Basic low-power critique

[microbug]

It is probably not advisable to power the speaker via the button battery.

If you have to have some sound, you may consider piezo elements.

Why? I've got a dual common anode zener diode across the piezo transducer to protect against kickback.

[8086]

Using two pins driven anti-phase, you get a waveform which goes from -3V to +3V, a peak to peak voltage of 6V.

The ground reference shifts as well as the 3V. So at 180 degrees phase difference, and no capacitance, you end up with either +3V or -3V between the two pins, but only relative to each other, not relative to ground, so you really only have 3V between them either way, like you said, the peak voltage. This part I understand - but this will only ever result in 3v across the outputs at any one time, unless there is something else at play.

Surely the only way to end up with the result you describe is to use the capacitance of the piezo to create a sort of semi-persistent virtual ground/3V reference, in order to give the 6V peak-to-peak.

Please tell me if I'm wrong, but if you do, tell me why I'm wrong as well. You haven't said how you get a peak-to-peak (which is what I have meant all along, btw, no confusion) of 6V with this method, just that you do. I'm not necessarily doubting you or that it does work, but it doesn't make any sense to me without using the capacitance.

It's not just me, by the way: http://electronics.stackexchange.com/questions/15629/driving-piezo-buzzer-from-mcu-pin

All right let's define peak voltage and peak to peak:

Peak to peak voltage is the maximum amplitude of an AC waveform, from its positive excursion to its negative excursion.

Peak voltage is the maximum amplitude of an AC waveform with respect to zero.

A square wave going from 0V to +3V has a peak voltage of 3V and a peak to peak voltage of 3V.

A square wave going from -3V to +3V has a peak voltage of 3V but a peak to peak voltage of 6V.

I don't have a problem with any of those statements, but I thought it wouldn't work that way in practice.

As it turns out, it does. I just tried it myself. I stand corrected.  It works, at least on my 'scope.

[lewis]

It certainly does work, and very well. Google 'Amplifier bridging'.

[Zero999]

It is probably not advisable to power the speaker via the button battery.

If you have to have some sound, you may consider piezo elements.

Why? I've got a dual common anode zener diode across the piezo transducer to protect against kickback.

There's nothing wrong with your circuit and yes zener diodes are a good idea, as a piezo can generate fairly high voltages, in response to mechanical shock. I think the reason for the confusion was because you didn't change the symbol in your circuit.
http://electronicsclub.info/circuitsymbols.htm#audio

I don't have a problem with any of those statements, but I thought it wouldn't work that way in practice.

As it turns out, it does. I just tried it myself. I stand corrected.  It works, at least on my 'scope.

It's effectively an H-bridge. When one pin is high and the other low, the voltage is positive and when the logic levels are reversed, the polarity goes negative. The piezo will be louder because the voltage swing is double and it's being powered continuously.