RMS (Root Mean Squared) Power

    RMS measurement is a measure of "power density".  It is 0.707 of Peak-To-Peak sine-wave readings so that the roughly 30% deducted can be used to fill "voids" in the sine-wave power envelope of a given sine-wave.
    So what does RMS have to do with evaluating an amplifier's performance?  Actually an RMS rating has very little meaning in terms of actual dynamic performance of an amplifier, although it has some value when comparing different amplifiers from different manufacturers. If all manufacturers quote their RMS values honestly it is possible to determine which machines are more powerful under RMS test conditions.  Unfortunately many manufacturers can get very creative in their measurements, and so all RMS ratings have to be taken at less than face value just in case .......
    To obtain an RMS rating, a given amplifier is placed in a test jig, attached to a fixed load of a specified impedance, and a signal at a given frequency is increasingly applied until the amplifier cannot produce any more power without "clipping" the sine-wave it is trying to produce.  At this point a voltage reading is taken with an instrument calibrated to accurately indicate RMS voltage, or the waveform can be measured with a calibrated oscilloscope and a mathematical calculation is undertaken to convert its Peak-To-Peak reading to RMS.  Using another mathematical formula, the voltage, in conjunction with the fixed load, produces the RMS rating.
    What has been obtained is an indication of what power the amplifier can produce continuously at a given frequency, to a static, usually non-inductive load, connected to other test equipment.  As the reader might already suspect, this test is far removed from any real-world practicality as far as reproducing music is concerned.

    Dynamic Audio Power (DAP)

    Dynamic Audio Power is just that.  It is a measure of what an amplifier can do when placed in a situation where it is producing actual music, into a dynamic load (a loudspeaker).  It is an estimate of how an amplifier can handle any number of frequencies simultaneously into a shifting impedance, as any loudspeaker can have a number of impedances depending on frequency applied.  It is a measure of what reserve power is available to produce a smashing low bass note while at the same time some very subtle high frequency content.  In short, it is a measure of what an amp can do in the real world, with real people listening to it, not how it can communicate with a lot of test equipment in a laboratory.
    Dynamic Audio Power usually appears to be greater than RMS in any given amplifier, by a factor of two (twice as much).  This is because the amplifier is not totally consumed trying to produce a static frequency continuously as in RMS, so that when a particularly short term heavy load is placed on it (lets say a powerful bass note), the amp has almost all its reserve at hand to do that job alone, and so can handle the momentary task with relative ease.  This explains why amplifiers that are rated rather low in RMS  terms have the ability to produce audio results way more than the low figures would tend to indicate.

    So - which rating is more important?  Actually both have their place in evaluating an amplifier. The RMS value can be a useful standard by which all manufactured amplifiers' power can be compared, if all manufacturers would only tell the truth, or test under exactly the same conditions.  For instance any, poorly crafted amplifier may be able to produce sizable RMS wattage at 1000 Hz but do terribly at 30 Hz (where the wattage really counts), so the manufacturer will naturally quote the RMS at 1000 Hz.  We always quote our RMS power ratings at about 30 Hz (unless otherwise stated), because if the power output is great there, it can only be even better everywhere else.
    Dynamic Power is very useful because it predicts just what the listener will hear in real-world conditions.  An amplifier is performing an amazing task, when trying to reproduce thousands of interacting waveforms, and their harmonics, while driving a loudspeaker that is in every sense of the word, a "moving target".