the album.
The cover is translucent and flips open to reveal the different layers of the human body, including a spiritual layer representing vrajna, the transcendental wisdom of enlightenment or union with the divine.
The vocal on "Faaip de Oiad" is of a 1997 caller to Art Bell's radio program, who claimed to have been employed at Area 51.

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"MK: "I use the archetype stories of North American aboriginals and the themes or colours which appear over and over again in the oral stories handed down through generations. Black, white, red, and yellow play very heavily in aboriginal stories of creation."
Maynard now mentions the Spiral Sequence of Life, the Golden Rectangle, the Fibonacci Sequence and the Phi Ratio. For further information on these aspects of Tool's songs and ideas, there are several websites to consider for reference:
http://library.thinkquest.org/27890/theSeries1.html
http://library.thinkquest.org/27890/applications6.html
The mathmetician credited for discovering the sequence is Leonardo Fibonacci in 1202 (a.d.). Each number in the sequence is generated by adding the previous two, which produces a string of numbers like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987. To arrive at each number of the series, you simply add the two numbers that came before it. And so each number of the series is the sum of the two numbers preceding it. In nature, you see many patterns which displays numbers from this sequence e.g. pineapples, flowers, conk shells, pine cones (hmmm...), etc. What I get from the sequence is the relation of a ratio (Phi) which has fixed spatial constraints on biological organisms. And so you see the pattern repeat itself again and again because of these spatial constraints.
If you look at the syllable of the opening lyrics in 'Lateralus', you can see evidence of the Fibonacci sequence 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.)
The drummer of Tool, Danny Carey is very much interested in numerology, geometry, etc. His drum patterns are chosen very carefully to reflect some of the patterns he finds in the Fibonacci sequence and elsewhere. This has led me to consider to what degree there may be underlying patterns in nature, shape, and number, which resonate with us in musical notation. And that it is partially due to this pattern recognition which has had such a huge impact on Tools' fans.
The band is also very interested in what is called threedimensional sound. For some time, Maynard and I talked about Synesthesiathe perceptual sensation produced when a stimulus experienced by one sense is experienced in another, as when the hearing of a certain sound induces the visualization of a certain colour or geometric shape. I recalled listening to 'Schism' and noting how the metre of Maynard's lyrical cadence was offset from the bass and drums in certain parts as to invoke a type of sharpsidedness. I do not actually 'see' a geometric shape before me. But I do get a sense of what he meant. This ephemeral capacity to 'see' sound is about as close as I've gotten to a synesthetic experience. "
From Wikipedia:
Some time after Lateralus was released a minor flurry of interpretive activity arose around the album. In particular, Carey told an interviewer about Keenan's remark that the time signatures of the main riff in "Lateralus" (987) also represented a step in the Fibonacci sequence (the sixteenth step, as it turns out). This led some Tool fans to suggest that the tracks on Lateralus can be listened to in spirallike orders: 6,7,5,8,4,9,3,10,2,11,1,12,13 ("The Lateralus Prophecy") or 6,7,5,8,4,9,13,1,12,2,11,3,10 ("The Holy Gift"). Both arrangements produce different storylines for the album.
The cover is translucent and flips open to reveal the different layers of the human body, including a spiritual layer representing vrajna, the transcendental wisdom of enlightenment or union with the divine.
The vocal on "Faaip de Oiad" is of a 1997 caller to Art Bell's radio program, who claimed to have been employed at Area 51.
