FREQUENCY AND HARMONY
Succeeding superoctaves are pitches found at frequencies four, eight, sixteen times, and so on, of the fundamental frequency.

When expressed as a frequency bandwidth an octave A2–A3 spans from 110 Hz to 220 Hz (span=110 Hz). The next octave will span from 220 Hz to 440 Hz (span=220 Hz). The third octave spans from 440 Hz to 880 Hz (span=440 Hz) and so on. Each successive octave spans twice the frequency range of the previous octave.

HARMONY DEFINITION
The simultaneous vibration of two or more bodies whose harmonics do not produce discords, and whose funda mental pitches are harmonics of the lowest pitch, or are a unison with the resultant notes or overtones, or undertones, of any two or more of them.

Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength. Every term of the series after the first is the harmonic mean of the neighboring terms; the phrase harmonic mean likewise derives from music.

HARMONICS SERIES (MUSIC)
A harmonic series (also overtone series) is the sequence of frequencies, musical tones, or pure tones in which each frequency is an integer multiple of a fundamental.

Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. At the frequencies of each vibrating mode, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves. Interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series.

Harmonics of a vibrating string, showing how the frequency of each harmonic is related to integer multiples of the fundamental frequency f. The location of the nodes (red dots) can be used to define equivalent strings (on the right) with 1/2, 1/3, and 1/4 of the length of the original strings, having the same frequency.

FOURIER SERIES
In mathematics, a Fourier series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. With appropriate weights, one cycle (or period) of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). As such, the summation is a synthesis of another function. The discrete-time Fourier transform is an example of Fourier series. The process of deriving weights that describe a given function is a form of Fourier analysis. For functions on unbounded intervals, the analysis and synthesis analogies are Fourier transform and inverse transform.

Function s(x) (in red) is a sum of six sine functions of different amplitudes and harmonically related frequencies. Their summation is called a Fourier series. The Fourier transform, S(f) (in blue), which depicts amplitude vs frequency, reveals the 6 frequencies (at odd harmonics) and their amplitudes (1/odd number).

OCCULT REFERENCES FROM DASHED AGAINST THE ROCK
THE BASIS OF A NEW SCIENCE
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OCCULT REFERENCES FROM DASHED AGAINST THE ROCK
THE BASIS OF A NEW SCIENCE

OCCULT REFERENCES FROM DASHED AGAINST THE ROCK
THE BASIS OF A NEW SCIENCE

OCCULT REFERENCES FROM DASHED AGAINST THE ROCK
THE BASIS OF A NEW SCIENCE

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THE SCALE OF FORCES

First octave (unity per second) is approximately the lowest frequency capable of producing waves of rarefaction and condensation in the air. The atomic aggregate oscillating at this pitch can be experimentally determined, and the aggregate vibrating at a pitch one octave higher will have a mass lying between ^ and the cube root of the mass of the first-mentioned aggregate ; the exact relation under varying conditions of gravity, magnetic saturation, and pressure, can be determined only by accurate measurements. But assuming a body of a size represented by x, with a pitch represented by 1024 per second, then a pitch of 2048 per second will be produced by a body having a volume of some mean between of x and the cube root of x. By accurately determining the pitch of a volume of any metallic sphere capable of oscillating at the pitch of, e.g., the eleventh octave of sonity (1024 per second), under normal conditions of gravity, pressure, magnetism, and then successively diminishing its size by ^ of itself, we get the successive octaves of pitches higher and higher in period-frequency until we pass the domain of sonity and enter the domain of sono-thermity. The point where the one form of energy merges into the other lies approximately at the twenty-first octave, and this pitch also marks the point where the air is no longer capable of vibrating at that pitch in waves of transverse form. This first gamut of 21| octaves consists of three forms ; viz. sonity, sound, and sonism. The following is a tabulation of the pitches of sonity in octaves from one vibration per second to where the next form of energy commences.

If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.
Nikola Tesla