<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt"><div><span>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?</span></div><br>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~]?<br><br><span></span><div><span>-Jonathan<br></span></div><div><br><blockquote style="border-left: 2px solid rgb(16, 16, 255); margin-left: 5px; padding-left: 5px;"><div style="font-family: times new roman, new york, times, serif; font-size: 12pt;"><div style="font-family: times new roman, new york, times, serif; font-size: 12pt;"><font face="Arial"
size="2"><hr size="1"><b><span style="font-weight:bold;">From:</span></b> Charles Henry <czhenry@gmail.com><br><b><span style="font-weight: bold;">To:</span></b> Mathieu Bouchard <matju@artengine.ca>; pd-list@iem.at<br><b><span style="font-weight: bold;">Sent:</span></b> Wednesday, August 24, 2011 4:09 PM<br><b><span style="font-weight: bold;">Subject:</span></b> Re: [PD] Headphones question on pd list<br></font><br><div id="yiv448368947"><br><br><div class="yiv448368947gmail_quote">On Wed, Aug 24, 2011 at 2:15 PM, Mathieu Bouchard <span dir="ltr"><<a rel="nofollow" ymailto="mailto:matju@artengine.ca" target="_blank" href="mailto:matju@artengine.ca">matju@artengine.ca</a>></span> wrote:<br><blockquote class="yiv448368947gmail_quote" style="margin:0pt 0pt 0pt 0.8ex;border-left:1px solid rgb(204, 204, 204);padding-left:1ex;">
On Wed, 24 Aug 2011, Jonathan Wilkes wrote (outside of pd-list):<br>
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<blockquote class="yiv448368947gmail_quote" style="margin:0pt 0pt 0pt 0.8ex;border-left:1px solid rgb(204, 204, 204);padding-left:1ex;">
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.<br>
</blockquote>
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a harsh-clipped [noise~]-[*~ n] is probably close to the highest loudness you can get, even for not-so-high values of n. <br></blockquote><blockquote class="yiv448368947gmail_quote" style="margin:0pt 0pt 0pt 0.8ex;border-left:1px solid rgb(204, 204, 204);padding-left:1ex;">
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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.<br>
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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.<br>
</blockquote><div><br>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.<br>
<br>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.<br>
<br>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.<br><br>Same goes for a repeating sequence, +1,+1,... or -1,-1,... for which no response is expected.<br>
<br>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.<br>
<br>Chuck<br></div></div>
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