I think the trick here is that the resistors are much more precise than two batteries of unknown origin will be at providing a symmetric supply voltage without further stabilization. So they serve as a 50/50 voltage divider whatever the input voltage is, 7+9 or 6+8 on half full (or half empty, depending on your mental make-up) batteries, it would still work just fine.
Binding the central line between the two 9V batteries to GND would give you the situation you describe, indeed you could then drop the resistors but now you have a fairly high risk of ending up with an asymmetric supply voltage, which means one side will clip earlier than the other.
Is this really a common thing? I don't really have experience with battery powered audio processing circuits. In my experience you usually create a virtual ground when you've got no other choice, like say signal conditioning with a single ended supply.
Yes, in battery powered stuff it is pretty common. When working from a single supply it is a quick and easy way to use operational amplifiers.
That the author used two batteries in series did not change much in that respect (and internally those 9V batteries are a stack of 6 cells anyway). The alternative would be to use the common rail between the two batteries as a ground and then two regulators (or simply a Zener and a follower transistor, same effect for less cost) to get say plus and minus 7 or 8 volts depending on how far you want to run the batteries down and what kind of specs that op-amp has.
Most op-amp circuitry would be +- 15V, but they usually work on much less than that. The circuit as presented here probably has a DC bias that is in the 100's of mV, there is no adjustment for it either so it is a bit of a kludge the way it is set up. There are better ways to do this, it all comes down to part variation and that should not be a factor in a good schematic.
There are single supply op-amps too, but in this case I suspect the voltage required to drive those headphones properly was the major deciding factor in using two stacked 9V cells.
> But in this case I suspect the voltage required to drive those headphones properly was the major deciding factor in using two stacked 9V cells
Maybe it was the deciding factor for whomever designed the original circuit. But in this incarnation with the 11x attenuation, the input signal would have to be above 80V for this to matter! It's obviously modified from some folk audio design, I'm just trying to figure out how much of its oddity actually has some purpose.
Yes, it definitely looks like a 'stacked hack', not something that was designed with purpose by someone who really knew what they were doing. No mention of distortion, no bias adjust, DC coupled (could be good, could be really bad depending on the bias...).
There are some pretty good headphone amplifier circuits out there, most of them a little bit more complex than this but with what I would expect to be far superior specs.
You do not need an absolutely precise dead-centre reference voltage for this application! It just has to be far enough from the either rail to avoid clipping.
If the batteries have gone that far south, they need replacing.
Binding the central line between the two 9V batteries to GND would give you the situation you describe, indeed you could then drop the resistors but now you have a fairly high risk of ending up with an asymmetric supply voltage, which means one side will clip earlier than the other.