4/18/2020

NEW INSIGHT INTO THE SCHUMANN RESONANCE FREQUENCIES - Part 1       (c)2020 by Rick Andersen

The "Schumann Resonances" are found, by observation on a spectral plot, to occur at the frequencies of 7.83, 14.3, 20.8, 27.3 and 33.8 Hz. The individual frequency components within that spectrum typically vary within about +/-0.5 Hz, depending on time of day and other variables. The values given above are "nominal" and may be found in illustration of spectral plots found online, or in articles such as that at Wikipedia and other resources.

It is typically assumed that the higher "modes" of the Schumann fundamental resonance are its "harmonics". A close look at the actual values of these "modes" or "overtones" reveals that they are NOT "harmonics" of 7.83 Hz, because harmonics, by definition, are INTEGER MULTIPLES of a base or fundamental frequency. The second harmonic of 7.83 Hz would be 15.66 Hz -- not 14.3! The 3rd harmonic would be 7.83 x 3 = 23.49 Hz -- not 20.8! The error increases as you go up the spectrum -- in fact, by the time you reach the 5th frequency [33.8 Hz, which would be the 4th overtone], the error has grown to more than 5 Hz, or nearly 16% off, between the harmonics of 7.83 Hz and the "overtones" that we measure in the Schumann resonance spectral peaks.

In the normal generation of harmonics, the spacing between them is always equal to the fundamental frequency; we should expect to see a fundamental frequency of 6.5 Hz, but instead we observe 7.83, or 1.3 Hz "too high". Can this phenomenon be explained? It looks as though all the harmonics of 6.5 Hz have been "slid upward" such that they still maintain their original 6.5 Hz spacing, relative to one another; yet their "fundamental" frequency is "off" by 1.3 Hz! This is NOT how a fundamental frequency and its true harmonics are related in nature!

A vibrating string can support standing waves [make musical tones] if you pluck it, divide it in half and pluck it [for twice the vibration frequency or pitch], divide it into thirds, 4ths, 5ths, and on up to whatever practical limit. These new pitches will be equal to the 2nd, 3rd, 4th and 5th harmonics of the original, undivided string tone [the fundamental pitch]. Dividing the string in some random, non-integer way will still get you a tonal pitch, but it will be somewhere in-between and not a harmonic of the original undivided string's pitch!

SYNTHESIZING A CORRECT SCHUMANN SPECTRUM

To my knowledge, no one has seriously considered or explained the above discrepancies, observed within the Schumann spectrum. Instead, they have blithely slid past the misuse of a well-defined term in wave mechanics, electronics and physics. NOTE: "Overtones" can be "partials" [from Music Theory] and they are not necessarily the same as "harmonics", which are defined as Integer Multiples of a fundamental frequency.

Without attempting to explain how a series of resonances can be skewed out of harmonic relationship by earth's geometry, let us just take, as an observation, that this somehow occurs.

Can we understand [and synthesize] this in terms of radio theory and modulation artifacts?
Yes, we can:

The Schumann resonances may be synthesized by putting 2 frequencies into a nonlinear mixer [a Balanced- or Ring Modulator] and eliminating the Lower Sideband [LSB = difference] at its output, retaining only the USB [sum]. This upward-shifted USB spectrum is essentially identical to what we observe in the Schumann spectrum.

The two frequencies are 1.3 Hz and its 6th harmonic, 6.5 Hz. [Conversely, this can be synthesized as f1= 6.5 Hz, then dividing that frequency by 5 to give f2= 1.3 Hz.]

The USB or sum of 1.3 Hz and 6.5 Hz = 7.80 Hz.
Assuming a harmonic-less sine wave of 1.3 Hz modulating a non-sinusoidal (=harmonic-rich) wave of 6.5 Hz, the fundamental and HARMONICS in the original 6.5 Hz waveform will be transformed: In the upper sideband they will now be spaced 6.5 Hz apart: 7.8, 14.3, 20.8, 27.3, 33.8, etc., Hz. This synthesis duplicates the Schumann resonances to within .03 Hz [0.4%] of their nominal "textbook" values.

Here is a table of values illustrating the "original" and "converted-to-Upper-Sideband" spectra:

Original freq. | Modulated with | Difference=LSB | Sum=USB
----------------------------------------------------------------
Fundamental 6.5 Hz | 6.5/5 =1.3 Hz | 5.20 Hz | 7.80 Hz |<-- "fundamental"
2nd harm. 13.0 Hz | 1.3 Hz | 11.70 Hz | 14.30 Hz |<-- NOTE*
3rd harm. 19.5 Hz | 1.3 Hz | 18.20 Hz | 20.80 Hz |
4rd harm. 26.0 Hz | 1.3 Hz | 24.70 Hz | 27.30 Hz |
5th harm. 32.5 Hz | 1.3 Hz | 31.20 Hz | 33.80 Hz |

*These are no longer "harmonics" of either 6.5 or 7.8 Hz; we now properly refer to them as "overtones" or "modes" of the 7.80 Hz fundamental frequency. The 14.3 Hz peak is the 1ST OVERTONE, and not the 2nd harmonic.

SIGNIFICANCE TO MAKERS OF SO-CALLED "SCHUMANN GENERATORS"

The implications of the above are obvious:
Those who are manufacturing "Schumann Resonance Generators" are most likely using simple pulse generators set at 7.83 Hz. Pulses are by nature the sum of a fundamental and its real, integer-multiple harmonics. If exact frequencies are important [as some have intimated]; e.g., ELF generators intended to influence brain waves or other aspects of human physiology, ought to be capable of high-precision in their frequency output [to 2 decimal places within the ELF "Hz" range], and if spectral content is important [the overtones above the fundamental] then we've been 'doing it wrong' up til now.

[End of Part 1]


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