The Fibonacci Coriolis Sequence Paper
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Today while transposing a musical composition to a different key I pondered on the Fibonacci Sequence and its relationship to Music, Biology, Physics and Linguistics. Strangely enough, unrelated thoughts like “The Doppler-Effect, “Red-Shift,” “Relativity,” “Frame of Reference” and “The Physics of Motion,” came to mind. Completely unrelated to Musical Compositions i’d assume; However “The Doppler Effect” and “Red Shift” makes sense because the frequency of a sound/wave emanating from an object in motion towards a source becomes higher in pitch. Made sense. Nevertheless, i’ve aggregated my thoughts disparity and consolidated a theory.
Fibonacci Sequence is a numbering system that’s a recursive sequence in nature, a mathematical formula that calculates the subsequent number by adding the past two preceding numbers. Primarily, 1, 2, 3, 5, 8, 13, 21, 34, 55, into infinity, basically 1 and 2 equates 3, 2 and 3, equates 5, 5 and 3 equates 8, and this indefinite cycle is perpetual. The numbering system appears in subset-incremental patterns in nature, a visual depiction of growth effect promulgating the sequence in all forms of symmetry.
In a Fibonacci sequence spiral there’s pattern propagation in pineapples, the outer layers reproductive patterns gradually widens in contrasting directions, both clockwise and counterclockwise. When both spirals are counted each spiraling patterns have Fibonacci sequences, a numbering system when the patterns are counted.
The number formula that unravels the mysterious patterns in nature, demystifying the enigma of sheer improbability into a probabilistic theory of chance variations. There’s an increase expected value based on the Fibonacci sequence symmetry of geometric patterns, whether animate or inanimate, intangible or tangible objects seems to propagate under the governed underlying sequences in the increments of symmetry.
The Coriolis Effect is an artifact of the earths rotation on its axis; there’s a curvature in the oceans current, global wind and everything that’s in motion across the earths surface. Objects in motion above a rotating surface will curve in relation to the surface revolution of that object; a geographical phenomenon where the uniformity of a moving object in the Northern Hemisphere is deflected to the right, while objects in the Southern Hemisphere is deflected to the left.
Here’s an analogy; two people are rotating counterclockwise in the diameter of a circle opposite of each other, if one person “Yells!” or “throws a ball,” from the center to someone on the edge it gets deflected to the right, and in a clockwise motion the “sound” or “object” gets deflected to the left. There’s also a velocity component involved because the thrower is in motion.
Newton’s First Law describes an object in motion stays in motion unless acted upon by and external force, hence the deflection of an object derives from a force acting upon on it. Objects traveling in a straight motion above the earth deflects towards a curved path to a stationary observer above the surface; am i being monotonous? Chuckle Ostensibly!
The Chromatic Scale is a 12 pitch musical scale, octaves derive when frequencies are doubled, between the doubling of vibrations or high and low octaves consist of 12 notes: “C C#Db, D, D#Eb, E, F, F#Gb, G, G#Ab, A, A#Bb, B, C, 13th note constituting the octave. Sharps “#” and Flats “b” are essentially the same notes, and there’s no # or b between E and F, B and C. The theory behind this is unrelated to the subject and requires another discussion.
The W-W-H-W-W-W-H Formula is used to create a scale comprising of 8 notes: “C, D, E, F, G, A, B, C,” this is the C Major Scale, C1, D2, E3, F4, G5, A6, B7, and C8. When you hear a 1,4,5, it’s a Blues progression C,F,G, also called I IV, V. I’m mentioning these factors to illustrate how the Fibonacci Sequence compositional process is done in music; instead of extracting the notes in order of their frequency or pitch intervals based on the Western music system, the Fibonacci Sequence replaces the W-W-H-W-W-W-H formula with, 1, 2, 3, 5, 8, 13, etc…
In a musical scale the notes repeats when the frequencies are doubled an octave higher, but the numbering system continues, so a Fibonacci Sequence chord progression would look like this; 1, 2, 3, 5, 8, 13, the chords would be C, D, E, G, C, and the A constituting the 13th note. What’s interesting about “C, D, E, G, C, A, is the peculiar sound of this chord. This chord has the 1st, 3rd and 5th note constituting a C-Major chord, but it also has the D, making it a sus2, also known as a sus9.
