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A Sufi Discourse on Number, Rhythm and Melody
By Ian Beardsley
Herein we will consider things that tessellate, that is that can be layed side by side without leaving gaps, or the
platonic solids, which are geometries that occupy space and have all of their faces the same shape and are equal sided and
equal angled. We will discuss the Fibonacci series, the sequence starting with 0 and 1, each successive term the sum of the
previous two (i.e. 0,1,1,2,3,5,8,13…). We will consider the set of numbers 1,2,3,4,5,6,12 because of their properties.
And we will state the data for melody and rhythm and we will see how this all ties in with the possibility of answering how
we got here. And finally we won’t say anything about the numbers 7 and 11 but will mention the number 9.
It is as if the five senses are the dimensionality of ourselves, and we exist in three dimensions, physically. Five
and three are two consecutive fibonacci numbers, and their ratio is a good approximation to phi, the golden ratio (1.618...).
Eight, the fibonacci number after five, is the octet truss, or stable brace... The next fibonacci number is thirteen, which
is the twelve around one, or closest packing of equal radius spheres around one, which determines the most transformable shape,
the vector equilibrium, or isotropic vector matrix. The consecutive ratios between fibonnacci numbers become closer and closer
approximations to phi.
I was wondering what made me play melodies on the guitar with the tempo that I do. Thinking about it, it would be
the culture in which I was
raised, and that is determined by circumstances, and those by the laws
of the universe -- i.e. I can't fly like a bird to get where I am going
-- and the laws of the universe came from whatever the source was, thus
anything we do is the source speaking through us. Perhaps, if our
actions are an embodiment of the source, who is to say we can't deduce
what it is by looking at ourselves.
In fact, I would say we are evolving towards becoming the source, as
nature unfolds, with us at the apex. So, from looking at ourselves, what can we say about the source of the universe?
I would say that it has five fold symmetry, or any symmetry that is a multiple of five, because the aspect of ourselves that
builds things, or creates things are our five fingered hands with their four fingers and an opposable thumb. Add to that our
five senses, or our two legs, two arms and a head that add up to five. In fact, it is well understood that where living things
are concerned in general, we are dealing with five-fold symmetry. Notice that most flowers have five petals. Where non-living
things are concerned we are usually dealing with six-fold symmetry. An example of that would be crystals and snowflakes.
Rhythms that are multiples of five are the easiest to do a lot with. Five note musical scales in the system of twelve
notes per octave, are the fewest notes for a scale you can have that will play with all six chords in a key, and that system
is based on harmonic interrelationships allowing for the triad. It thereby achieves the most with the least. It has the most
freedom.
So let us say that five-fold symmetry, and its multiples, is the least with which you can do the necessary, and that
the source of the cosmos is five-fold, and we have evolved into its form.
The key to Middle Eastern drumming is in contrasting events with
intervals. There are two ways to play five as such. You can start with
two beats, leave a space and play another two beats, or you can leave a
space, play three beats, and leave another space. If you play one method
after the other you are playing in ten. With ten you have exhausted all
of the possibilities for symmetric arrangements, and it breathes, with a reversal in the placing of rests and beats for
each group of five. You have two beats on each outside, and a silence in the center, or three beats in the center with one
silence on each outside. But I have not really said what a meter of five means in Middle Eastern percussion. Just as we saw
that the five note scale was the minimum to achieve the neccessary in melody, so it is with rhythm. If two is symmetry, then
three is asymmetry. Thus two and three are the structural units of dynamics and all rhythms should be a sum of either of these
or both. Five is the smallest number that contains both in that it is two plus three. Thus in Arabic music we have meters
of 2,3,4,5,6,7,8,9, and 10. All of these can be broken up into twos and/or threes. Likewise, there are five notes outside
of any key, and the source of nature would stand outside of nature. Furthermore, the fifth note in a minor key is the same
note as the fifth note in the same major key, and the interval of a fifth is 3/2 in vibrational frequency, which is a ratio
of two Fibonacci numbers, and an approximation to phi. The regular pentagon contains a golden triangle, or triangle that has
two of its sides in the ratio of that value. The golden ratio allows for the most efficient packing, and thus we see that
once again there is every reason to believe that the source is five-fold.
There are only living things, and non-living things (Schrödinger’s cat
excepted), which means there is only five-fold symmetry and six-fold
symmetry respectively to be considered (and their multiples). A regular pentagon is a five sided structure with all of
its sides the same length and a regular hexagon is a six sided structure with all of its sides the same length. Notice that
the regular pentagon does not occur among the regular polygons that tessellate and the regular hexagon is not a face of any
of the platonic solids. The regular hexagon has its radius the same as its side and the regular pentagon contains a golden
triangle. Notice that the equilateral triangle (three fold symmetry), and square (four fold symmetry), are common to both
the platonic solids and regular polygons that tessellate. One and two are too small of values to create a closed object of
straight lines in the plane, let alone in space, but two represents the observer and the observed, subjective reality and
objective reality, deduction and induction. One, or unity, represents that to which we wish to reduce all knowledge.
Twelve is the most divisible number for its size and nine is a multiple of three. Therefore we have considered all
of the numbers between one and thirteen, except for seven and eleven. They are not spoken for, perhaps that is why they are
lucky.
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