Can someone help me understand this transistor circuit?
The circuit works as follows: @WhatRoughBeast is correct, the voltage must be low enough so that everything stays under the power supply voltage.  The input is level shifted with C3, R7, and R8 so that it is basically the same signal at the base except that it is centered about midway between V1 and ground.  Q1 emitter is basically a voltage follower one diode drop below this midpoint.  So the signal at Q1 is pretty much the same amplitude and phase as the input.  Because the gain (beta) of the transistor is high, we can say that the collector and emitter current is almost identical, so that the voltage on the collector is the same amplitude as the voltage on the emitter, but is 180 degrees out of phase.  So you have two voltage sources, one in phase and one out of phase, and they are connected to your load through different impedances.  You can do the math but intuitively you can see that as the frequencies change, the contributions from the two voltage sources also change so that the phase shift does not change as much with frequency as it would with a simple RC.  It does not provide a true constant phase shift.  If you want a constant 90-degree phase shift, you can do a much better job with a simple op amp circuit.  However, musician types looking for new sounds often experiment until they get what they want, especially in the era you mentioned when op amps were not available.