I put the schematic of post#1 into LTSPICE and ran some simulations. I found that the square wave output of the 555 IC, produced unpleasant looking waveforms at the "output inductor" L1.
Since the L/R timeconstant of the network on pin3 is only 5 nanoseconds (!) the exponential rise and fall of the inductor current is very quick, and the current is an excellent approximation of a square wave {red waveform}. Because the inductor voltage is proportional to the derivative of the inductor current (V = L*dI/dt), the voltage waveform is a Dirac delta function. An impulse. {green waveform}
Square waves and impulse trains are not the types of waveshapes found in resonances in the physical world. Plucked strings, struck bells, splashed pools all resonate with (slightly damped) sine waves. Thus I would expect the Schumann Resonance to be a sinusoidal phenomenon, personally. So I would expect that the optimum way to synchronize with it would involve sinewave, not square wave, currents in an inductor.
Thus I would expect better Schumann Resonance performance (whatever that is!), when people built a different circuit using opamps. This alternate circuit would generate a 7.83 Hertz sinewave, and apply this voltage sinewave to a "voltage controlled current source", thereby creating a sinusoidal current in the inductor.
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