Todd H. writes:

My answer to Andreas' question was not specific to the human ear.

LOL.. Nice try. You're being defensive...which is actually kind of
fun!

On the contrary, I'm simply explaining the situation. Your fun is
irrelevant.

Indeed, it didn't refer to the human ear at all. It could just as
easily been referring to a microphone.

But you should concede on this nit...see, once you used the term
"twice as loud" you were screwed.

You're erroneously presupposing that I need to concede anything
or that I am screwed.

NO biggie, though--it's a technical
nit, and I'm feeling geekier just talking about it.

Save your geekiness for someone else. I'm not in the mood to play
with you.

Your folly is threefold.

You're erroneously presupposing any folly on my part, Todd.

First, because loudness and what's seen in a
WAV editor are not directly propotional,

Irrelevant, given that I didn't speak of what's seen in a WAV editor.

two because the ear _is_
involved by the very definition of "loudness" (for which there are
actually units...Phons),

Irrelevant, given that I didn't make any reference to human ears.

and third, because these scales are
logarithmic so the quantification of a linear scale number 5000 being
"twice as loud" as 2500 was then wrong too.

Irrelevant, given that 60 dB isn't twice as loud as 30 dB, yet the dB
is on a logarithmic scale.

Hence, you can't speak of what you see in a graphical WAV editor and
equate its dimensionless amplitude scale it to loudness without
Fletcher-Munson curves which correlate dB SPL at a given frequency to
perceived loudness in Phons.

Irrelevant, given that I didn't speak of what I see in a graphical
WAV editor, nor about any perception of loudness. A sine wave with
peak value at 5000 is twice a sine wave with a peak value of 2500,
regardless of someone's perception.

And the F-M curves wouldn't exist if
there weren't ears...because well, ears were kinda involved in the
"perceived loudness" scale studies that created the curves.

Irrelevant, because I said nothing about Fletcher-Munson curves.

Microphones alone can't do that.

So now maybe you understand why I didn't need to say anything about
Fletcher-Munson curves.