[PD] Headphones question on pd list

[Charles Henry]

On Wed, Aug 24, 2011 at 5:40 PM, Jonathan Wilkes <jancsika at yahoo.com> wrote:
>
> Without knowing anything in advance about the speakers being used, is there a way to construct some kind of [aural-faxbomb~] that outputs in the -1 to 1 range which could be used generally to at least get in the ballpark of what you want the maximum level of perceived loudness to be when wearing headphones?

You should be able to pick a suitable frequency band.  A reasonable
expectation is that headphones can produce sounds between 200Hz and
20kHz.  Loudness seems to fall off pretty quickly above 10kHZ, so
there's no point in including much of the higher frequencies, if
avoidable.

> Maybe another way to ask: can you construct an example patch with output that is louder than [noise~]--[*~ max_float_value]--[clip~ -1 1]--[dac~]?

The spectrum distributes energy to frequencies that will not be
reproduced or perceived loudly (which should be the case for the
above, having a very flat spectrum).  If the sound gets focused into a
smaller band, which is more relevant for speakers/hearing, the
loudness will be greater.

I think one place to start looking is a non-bandlimited square wave
function.  It's known that this kind of function has odd-numbered
partials that fall off according to 1/n, or in other words, the power
spectral density falls off at -6dB/octave.

The only problem with this function is that again the sound could be
more focused into a narrower band.  One thing that comes to mind is
multiplying square waves together (since this keeps the values at
+1/-1), but that would only distribute more energy to higher
frequencies.  What about PWM?

I think we are designing the worst possible sound here.  "Sound check.
 Play the horrible noise, so we know nothing that comes after that can
sound as horrible."