In article <46910fe5$0$8925$4c368faf@roadrunner.com>,
"Ron Baker, Pluralitas!" <this@aint.me> wrote:

> "isw" <isw@witzend.com> wrote in message
> news:isw-664E24.21491207072007@newsgroups.comcast.net...
> > In article <468fe7df$0$16560$4c368faf@roadrunner.com>,
> > "Ron Baker, Pluralitas!" <this@aint.me> wrote:
> >
> >
> > --snippety-snip--
> >
> >> >> You said you are a physicist/engineer.
> >> >> What does "linear" mean?
> >> >
> >> > Let's not get too far off the subject here. We were discussing whether
> >> > the "tuning beat" that you use to tune a musical instrument involved a
> >> > nonlinear process (ie. "modulation").
> >>
> >> Then linearity is at the core of the matter.
> >> What does "linear" (or "nonlinear") mean to you?
> >
> > OK, if you insist -- *in this case* it means "linear enough to not
> > produce IM products of significant amplitude".
>
> Good enough.
> Then spectrum analyzers and the human auditory
> system are not linear.
> Stay with me here.
>
> >
> >> > I said that it does not, and that
> >> > it could be detected by instrumentation which was proveably linear
> >> > (i.e.
> >> > not "perfectly" linear, because that's not required, but certainly
> >> > linear enough to discount the requirement for "modulation").
> >>
> >> No nonlinearity is necessary in order to hear
> >> a beat?
> >> Where does the beat come from?
> >
> > As the phase of the two nearly equal waves move past each other, there
> > is simple vector summation which varies the amplitude.
> >
> > Consider two sine waves of precisely the same frequency, where one of
> > them is adjustable in phase -- use a goniometer, for instance. Use a set
> > of resistors to sum the two signals, and observe the summing point with
> > a 'scope or a loudspeaker. By altering the phase of one source, you can
> > get any amplitude you want from zero up to twice the amplitude of either
> > one.
> >
> > Now just twiddle that phase knob around and around as fast as you can.
> >
> > You've just slightly altered the instantaneous frequency of one of the
> > generators (but only while you twiddle), and accomplished pretty much
> > the same effect as listening to the beat between two guitar strings at
> > nearly zero frequency offset. With no nonlinear processes in sight.
> >
> > Isaac
>
> You put some effort into that. I give you
> credit for that.
>
> The socratic thing isn't working, so here
> you go.

I would appreciate it if you would take the time to list *in detail* any
errors in what I wrote. If it "isn't working", I need to know why,
because I don't like to be confused about things.

> Is an envelope detector linear? The answer is no.

That's correct, and I'm well aware of it, but so what?

--dissertation on how an envelope detector works snipped--

> Do you see how this applies to spectrum analyzers
> and the human auditory system?

Sure. But

1) It is possible -- if not practical -- to build a "detectorless" (in
the nonlinear process sense) spectrum analyzer, and

2) None of it is even remotely significant to the subject at hand.

Here it is again: the "beat" one hears when tuning a guitar or other
instrument does *not* require any nonlinear process for its production.
Period.

Isaac