Check also the physical condition of the speakers. Sometimes, if the spyder is loose, or the voice coil bobbin and coil assembly is deformed, you could hear some rattling or what they call, "sayad." This becomes more evident at high volumes. And depending on the condition, it may also be triggered by some frequencies, even at low volumes.
Speakers also will distort at their break-up nodes and this may not be obvious until they reach a volume level where the break-up distortion becomes unacceptably audible.
In general, speakers will distort if it gets square waves instead of sine waves it expects from amps. That happens when the amp is underpowered and you are operating the amp into its clipping regions.
Speakers will also distort when its compliance is exceeded so that its cone cannot go where the amplifier wants it to do, so you get clipped accoustic waveforms. This happens more due to some construcction deficiency in the speaker, rather than power handling.