Normally the 3rd note is moved a step down to create the C, D, G, making the position a Csus2 or Csus9 chord. However the sus2 is added while the 3rd remains, and there’s the 13th note which constitutes the A, making it a major6; When we conglomerating these milking-pot of notes centered around the Fibonacci Formula and not the Western system of musical formula we get an interesting chord, “Cmajor6/add9 or C6add9. Ironically this is a popular Jazz-Chord.
I call it the “equilibrium-sound,” because it encapsulates both consonance and dissonance simultaneously, it’s ambiguous and indecisive, it sounds melodic while craving to be resolved, yet has an unappealingly balanced appeal to the ear. The root note, major-third, perfect-fifth, major-sixth, and major-ninth intervals, it’s a peculiar sound because you get the suspended sound with the major-third and major-sixth.
“Tools” is an American metal band pervasively known for incorporating the Fibonacci Sequence in their musical time signatures and lyric patterns, 9/8 to 8/8 etc…I’d like to explore their ironic use of the sequence in their song called “Lateralus,” in the opening lyrics to the song the Fibonacci Sequences were embedded in the numbering of syllables, making the inherent nature of the Fibonacci Sequence applicable beyond the parameters of music, but into writing, poetry and other sorts of linguistic usage.
Fibonacci Coriolis Effect: There’s a strong correlation between biological structures and the physics of motion, would “electromagnetism” be an inappropriate metaphor? Because although electricity and magnetism are intertwined, the former is an electric charge and the latter is a force and repel, and it became “electromagnetism” after Maxwell’s juxtaposition of their inner mechanisms in his unified equation.
Fibonacci Sequence are in the Coriolis Effects, the sequences are in the non-transparent symmetry of the wind, synonymous to the propagating patterns in pineapple pine-cones outer layers. There’s pairs of spirals widening to the left and right where the numerical systems are found, seems prevalent in the symmetry of Botany. Equivalent to objects in motion on the earths surface that curve in relation to the revolution, Northern Hemisphere deflecting to the right and the Southern Hemisphere deflecting to the left.
In “Cymatics” we can visualize the vibration of sound, analyze the arrangement of frequencies through the power of sight rather than the study of auditory and notations, opening another academic arena of interest by allowing sight to engage reasoning beyond the parameters of our sense of hearing. See octaves, unisons, sus-chords, notes, keys, frequencies, pitch, amplitude, velocity etc…….
There’s two postulations for this concept, and i’m hypothesizing a “false dichotomy,” the Fibonacci numbering system in nature derives from a biological propagating source that deflects the symmetry in nature, causing the symmetry to curve relative to its infinitesimal source in motion. So although the arrangements and sequences in leaves, plants and sunflower seeds share the numerical system, there’s an infinitesimal motion that’s predicating its clockwise and counterclockwise deflection.
My second postulation is the Fibonacci Sequence in the Coriolis Effect, although the numerical arrangements are so pervasive in nature, it’s constricted to a symmetry, outside the parameters of a symmetry Fibonacci Sequences would lackluster, it’s a logical sequence contingent on an arrangement between parts.
The method in which the numerical arrangements propagates can be categorically measured in two incremental sequences.
Subset Incremental Sequences: Where the motion of animate, inanimate, intangible or or tangible objects in motion deflect in subset increments; a progressive propagating motion that breaks into incremental velocities.
Air Molecules Sequences This postulation correlates to the propagating of sound, within the context of the velocity of molecules colliding during it’s travel. Energy fragmented into fibonacci sequences as they propagate.
The Coriolis Effect in Physics share a clockwise/counterclockwise common denomination with the symmetry in nature. Although this is an analogical correlation to illustrate a metaphor of comradery, the transpositional nature of these two phenomenons are scientifically applicable. Next paper will be on “The Golden Ratio” “Phi” etc…
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