But there is one. In electrical engineering, it's any process that arbitrarily limits a signal's amplitude. By far the most common meaning is a signal that exceeds the voltage range of an amplifier or signal pathway.

> nor any definition that fits the context of this discussion, that allows for a signal's peak value not to be reduced.

See above.

> It's called clipping because the extreme values look to have been clipped away, as if by scissors.

Yes, but this can result from trying to pass a signal too large for the circuit, or it can mean an intentional scheme in which a fixed signal amplitude is truncated, the meaning you're discussing.

In the present discussion, in which a volume setting is increased until the speakers are jeopardized, the meaning is clear -- it's an increase in signal amplitude that the amplifier cannot support, resulting in the waveform being clipped at the maximum available amplifier voltage.

> The parts that have been clipped away contain energy, don't they? So won't the clipped signal will carry less energy than the original?

Not if the signal amplitude is increased. In the present discussion, the problem is being caused by raising the volume level too high, which causes the signal to exceed the available amplifier voltage. My diagram shows this case:

http://i.imgur.com/oE5NFZ9.png

The red trace is the maximum volume setting that the amplifier can support without distorting the signal. The green trace is a much higher volume setting that essentially reduced the output to a square wave. In both cases, the peak voltage is the same.

> When you take a sine wave of peak value 1 and clip it, what you get is not a square wave with a peak value of 1.

That depends on how you define "clip". If you increase the size of the sinewave, clipping takes place at the maximum voltage. If you clip by reducing the possible range of voltages, the sinewave remains the same size but maximum amplitude goes down. The present discussion revolves around the first of these choices.