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I would agree here, because different wave shapes will sound different.

A small nit to pick: a square wave has fundamentals and odd harmonics of the fundamental, but not "all" frequencies. Triangle waves have even harmonics. (If I remember my math right) Varying the fundamental frequency will get you through the spectrum like a frequency sweep, but not all frequencies simultaneously. Square waves are used in testing because if the square wave shape is well-preserved, then the bandwidth extends to at least 10x the fundamental. That means that a good looking 1 KHz square wave response means that the system is "good" up to 10 KHz, or more. If the system shifts the phase (timing) of any of the harmonics, the square wave will distort its shape. Look at square wave responses of some speakers and you'd wonder why those were ever highly recommended.

In addition, the Fourier decomposition of the square wave into odd harmonics is infinite. The reconstruction back to a perfect square wave is not possible, but only approximated if the frequency band is limited, as in practical systems. That's why you will see rounded-off square waves at 10 KHz fundamental, if the system cuts off at 20 KHz.

Anyone who is more expert than I in Fourier mathematics may wish to explain further.

Other tests are a pulse test or a step test, but those are just a few available from the many that can be done.

If you could somehow couple perfectly non elastic air in a tube ..between the microphone and the driver in question, there is little doubt that it would ultimately allow the recording of a near perfect square wave.

Just so the average reader does not get lost, the lossy characteristic of the air surrounding the driver...prevents a perfect recording (recording by the microphone/amplification/recording system) of a squarewave from occurring. Think if it as trying to pressurize the surrounding air by poofing air out of your mouth. Not gonna happen.

Just about the best you can do, is get the compressive wavefront correct and coherent. It is still a tough call to see how this particular measurement (which UHF magazine was still doing to up to a while back, and still may) applies to perceived loudspeaker quality.

The inability of 'loose' air to maintain a unaltered pressure condition and the resultant 'transient only' aspect of 'through the air' acoustic transmission, is key to understanding the fundamental considerations of how the ear works. If the backwave is also simply a reset for the next transient wave cycle, then it is redundant information, and the ear/brain would tend to be designed to ignore this. Why process twice the data, when tuning the system's sensitivity to the information that is actually transmitted, brings more information and communication to the table for that given ear?

And if the nerve 'fires' on the positive (compression) transient cycle...and also on the rarefaction (backwave) cycle..and the nerve pulses are only 'singular' or a '1' (fire nerve!!), and the absence of nerve impulse is the '0', then how could the ear even remotely differentiate between the two? It could not. Hence the disposal of the backwave, or rarefaction cycle. It is predominantly a single sided transient device, due to the very thing it was designed to measure and deal with.

This is a case where the oscilloscope and the math do not add up to the ear's perception. the measurement device, the ear, takes the signal to the place where it is figured out, the brain. In the same way the eye takes the signal to the place where it is figured out, the brain.

Put a similar algorithm or 'brain' on the electronic measurements, with respect to knowing how the ear works, is the fundamental point, here.

Get the weighting correct, ie know what it is we are attempting to measure, and why. Then design the measurment system.

It should then show considerably more correlation to what we as audiophiles say we hear.

Huh? Whatever makes you happy!
For me, accuracy is important in getting "close" to the music.
It increases my enjoyment of the music. Being of limited budget(hence my name)it's not easy, but I get as "close" as I can afford. I'm not too bright, but I thought that's what being an Audiophile was about. As food for thought I'm posting a couple of links here from Chesky's site. But hey,whatever floats your boat!!

Chesky Records Chesky Records

Since being enlightened that the ear only hears the positive pressure, I decieded to disable the negative supply of my amplifier (after checking for non-inverting polarity). I am very unhappy with the results of half-wave rectified music.

Doesn't the ear drum move in both directions when it gets air movement on it? How does it only hear in positive? How come speakers move in two directions, and it mattters that they are in "phase", like your brain and ears, how else can you hear direction, or other effects in audio. Maybe your ears are uni directional, like wires and cables? Do you have arrows on your ears for what direction you need to listen in? What the heck are you talking about, Willis? To quote a famous tv show.... My ears go both ways...oooooogaaaahhhhhhh

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My entire audiophile life has been spent in the pursuit of accuracy. Euphonic colorations were simply wrong, they were something to be avoided like the plague. Truth, not beauty, was the only worthy goal. If there was beauty to be heard in a recording, then the accurate system would reveal it. If there was not, the recording itself was not worthy. I believe many of us feel this way.

If you happen to have the current copy of TAS (#181), you might find the reviews performed by Tom Martin and Anthony Cordesman instructive and a bit thought provoking.

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... And if the nerve 'fires' on the positive (compression) transient cycle...and also on the rarefaction (backwave) cycle..and the nerve pulses are only 'singular' or a '1' (fire nerve!!), and the absence of nerve impulse is the '0', then how could the ear even remotely differentiate between the two? It could not. Hence the disposal of the backwave, or rarefaction cycle. It is predominantly a single sided transient device, due to the very thing it was designed to measure and deal with. ...

I really don't know that this is so, as I have not researched the neural firings in the ear in response to varying pressures on the ear drum. Have you got a scientific paper reference to this?

What I do remember is that the variations in pressures move the membrane into vibration, with the highest frequencies near the beginning and the lower frequencies further down the membrane. The nerves firing at a specific location along the membrane separate out each frequency or band of frequencies, which when combined is the sonic waveform. How the nerves sense this is not known to me, but the membrane must respond to both compression and rarefaction.

If you say that nerves fire only on one direction, that may or may not be so. One could DC shift the entire sine wave or musical waveform into the positive side, or the negative side and output the sound via head- or ear-phones to only give compression or only give rarefaction pressures and see what happens. This still does not answer the question of the neural firings per se.

You are what is referred to as a Suppressive Person or SP for short. DUP and I are also SPs. You can choose your own equipment based on your knowledge as well as what you hear. It's OK.