This is the most AMAZING video… It shows the direct correlation between the song “LATERALUS" as performed by TOOL and the Fibonacci Sequence, which is the mathematical formula for (some say) the basis for all life and can be found all throughout Sacred Geometry…
A visual of this sequence of numbers would appear as an arch that keeps “Spiraling Out" - Called the Golden Spiral and who’s root comes from the “Golden Rectangle" (see below for more information). This same sequence is repeated in the Flower of Life and just like the petals of the flower, can go on infinitum!
When you listen to this song, you can see the timing matches perfectly the numerical value of Fibonacci and does all throughout the song. There are many levels of complexity at work here and even talented musicians have found it difficult to fully identify all the time signature changes in the song (some say there are 47 changes), but it seems that Fibonacci is above anything else the basis for everything going on!
Maynard has even written lyrics that hint at the meaning to life and our purpose and his interpretation of what the spiral is and means… Humanity and Divinity combined as one! ”Swing on the spiral… Keep Going" encourages us to not accept anything as a human limitation and to keep "pushing the envelope- watch it bend"… And he points out that if we keep going, who knows what we might discover!
The person who created this video, Phil Riehl, also found that when you re-order the tracks on this album according to the Fibonacci sequence order… The songs all play perfectly one into the next - each song’s last note going right into the first note of the song following it. I have to say, it truly is a beautiful experience when listened to that way - You can do just that here:
Lateralus Album in Fibonacci Order
Download his Phil Riehl’s version of Lateralus
I am not a musician, but I do have a deep appreciation for the art of music as well as the science of it - I also am someone who is fascinated with Sacred Geometry and how it influences everything around us and Quantum Physics is something I really want to know more about… So when I came across the video - I was BLOWN AWAY!!
Having been a Tool fan for quite some time, I shouldn’t have been surprised at the genius behind this song and indeed the entire album - But I certainly was quite impressed that so much care and attention to detail was given by a band that can write their own ticket and need no gimmicks to sell records! This is for real, folks!! And this is DEEP! I must say I find Maynard James Keenan’s voice to be haunting and comforting all at the same time and I find his mind and heart to show signs of brilliance!
Here is a little info on Maynard James Keenan (singer for Tool, A Perfect Circle and most recently, Puscifier) ~ He is the writer of the song above (“Lateralus”) as well as most all of Tool’s music.
Also see my “NOTES" on Facebook for all my favorite lyrics by TOOL & Maynard James Keenan quotes! @ Brenda Herring on Facebook
Another example of Fibonacci as expressed in popular music is this video of Jeff Buckley's rendition of the song “Halleluiah" - see below:
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THE GOLDEN SPIRAL
The Golden Spiral is in abstract mathematics and chaotic nature. It was first discovered by Pythagoras.
The spiral can be derived through the golden rectangle; when squared, it leaves a smaller rectangle behind, which has the same golden ratio as the previous rectangle
If you connect these rectangles with a curve, you have formed the golden spiral.
You can find this shape almost anywhere in nature: the Nautilus Shell, Ram’s horns,the face of a Sunflower, your fingerprints, and the shape of the Milky Way galaxy.
Many artists and architects have proportioned their works to approximate the golden ratio, especially in the form of the golden rectangle.
The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement.
Leonardo da Vinci’s illustrations of polyhedra in De divina proportione (On the Divine Proportion) and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his paintings.( You should check out De divina proportione on wikipedia, you’ll see the proportions of a face. )
It has even inspired some musicians.
In fact, the song Lateralus by Tool is completely based on the fibonacci Sequence. The Fibonacci sequence shares a relationship with the Golden spiral, which might be what the ‘spiral’ mentioned several times later in the lyrics is referring to. In fact, the syllables length itself spirals-in and spirals-out on the sequence: 1, 1, 2, 3, 5, 8, 5, 3, 2, 1, 1, 2, 3, 5, 8, 13, 8, 5, 3. Keenan begins singing at 1:37 into the song. 1 minute 37 seconds, or 97 seconds, is approximately 1.618 minutes. This happens to be the Golden ratio, which is also closely related to the Fibonacci sequence.
It is very amazing what they did, you should check it out.
(Click to link to song)
Adolf Zeisingfound the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves. He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors.
In these phenomena he saw the golden ratio operating as a universal law.
In 2003, Volkmar Weiss and Harald Weiss analyzed psychometric data and theoretical considerations and concluded that the golden ratio underlies the clock cycle of brain waves.
In 2008 this was empirically confirmed by a group of neurobiologists.
In 2010, the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals.
It is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
( Source/sources: http://en.wikipedia.org/wiki/Golden_ratio ; and possibly some of the sources listed on that wikipedia page.)
The Fibonacci Number And The Golden Rectangle.
THE FIBONACCI SEQUENCE:
Fun With Fibonacci
The Fibonacci sequence is an extremely well known sequence of numbers, with several interesting properties. The sequence itself, is made by adding the most recent two numbers together to find the next one. However, as you may have inferred, you need two numbers to start with. The sequence starts with 0,1. If continued, it comes out as: 0,1,1,2,3,5,8,13…
Interestingly, the ratio between the numbers is virtually the same as the golden ratio. This ratio is symbolized by the Greek letter φ, pronounced “phi.” The golden ratio is said to have an aesthetically pleasing effect when applied to the sides of a rectangle (with a unit of 1, the ratio would be 1:1.618). These rectangles are said to appear commonly in nature, and are used in many famous buildings, such as the parthenon (picture shown above). Because of their ratio, these rectangles are called golden rectangles.
An interesting property of golden rectangles is that, when cut into a square and a rectangle, the new rectangle has the same side ratio as the original.
Another cool property of the Fibonacci sequence, is that you can use it to convert miles into kilometers, and vice-versa, quite accurately. This is because the ratio between the numbers in the sequence, and the ratio between kilometers and miles is quite similar. Suppose you want to know how many miles 13 kilometers is. Because the number before 13 in the sequence is 8, you would know that 13 kilometers is about 8 miles. If you wanted to know the conversion of a number that is not in the sequence, you would use multiples of that number. ex. for 10, you would use two 5’.
You can find a never-ending list of resources on the internet about this subject, especially on YouTube.com — I hope you will become as fascinated as I am about it and do some research!