On Sun, 08 Jul 2007 11:12:56 -0700, Jeff Liebermann
wrote:

isw hath wroth:

I beg to differ. There's no mixing happening in the air. compression
of air is very linear (Boyles Law or PV=constant).

In general, that's true, but take a look at what happens in the throats
of high-powered horn loudspeakers. You can find info in e.g. "Acoustics"
by Beranek.

Isaac

What am I suppose to look for? I appreciate your recommended research
project, but frankly, I don't care what happens inside a high powered
horn loudspeaker. I prefer to stay fairly on topic about the original
allegation that mixing somehow occurs in open air, which is not true.

---
That's not true. The original allegation was mine, and was that
since the ear is a device with an "output" which doesn't change
linearly with linearly changing input amplitudes, it's a non-linear
device, is incapable of _not_ producing harmonics and heterodynes
and, as such, is where the mixing occurs.

My contention was that zero-beat was the difference frequency
between two input tones close to unison, and I still maintain that's
true and that that difference frequency is in there. However, your
contention that zero-beat is the result of the vector summation of
two tones close to unison is also valid, since a non-linear detector
is capable of doing that summation well enough to allow that be the
dominant phenomenon as evidenced by the fact that the ear is
incapable of directly detecting (say) a 1Hz tone but is fully
capable of hearing the 1Hz amplitude warble which would result from
the vector addition of the two tones.
---

Incidentally, if mixing did occur in open air or inside the ear, you
would not be able to comfortably listen to hi-fi music, as all you
would hear would be intermodulation products.

---
_All_ you would hear?

That's grossly untrue. What do you think would happen to the
_played_ notes?

They'd all disappear in a cacophony of chaos just because some
lower-level cross-products were being produced?

Nonsense.

In fact, contrary to what you may believe, the ear _is_ a non-linear
detector and, consequently, _cannot_ help but heterodyne its inputs.

That's why, after thousands of years of experimenting with what
notes sound good when they're played together and which notes don't,
music is written the way it is.

Something else you may not be aware of is that musical instruments
are inherently non-linear and, as such, will generate harmonics of
any fundamental notes played on them and heterodynes if two or more
notes are played simultaneously.


--
JF