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Flower of life part 3 the golden ratio, Fibonacci and how they relate to music!

Last time i left off discussing the phi ratio and how its found in architecture from the ancient civilizations, but the phi ratio has more to it that pretty buildings and the patterns/ scales in nature, through it you can find the music and harmonics of everything in existence.

It is believed that Phi is the root of all all other sequences, because  every mathematical sequence needs a minimum of 3 numbers to figure out the sequence, except Phi, which only needs two, this is the only sequence that has this property.

However, Phi has no beginning and no end, it is an infinite sequence, but it when it is applied to life, life does not know how to deal with something with no beginning, if Phi is the source of life, and it says "create this" life doesn't know how, because it has no beginning, so where should it start? So it has to start with something crude and very basic, and then strives and evolves towards source, which is Phi, now, what sequence do we know that starts crude, and then pushes closer and closer to Phi? Thats right, the Fibonacci sequence,  you might be wondering why i'm bringing this up now, but it becomes clear, don't worry.

The other important sequence you need to know to understand how the Phi contributes to music, is the binary sequence, where you just double the last number instead of adding it to the previous one:
2,4,8,16,32,64,128,256,312....

Binary sequences are also found in life, for example, mitotic cell divisions are binary, we start as a single celled organism to having over 100 trillion cells in only 46 divisions.

Okay, so that's the basics behind this post, now, to move on to how Phi, Fibonacci and the binary sequence all come together.

This is what a polar graph usually looks like, with 36 radial lines at 10 degree increments, representing the full 360 degrees around the circle:

then concentric circles are drawn, equal distances apart, creating 8 demarcations as the one before, counting the inside circle as the first, this is a 2 dimensional drawing of a 3 dimensional sphere, which is one of the sacred forms, by projecting it onto a flat surface, this is also known as a shadow form, and casting shadows is considered a scared way to obtain information.

Also, the polar graph has both straight lines, which is seen as male energies, and curved female lines, so both male and female energies are interacting with each other at once.

Plotting a golden mean spiral at 0 degrees on the polar graph, gives a pattern as shown below, it loops all the way around before hitting 0 again, exactly at the eighth circle.

This golden mean line crosses 5 specific places as it goes out, these places are where the female circular lines, meet the male lines, it crosses at 120 degrees, 190 degrees, 240 degrees, 280 degrees and then jumps to 360 (or back to 0) 

This creates both a Binary and Fibonacci sequence, looking at the radial increments from the center, it crosses at 1, 2, 3, 5 and 8, that's Fibonacci!

But it also crosses at 2, 4 and 8, and that's a binary sequence, we're going to look at the binary sequence in detail though, because what you find is very interesting,

if you draw lines from the outermost circles on the lines where the binary sequence was formed, you get an image like this below, it is clearly an equilateral triangle, the 2D representation of the platonic solid mentioned in previous posts.

If you continued the spiral outwards it would hit these exact same points time and time again, each time creating larger and larger equilateral triangles, this is where Phi and Fibonacci begin to appear in the musical world, Keith Kritschlow discovered something very important to understanding the geometry of music, he found that if you draw a straight line through an equilateral triangle and measure from the middle central line and draw a line up to the top edge, and then back down to the bottom corner, and repeating this but by passing through the center line at the top and back down again (you can keep doing this on either side as well) you will find that "continuing  in this way, each successive proportion will be the harmonic mean between the previous proportion and the total length, and all of these proportions will be musically significant. 1/2 being the octave, 2/3 being the fifth, 4/5 being the major 3rd, 8/9 being the major tone [step], and 16/17 being the half tone [half step]" in otherwords, Kritschlow discovered the geometry of music, or at least one aspect of it.

Then he tried measuring it a different way, starting at a different point on the center line, at 3/4 of the line he found the measurements for 1/7, 1/4, 2/5, 4/7, 8/11, 16/19, all of these numbers have significance in music

This is very interesting, this means that the harmonics of music are somehow related to the proportions of the center line moving through a tetrahedron, looking back at the polar graph, it should now be clear that this drawing has much greater value than before. The polar graph itself makes your calculations easier, you can just draw a straight line through the drawing on the graph, and it will give you the center line!

This information has been taken sooo much more further than this though, a group of researchers found that you can draw these lines, not just from the center, but from any nodal points inside the upper half of the triangle and you will come up with all known harmonics in existence, basically this means that anywhere the straight (male) and curved (female) lines on the polar graph cross from 0 to 120 degrees and start making a pattern , you get all known harmonic systems, not only the western keyboard, but the eastern, and even many more unknown systems we have yet to find proof that they have been used, if at all.

Thats it for now, next post will be on the fruit of life, which shows how everything I've discussed so far comes together!

