The Estey Organs of the early sixties used relaxation oscillators to produce the twelve high octave notes, and then a series of frequency dividers for each of the lower octaves. A relaxation oscillator is a light-weight, low amperage draw method of creating a sawtooth frequency oscillation. This basic oscillator was adapted as guitar amp vibrato oscillators for the Pro Series vibrato from 1966-1968, as well as the echo effect for the reverb on M15's in 1965.
Below is an excerpt from a MP3/MP5 schematic. The relaxation oscillator is only a small component of it, so the key components are spelled out at left:
at "C" is 220V
The center of this oscillator is the Neon Lamp. As you would expect, the lamp has two elements and will glow when either AC or DC voltage is applied across the two elements. Of course, there is a minimum voltage to make the lamp glow. This is called the fire voltage. The lamp has a low current requirement to glow (maybe 0.1ma), but it will conduct a very high current without any self-governance and will instantaneously burnout! To prevent self-destruction, a ballast resistor must be placed in series with the lamp. Each lamp type has a designated minimum ballast. In the case of a NE-2H, it is 30KΩ. In the example schematic, the ballast is provided by the series 2.2MΩ R1 and the 5MΩ P1 to ground underneath the lamp.
The key to the oscillation is the presence of C1 in parallel with the lamp, and this key characteristic of a neon lamp: when voltage is below fire voltage the lamp's resistance is so high, it can be thought of as being an "open circuit", but it has a completely different behavior when voltage is above the firing threshold, as its resistance becomes negative.
As it begins (amp is turned on, or the vibrato switch is closed), the capacitor C1 begins to charge because the parallel lamp is an effectively an open switch. Once the voltage difference across C1 exceeds the lamp's firing threshold, the lamp fires, and its resistance becomes negative, or effectively, a short. This immediately discharges the C1 capacitor, and voltage across the lamp's elements drops down toward 0v, falling below the firing voltage threshold, which opens the lamp's conductiveness, and the C1 cap starts charging again.
The rate of the oscillation is a function of the C1 capacitor size (smaller cap charges faster) and the combined resistance of R1 and P1 in series. As that resistance increases, the voltage discharge of C1 slows. This is how P1 becomes a speed control.
Another piece of this is the voltage at "C", which in the case of the example, is 220V. The higher the voltage the faster C1 charges. This means if the amp was originally designed for 117VAC mains voltage, the oscillator speed will increase slightly when run at 120V volts! If you want to slow down the vibrato, the easiest way is to increase R1.
Continuing the topic of supply voltage at "C", in general terms, higher operating voltages will result in a more consistant oscillation frequency.
It the case of the NE-2H, the mimimum supply voltage should be 150V.
During this charge/discharge cycle, the different between the dynamic firing voltage and the extinguishing voltage potential of a NE-2H will determine the peak-to-peak voltage of the AC voltage signal produced.
At any oscillation frequency below 20kHz, a relaxation oscillator will always produce a sawtooth wave. In the 2.1 figure (above right), the Magnatone MP3/MP5 is type (b).
At right is the M15 relaxation oscillator used to provide an echo tremolo effect for the reverb signal on some M15A amplifiers. The flashing lamp, controls the LDR (Light Dependant Resistor) below. the LDR probably ranges from 10K when it detects light, to 1M or more, when dark. The fluctuation of the LDR's resistance varies the voltage divider resistances of P2. The reverb signal appears as V(in), and the echo effected signal leaves as V(out).
The MP3/MP5 arrangement is a little more complex because the engineers wanted to add an intensity control. To vary the dimness of light that the operates the LDR, the oscillating AC signal first goes through a .047uf coupling capacitor, C2. C2 is required, because there is a high DC voltage on the oscillator side that would upset the bias of the triode, and put DC voltage across the P2 pot (which would make the pot scratchy).
P2 allows the musician to attenuate the oscillating AC signal down, R2 & C3 form a low-pass filter (I think, although there are some impulse-response effects such an RC circuit might play as well). The signal then goes to the grid of the low-mu triode of a 12DW7. The triode is setup as a current driver, and a 1869-D incandescent is in series with the cathode. From there, an LDR is controlled which attenuates the instrument signal based on the brightness of the 1869-D light, and the frequency that it is lit.
Unlike the NE-2H bulb, the 1869-D has a dim/bright level that is much more controlable with the voltage supply. In the case of this design, Fiddling with the R1 and P1 only change the frequency of the oscillation, they cannot effect the brightness of the lamp.
The 1869-D could have been connected directly to the center sweeper of P2, however the oscillating signal, once attenuated, doesn't have the current to drive the 1869-D.
Luckily, LDRs, the NE-2H and 1869-D bulbs are still available. Although, I'm not sure in current 1869-D bulbs have the came characteristics of the GE bulbs of yesteryear. When these amps were designed, LEDs were extremely expensive and would not have factored into anyone's design. LEDs are cheap now, so it is possible to replace the 1869-D (and the triode) with an LED that has a good range of dim/brightness levels (lumens) to replace the function of the triode and 1869-D.