the fibonacci numbers in frequency
Here’s an interesting observation found in the Fibonacci number sequence:
0 1 1 2 3 5 8 13 21 34 55 …
If directly translated into Hertz (Hz) a unit for measuring frequency, we may conceptualize:
0Hz is complete silence, zero vibration, zero movement.
1Hz is the first ripple of vibration, the very act of creation itself.
Humans cannot hear frequencies below about 20Hz, and the few frequencies in the 20Hz – 40 Hz range are very hard to define by most hearing even among the most seasoned listeners. Instead, these frequencies are simply energy. Astoundingly, the tenth number of the Fibonacci number sequence is 55, or 55Hz in our case. This is the first recognizable musical pitch in the Fibonacci sequence. It is a perfectly in-tune A in equal temperament, when A=440Hz. Quite appropriately, the frequency has been given the name A, after alpha, the beginning. Analyzing the other numbers in the sequence yielded an interesting find: every 3rd number in the sequence is a frequency in tune a pitch of equal temperament.
Quickly these frequencies go well above the threshold of human hearing – us humans only hear frequencies up to about 20kHz if we’re lucky. Up above 12kHz, sound is less as pitch and more as air. These pitches above human hearing can still be named by applying a simple octave adjustment calculation. For example, an A at 220Hz is a perfect octave below an A at 440Hz, and an A at 880Hz is an A a perfect octave above. Given this rule, we see the following pattern:
From F10 – Every 3rd number results an “in tune” pitch as it correlates with equal temperament.
Order of appearance:
A Bb B E Db D Eb E F Gb G Ab A Bb B C
These pitches are a list of points along an exponential, infinite spiral arc.
It takes 55 Fibonacci numbers to record all our 12 pitches.
It is also interesting to see the predictable sequence of our fundamental A and it’s harmonic E as noted in bold.
This requires further study. Anyone have insight?
COMMUNITY IMMUNITY – 2011
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