Read the flower of life part 2

Flower of life part 2 nature and structures

Intended to do this tomorrow, but i'm in carlisle, and there's fuck all else to do, so:

My last post finished off talking about the platonic solids and the historical shapes found in the simple flower of life, and the expanded version.

Now i am going to move on to look at the ratios and mathematical constants that can be found within the flower of life, which was first re discovered (wasn't mentioned in my last post, but the Mayans, the Egyptians and many other ancient civilizations knew about the flower of life and its potential, but that's another topic (watch the video on my last post if you're interested in the true history of this symbolic pattern)

In the late 12th, early 13th lived Leonardo Fibonacci, whom was an Italian mathematician, he introduced the "Hindu-Arabic number system" (which we now call the "decimal system") he was well known for many texts that he either published himself, or contributed to, but as far as the flower of life goes, the most important subject Fibonacci contributed to the world was his "Fibonacci sequence" which is actually a very simple sequence where you add the previous two numbers in the list together to form the next (1,2,3,5,8,13 (there's 13 again), 21, 34, 55 ... etc.. however, if you divide any number in the Fibonacci sequence by the number previous to it (such as 55/34) the answer is close to 1.61803, this is known as the golden ratio (or the Phi ratio), and the further away you go from the origin, the nearer you get to this magic number,  1/1 = 1, 2/1 = 2 , 3/2 = 1.5, 5/3 = 1.666, 8/5 = 1.6, 13/8 = 1.625 , 21/13 = 1.6154 etc. no matter how long you continue this sequence, however, you will never quite reach phi, always oscillating from above, to below phi. 

One of the most significant activities that combines the sacred geometry and the Fibonacci sequence is the production of the "golden mean spiral"

The Golden mean was used to aid the design of sacred buildings in ancient  architecture so PRODUCE spiritual energy that aided connectivity with the spiritual realms through prayer, the reality we exist in is very structured, and life is even more structured, this is shown throughout nature in the forms of geometry, geometry is the very basics of our reality, these are always present in our world, the golden mean governs the proportionality of  our world and can be found in what seem to be the most proportion-less living forms.

There are uncountable examples of sacred geometry and golden mean geometry in nature and matter (didn't i just say it governs everything? it does, therefore, uncountable) but some of the clearest examples are:

All types of crystals, both naturally formed and grown by man.

The hexagonal geometry of snowflakes

creatures with logarithmic spiral patterns (snail shells, and various shellfish)

Birds and flying insects, all display clear golden mean proportions in bodies and wings
The geometric molecular and atomic matters evident in all metals

The way a tree branches out so all its branches receive sunlight.

However, one of the most significant (to life anyway) but less obvious example of the golden ratio is in Deoxyribonucleic Acid or DNA the foundation and guiding mechanism of ALL living organisms on earth (and, if there is life out there, it stands to reason this ratio applies to alien DNA to, even if the building blocks (amino acids, phosphorus and nucleotide bases) are different, it can be assumed the structure will still be based on this golden ratio.

The understanding of geometry as an underlying part of our existence, however, dates back way beyond the time of Fibonacci, the golden mean and many other forms of geometry can be seen embedded in many of the oldest, most ancient  structures that still exist to this day, the oldest, and most significant, is the Great pyramid of giza, the height of the pyramid is in Phi ratio to its base, the geometry in this particular structure, is more accurate than that found in today's modern buildings.  (another very interesting example is in the parthenon in greece, search "NOVA: secrets of the Parthenon" on youtube to learn more, some of the stuff they find is amazing!)

phi present in the Great pyramid of Giza 

This gives reason to why spiritually significant shapes are pyramids and hemisphere (like that found on a mosque) these particular shapes are energy emitters, they are geometric shapes that produce a type of penetrating energy known as "negative green" ,and act like a radio waves that carry sound information, the vibrationional quality of the golden mean gives these religious buildings very strong communicating properties,  which aid resonance with higher realms in prayer. Religion doesn't seem so full of crap anymore does it?

  

This golden ratio can be seen everywhere in nature, look at your hand, excluding the thumb, each finger consists of 4 bones, not only does each finger have its own ratio moving up the finger, which is Phi to the next bone, but it oscillates back and forth from the tallest finger to the thumb, again, at this ratio, another coincidence? or more proof of design? This relationship is not just found in your hand either! It is all over your body, moving up the arms and legs, in your face, throughout your entire body!

The greeks understood this ratio in the human design and applied it to their art, they were very precise about this, and you can see when the romans took over greece, the perfection of the statues produced completely disappeared, why? not because the romans weren't good artists, but because they didn't understand the Phi ratio!  you can look up more examples of the Phi ratio in nature (in butterflies is definitely one to look at)

Thats all for now, next time i plan to look at the effects of the golden ratio, Fibonacci and how they relate to music!

Read the flower of life part 1                                                                            Read the flower of life part 3