[PD] Headphones question on pd list

[Charles Henry]

On Wed, Aug 24, 2011 at 2:15 PM, Mathieu Bouchard <matju at artengine.ca>wrote:

> On Wed, 24 Aug 2011, Jonathan Wilkes wrote (outside of pd-list):
>
>  If I do this, can't I be fairly certain that I won't get a sound with
>> greater perceived volume than the clipped [noise~]--[*~ 999999] that I
>> started with? [...] I'm just talking about things that could potentially
>> cause ear damage.
>>
>
> a harsh-clipped [noise~]-[*~ n] is probably close to the highest loudness
> you can get, even for not-so-high values of n.
>

> However, if you want to find the loudest, you'd have to start from the dBA
> loudness curve, and try to solve an equation involving a bunch of samples
> that can range from -1 to +1... at 44100 Hz over 1 second, that'd be 44100
> variables, for example, though a lot less variables could be enough to get
> an idea. It doesn't look like an easy problem to me, but I haven't tried.
>
> And then, the loudness curve, the pain curve and the damage curve are three
> different things. I don't even know whether the latter two have been
> computed. My only real experience with the loudness curve(s) is from writing
> Alexandre T Porres' externals (for what he presented in Weimar). I haven't
> studied the topic much more than that.
>

Maybe the equal loudness curves aren't as important as the peaks in the
loudspeaker transfer function.  Gotta add that to the analysis, too, but
you'll never know what those are like unless you actually have them and
measure it.

I think the math makes sense: if a sequence of samples has only -1,+1 as
values, then the intensity must be maximized--only the frequency spectrum
has to be known.  We have by isometric property of the Fourier tranform that
the total energy in the frequency domain matches the energy in the time
domain.  So, it's only a matter of distribution.

So, if we made a simple alternating sequence +1,-1,... then only the Nyquist
frequency has any energy, but because most speakers (and ears) will weakly
respond at this frequency, it's not very loud.

Same goes for a repeating sequence, +1,+1,... or -1,-1,... for which no
response is expected.

The next thing to notice is that you can't produce a single frequency with
some signal that is only distributed as -1 or +1 on each sample.  So, it's
no good just finding the peak of the loudspeaker + loudness curves either,
we need big bands of frequencies that respond loudly.

Chuck
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.puredata.info/pipermail/pd-list/attachments/20110824/30ca47ab/attachment.htm>