There are plenty of explanations on the web of why an amplifier with a low output impedance will produce a better sound. One example shows how a loudspeaker exposed to a transient will ‘dampen’ the movement of the cone by fitting a low impedance resistor across the terminals of the speaker. It does dampen the movement of the cone, but is this going to give an improvement in the sound? Anything that produces an additional force on the cone, and damping factor is an additional force, will need to be considered for its contribution. Is it linear with frequency, and with displacement? I am going to suggest that a high output impedance amplifier will actually produce a better sound than one with a low output impedance. There are not many of us who think this, but I am not the first to think it.
Lets consider the force equation. F = Bil , The force in Newtons resulting on the speaker cone is proportional to B- the magnetic flux density produced by the magnet in the speaker, multiplied by i- the instantaneous current flowing in the coil of the speaker, multiplied by l- the length of the current carrying coil wire in the magnetic field. Notice that the electrical factor producing this force is current not voltage. Almost all audio amplifiers are voltage amplifiers with a low output impedance, not current amplifiers with a high output impedance. I would like to suggest that a high output impedance current amplifier would actually be better.
There is an equation relating voltage and magnetic fields, but it is better suited to microphones, and it is: V=Blu. This states that the voltage output of a microphone is proportional to B- the magnetic flux density, multiplied by l- the length of wire in the magnetic field, multiplied by u- the voice coil velocity. So the loudspeaker, which will act like a microphone as well as a speaker, will generate a voltage output dependent on its velocity. The problem is, that this will subtract from the voltage being applied to the loudspeaker affecting the sound. Note also that for most of the frequency range of a loudspeaker it is acceleration limited, not velocity limited, so this voltage is not going to be linear across frequency. Note also that a high output impedance current amplifier will not be affected by this microphone voltage. The drive current will stay the same.
If you are like me, the obvious next thing to do is to make some measurements, comparing a standard voltage driven amplifier with a current driven amplifier to see which has the lowest inter-modulation distortion, through the same loudspeaker. Improvements of the order of 5dB were measured on a mid-range 5″ SEAS speaker I tried. Taking into account that the loudspeaker is the part of the chain that produces the highest inter-modulation distortion, 5dB is worth doing.