square or rounded

Analyze/Statistics has two options for 0dB under RMS Settings: sine wave or square wave. While the documentation mentions that the square wave reading is 3.01dB higher than the sine wave, it give no hint of why one might choose either over the other.

Why are there two options?
Who should care?
When should they care?

[0dB = FS Sine Wave]

Why are there two options?

I don't know.

Who should care?

"Some users" (see below*)

When should they care?

On Tuesdays, perhaps? (Nominate any other day you like if Tuesday doesn't suit you - I really don't care.)

From the help files:

RMS Settings
0dB = FS Sine Wave

If this option is checked, then this means that 0 dB displayed in any of the RMS boxes is equivalent to a sine wave at full scale (with peak amplitude at 0dB – using every sample value in the 16-bit range). If you generate a max amplitude sine wave, it’ll read 0dB if this button is chosen.

0dB = FS Square Wave

If this option is selected, then a full scale square wave will read out as 0dB for the RMS.

*Some users expect a full scale square wave to be 0dB, while others expect a full scale sine wave to be 0dB. Since a full scale square wave is about 3.02dB louder than a full scale sine wave, these RMS boxes will adjust by about 3dB when you toggle between them.
[/list:u]

I didn't know the definition of RMS was negotiable. (yes, I've seen the check boxes - just never messed with them).

I didn't know the definition of RMS was negotiable.

The definition is not. The reference level for expressing RMS on a dB scale is negotiable.

The definition is not. The reference level for expressing RMS on a dB scale is negotiable.

maybe I'm missing something rather fundamental here, but the numbers going INTO the RMS calculation are based on a scale of a known level - it seems to defeat the point of an RMS calculation if you interpret the results of that function on a different scale.
 

maybe I'm missing something rather fundamental here, but the numbers going INTO the RMS calculation are based on a scale of a known level

The RMS procedure is just a way of averaging the waveform level. The numbers which go into the calculation depend on what you measure. They may be volts if you measure voltage, pascals if you measure sound pressure, or watts/sq meter if you measure sound intensity. Or meters if you measure sea waves (you could probably use meters to measure displacement of air particles). You will get your average in volts RMS, or pascals RMS, or W/m^2 RMS.

You can convert them to a dB scale, but you need a reference level. There are some conventions, like 0.775 V for "dBu" or 1V for "dBV". Or 20 μPa for dB SPL, but you can choose any reference level. You just need to make sure it is known to the reader.

For digital sound data the only numbers you have are sample values. Which are completely arbitrary, and they even depend on the data storage convention. Like 16-bit is stored as a number from -32768 to 32767, 32 bit as -1 to 1, I think, and 8-bit as 0 to 255. So I would say that for digital audio only a dB RMS value makes sense.

But there is still a question of reference level. The only meaningful reference level in digital is full scale. Still, various shapes of waveforms which peak at full scale produce different RMS values. A square wave is an absolute maximum because its amplitude is at full scale all the time. There is nothing but a continuous mega-peak . So no digital wave can have an RMS level larger than 0dB re fs square wave (putting the non-clipping over-0-dB capabilities of 32-bit audio aside), which makes square wave a good candidate for reference. On the other hand, everybody likes sine waves, and this is probably the reason why it is used as a reference as well.

But to say that a sine wave that peaks at 0dB has an RMS value of 0dB is simply incorrect.  I guess I just don't grasp the concept of "adjusting" an RMS value so it matches someones "expectations".

But to say that a sine wave that peaks at 0dB has an RMS value of 0dB is simply incorrect.

I would say it is correct, as long as you say "0 dB re full scale sine wave". In the same way, you should say that a square wave which has peaks at 0 dB has an RMS of 0 dB re fs square wave.

I guess I just don't grasp the concept of "adjusting" an RMS value so it matches someones "expectations".

The RMS value is not adjusted, it is the reference level of a dB scale which is adjusted.  It's like expressing temperature in °C or K: everything is fine as long as it is clear which reference point was used.

But I understand that the fs square may seem a more natural reference level for digital because it represents an absolute zero.

The RMS value is not adjusted, it is the reference level of a dB scale which is adjusted.  It's like expressing temperature in °C or K: everything is fine as long as it is clear which reference point was used.

But I understand that the fs square may seem a more natural reference level for digital because it represents an absolute zero.

There is no record I can find anywhere of anybody using a square wave as part of a dynamic range measurement - even though it might on the face of it seem like a reasonable thing to do. Partly for historical reasons, sine wave measurements are used. This first started to be a real issue with tape (it's always been more controllable with vinyl), and of course tape recorders simply won't reproduce a max amplitude square wave, because of the inherent increasing distortion caused by getting out of the linear part of the magnetic BH curve. So, a sine wave at a stated distortion level was what was used traditionally, and yes, you had really to state what the distortion figure was, the frequency, and also what tape you used. Incidentally, if you tried this on vinyl, you'd run into the same problem because you couldn't track a square wave on that either, by a long way.

Since the measurement is entirely academic, and in CE/AA's statistics it is only a statistical measurement, and therefore arbitrary, I really can't see what the point of introducing yet another variable is - so for convention's sake I would only have included a sine wave reference level, and simply not bothered with the square wave one at all.

And of course, since I can reproduce a sine wave at up to 3dB higher than 0dB anyway at sub-multiples of the sampling frequency, one wonders even more what the point was - you end up, strictly speaking, with the same reference level for both standards! (unfortunately for my argument, though, it's the square wave one...   )

It seems like with technical audio software there are two different perspectives:  One is a pro audio perspective.  The other is a computer science perspective.  Actually there are three perspectives if you include the mathematical perspective. 

It seems to me the computer science perspective encounters the same principles as in pro audio but interprets things differently.  Also in computer science there are always multiple solutions to the same problem.  The math and computer science perspectives don't always take into consideration how something actually sounds.  Meanwhile, the pro audio perspective is based upon the history of known studio technology and it's limitations. 

Seems to me that CoolEdit is presented as a program that appeals to all 3 types of perspectives.  I think it's for this same reason that the multiple bit formats are presented in the Save As... dialogue box.