Ok, so let's discuss the problems associated with mismatches. When you use a load that is lower than the intended load, the output has to drive the load (speaker) with more current because it is a lower impedance than is expected. Two inherent problems associated with transformers are flux leakage and regulation. Flux leakage is also referred to as leakage inductance. It is related to the current in the secondary, and these problems increase as the current increases. As the current draw in the secondary increases, the primary has a more difficult time transferring the signal to the secondary, so the secondary signal to the load gets squashed, or 'soft-clipped'. This soft clipping is called regulation. While regulation is desireable in a power supply, it is undesireable in a transformer. In other words, in a power supply, if the input voltage or the output load current changes, we don't want the output voltage to change. In a transformer, we want the output voltage to follow the input voltage and not regulate at all. When you put a heavier load on the output than was intended, it will pull the output voltage down, hence regulation. The leakage inductance problem arises because the current from the heavier load causing the regulation to occur reduces the efficiency of the transformer by not allowing the output to follow the input. Transformer designers simulate or view this problem as having extra inductance in series with the primary. The extension of this idea then, is that with the heavier load, you could affect the efficiency of the transformer, alter the frequency response (due to the extra leakage inductance in series with the primary), and cause other distortions to occur.
OK, on to mismatching the other way. A speaker is a current operated device in that it responds to the current through it to generate a magnetic field that works against the magnetic field of the speaker magnet to make the cone move in and out. Thinking in very short amounts of time, when the output charges up the voice coil with current, then the signal goes away or gets reduced, the cone system moves the voice coil back to its home or resting position. As it is moving back, it generates a voltage that is fed back up the line into the transformer and appears in the output circuit of the amp. This generated voltage is often referred to as flyback voltage, because we are charging up an inductor, then when we disconnect or stop charging the inductor, the magnetic field in the inductor collapses and induces this big voltage into itself. This big voltage then 'flies back' to the source of the charging current. There is a mathematical formula to determine how big the voltage is and it is related to the inductance of the voice coil, the amount of time it was fed current, and how much current it was charged with. The bottom line is that the voltage fed back to the output circuit is oftentimes much higher than the voltage that was used to drive or charge up the voice coil initially. This voltage gets transformed up by the turns ratio of the output transformer, and in many cases can be over 1,000 volts. What happens then is that arcing can occur between the pins on the output tube socket. Once this has occured, a carbon path forms on the tube socket between the pins. The carbon path allows a steady current to flow between the pins and eventually burns up the socket due to the heat that is generated. For example, it wouldn't be too uncommon to see a transformer turns ratio of 30:1. If we had a voltage fed back from the voice coil that was around 50 volts, 30 times 50 would be a 1,500 volt spike at the plate of the output tube. This is why you often see designers connect diodes in a string between the output tube plates and ground. They are trying to suppress these spikes and dissipate the energy in the diodes rather than allowing an arc to occur at the tube socket. So, when you use a higher impedance load on a lower impedance tap, the turns ratio is higher and resulting fed-back (flyback) voltage gets multiplied up higher than what it would have been with the correct impedance load.
