# [PD] making puredata headphone-safe

Mathieu Bouchard matju at artengine.ca
Wed Aug 24 20:52:11 CEST 2011

```On Tue, 23 Aug 2011, Jonathan Wilkes wrote:

> Hm... I'm not sure I understand the danger.
>
> Isn't this:
> [noise~]
> |
> [*~ 999999]
> |
> [dac~]
>
> an implicit version of:
> [noise~]
> |
> [*~ 999999]
> |
> [clip~ -1 1]
> |
> [dac~]
>
> ?

Yes. Thus it makes square waves. Their power is :

(integral of (±1)² on [a;b]) / abs(a-b)

which equals 1.

Sine waves, instead, have this power :

(integral of (sin t)² on [a;b]) / abs(a-b)

which is ½ on average.

There are further differences due to which frequencies are involved. Power
in freqs around 1 kHz is more hearable, and power in freqs above that
might be less hearable but still more painful, etc. But I don't know data

[noise~] and high-pitched [osc~] have more hearable power than low-pitched
[osc~]. Also, heavily-clipped signals have higher-pitched power, which
usually means more hearable power.

a [osc~ 100], when very clipped, will have power at 100 Hz, 300 Hz (nine
times less), 500 Hz (twenty times less than 100 Hz), 700 Hz (49 times less
than 100 Hz), etc., following the same pattern.

combinations of several [osc~] with one clipper will have many more
harmonics than that.

you may think of [noise~] is somehow similar to an average of a silly
number of [osc~] together, which cover the whole spectrum. any clipping of
them will also cover the whole spectrum, but differently.

I didn't read those articles, but they are on those topics :
loudness : http://en.wikipedia.org/wiki/A-weighting
clipping : http://en.wikipedia.org/wiki/Distortion#Harmonic_distortion

_______________________________________________________________________
| Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC
```