Digital BW, The Print

Hi, Oh Prolific Roy ;-)

> > > The kicker is that since all the dB's
> > > are perceived equivalently we can say StepSize = .5dB,
> > > Range = 60dB and voila: number of steps = 60/.5  = 120
> > > different loudness levels.
> >
> > That works for me as far as I can tell...
> >
> > > With a fixed step size, the
> > > dynamic range specifies both the Height and NumSteps.
> > > Only one independent variable.
> >
> > Well, I'm not quite with you here.  Dynamic range, in and of it
> self, only
> > specifies the "number of relative steps"...it has no reference to the
> > height, in and of it self, as dB doesn't relate back to what you are
> > determining the dB of.  In other words, you measured voltage
> of, say 6V, and
> > a "stepsize" of .01V, you would have a dynamic range of X dB = 20 (for
> > audio) log10(6/.01) = ~55dB.  But, there is no way to get back
> to 6V or .01V
> > just by saying 55dB.
> >
>
> Well, well, well, Austin, its good to see these two paragraphs together.
> The fallacy of your logic, your feeling of the whole dynamic range concept
> is well illustrated here.  I'm sure you've been able to do your
> job for years.
> Plugging in numbers is NOT the same understanding and feeling the concept.

Whether you believe it or not, I just don't plug in the numbers, I do
completely understand the concept of dynamic range...and we'll see if that
bears out ;-)

dB (as in the result of a dynamic range equation) does not translate back to
"Height" and "NumSteps", dB is merely a relative scale of power.  You could
have an absolute range of 1V with the exact same dynamic range as a range
with 100V, the "heights" as you call them, are entirely different.
Relatively, yes, the max/min are the same...but as I said, there is NO way
to get back to the original hard (as in actual values, not relative values)
from dB.  That's simple fact.

> The basic fallacy is the mixing of linear scales and exponential
> (or geometric)
> scales

Er, I didn't mix them anywhere...but you're right, that would be a
fallacy...

> You are
> looking at the DynRange formula and seeing the term (maxpower/minpower)
> and "feeling"  that its the same thing as the ruler.

The example of a ruler is fine, providing you understand what it means.  In
the example I've cited above using 6V/.01V, no matter where you are on the
scale, you can only measure to .01V.

Now, using a ruler for your example of power.  As an aside, every 3db is a
doubling of power, not 2x the dB value...but that may not matter...it
depends on what "unit" your measurement is in.  If you ARE measuring in dB
(which I would assume you would have to do to give two numbers like 60dB as
your largest swing, and .5dB as your minimum discernable), and your
measurements are in fact only accurate to a certain dB level (as your
example above), then a ruler works fine also.

Just as an aside note, in audio, just because you have doubled power, you do
NOT get double the "loudness".  That takes ~10x to double the loudness.

The fallacy would be applying steps of "hard" numbers to a power system, and
vice versa.  It doesn't work.  You couldn't say you had a max of 60dB and a
step of .01V.  Both numbers have to stay in the same measurement system
(unit).

> Its like
> minpower is the
> step size and when you divide it into maxpower you get "how many steps".

If you are measuring in power, then that works fine.

> This is exactly what you've said in the second paragraph above.

Actually, I used volts, not power, but it does still apply.

> This is completely wrong as a concept.  Why?? Because power is an
> exponential scale from a perceptual point of view.

It doesn't matter.  All that matters is that you understand what your
"system" is, and what you are measuring in.  Typically, minimum measurable
of a system is in the same "units" as the system you are measuring...  If it
's power, then it's power.  If it's volts, then it's volts.  Exponential
system or not...  That appears to a possible source of your confusion.

> I.E.  To get
> a "linear" feel
> of loudness in the audio system, the power output has to go up
> exponentially.

Correct.

> Here's a short audio example:
> We have an audio amplifier -- puts out 100 watts at the max end,
> and measuring
> the low end (smallest discernable signal) we get 1 watt.

A power output of 1 watt at the low end does not necessarily mean you have a
smallest discernable signal of 1 watt, BTW, but I'm fine with that number,
as it really doesn't matter.

> Let's
> throw that
> into the DynRange formula:  the inside term is (100/1), you are
> thinking that
> this is 100 steps.  Not TRUE!!

It certainly IS true, IF your measuring device is accurate to only 1 watt,
as YOU specified above, and you ARE measuring watts...  YOU seem to be
confusing systems here.  What ever your measuring system is, you are only as
accurate as the measuring system is...and if your measurement system gives
measurements in some log form (as a densitometer does, for example, or a
sound pressure level meter), then your steps are also in log form.

BUT if you are measuring in "loudness", well, then, you can't very well give
"watts" as your unit, as watts is NOT the same relative measurement of
"loudness".  I believe that is a clear mistake.

<big snip>

> See now have:
> DyR  = maxdb - mindb

Sure, note both are in dB.  Nothing wrong with that.  BUT...if you are
trying to claim somehow that has something to do with density range, it does
not!  Density measurements are NOT in dB, period.

> Example:   connect the dbmeter on amp at full power -- reads 40dB
> with amp at min power -- read -20dB
>
> So, DyR = 40dB - (-20db)  = 60dB
>
> QED

Yeah, I could say 1+1=2 QED, but your "claim" has to be applicable to what
the discussion is.  The arithmetic in your example is correct, but your
example has nothing to do with photographic density range being the same as
dynamic range.  As I've said countless times, because density values are in
a logarithmic scale, it does not mean they are the same as dB (which are
also in a logarithmic scale), and therefore density range is absolutely NOT
the same as dynamic range.

> All things called "ranges" are just a top end and a bottom end.

Correct, but then add the word "dynamic" to it, and adds another dimension
to the meaning, or why even bother adding it...especially considering
dynamic means "characterized by continuous change".  That hardly seems
applicable to two static numbers!

> Dynamic range is a range just like any other range,  the word "dynamic"
> is just a qualifier that says "perceptually interesting part of".

I don't mean to be snide, but that's just silly.  So many things have ranges
specified, and they aren't called "dynamic ranges", but they are the range
within which the device operates.  In fact, many specs include both a range
of operation, and a dynamic range.

BTW, things can only be perceived if you can "perceive" a difference, which
fits perfectly with what I've said ;-)

If I get one of THE "gurus" to say that "dynamic range is NOT the same as
density range" will you give?  You're on a crusade to prove something wrong
that isn't wrong, and you aren't going to be able to do it ;-)

Regards,

Austin