4/18/2020

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

The Schumann Resonances are an earth phenomenon predicted and discovered by W. O. Schumann in the 1950s. They are a band of electromagnetic resonances found in the E.L.F. [Extremely Low Frequency] portion of the radio spectrum between approximately 7 Hertz and 40 Hz. They are not continuous radio signals, but instead are natural resonances that are "heard" [not audibly; they are not sound waves, and their frequencies are too low for us to hear, if they were sound waves! But if we could hear them, they would occur at certain "pitches", like when we sing at just the right note, in the shower, and find our voice suddenly booming because of the resonance of the shower stall, which, in turn, depends on the dimensions of the shower stall] whenever lightning strikes around the world, sending these frequencies into temporary, "ringing" vibrations. They occur in the resonant cavity which is formed between the earth and the ionosphere, and, based on those cavity distances, the Schumann resonance frequencies are determined.

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.

Now what's interesting is that scientists have noted that the band of frequencies occupied by the Schumann resonances pretty much overlaps the frequency bands observed by EEG technicians when they record the brain waves of human beings. The upper Theta, Alpha and Beta bands fall into the same frequency range as the Schumann resonances. One question that pops up amid all the speculation that these observations lead to is, Are our brain waves, and possibly moods and thoughts, at all influenced by this sea of electromagnetic resonances occuring naturally all around us? Could this be part of the mechanism by which "mystics" and meditators "tap-in" to external information, via entrainment or synchronization of their brain waves with the "vibrations" of the earth-ionospheric cavity [which happens to be shared with billions of other minds]? Is ELF the medium by which minds connect? Can we "influence" the 'field' out there, by magnetically connecting to it by entering into a certain coherent state of consciousness?

Well, before going down those fascinating rabbit holes, I'd like to discuss some harmonic wave theory first, as it applies to our understanding of the Schumann resonances. Once we clarify a few things, maybe we will find it easier to speculate on how it might be possible for minds to be linked, when conditions are right, for spontaneous spurts of communication-- whether on a general level of mood influence, or influence over the health and processes of the body, or, on the wilder side, over the "telepathic" communication of thoughts... which we will not be addressing in this introductory article!

OVERTONES, MODES and HARMONICS

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!

"But", someone objects, "the Earth is not a stretched, straight string tied between two endpoints; it's a sphere, and therefore different rules come into play."

No-- it's still a finite area, and the nodes and antinodes of a standing wave can still only form at integer intervals of the total distance around the globe, in which the wave energy can travel before crossing through itself on the return trip. In other words, just as curving the brass tubing of a French Horn doesn't skew the relationship of its harmonic frequencies because the tube is curved, so it is with the curvature of the earth-ionosphere cavity. If the curvature of that waveguide could skew the 2:1 frequency ratio of the first Schumann mode or overtone, with respect to the fundamental frequency of 7.83 Hz, then we should expect further "skewing" to occur with each successive "overtone"... but that does not happen. Instead, the entire series of overtones stays locked, in a 6.5 Hz relationship between successive overtones.

What does happen, looks oddly familiar... like a 6.5 Hz fundamental and its integer harmonics have been moved up together such that the fundamental is now 7.83 Hz, while keeping the harmonics at a constant 6.5 Hz difference from one to the next... like the kind of skew upward that is seen in a radio upper sideband!

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 "apparently" 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 5th 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, which also happens to be the 6th harmonic of 1.3 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 upward. In the upper sideband they will still be spaced 6.5 Hz apart, as 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 all wrong up til now.

[End of Part 1]


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