# differences heard between random high frequency sound and sinusoids

```Dear Gilles,

At high frequencies, it is "often said" that we do not perceive differences
between random and deterministic components.

No this statement is erroneous. We definitely hear great differences. They
depend on the ?composition? of the contributing sinusoids. But also on the
length of the period of listening.

And in such compositions both the choices of frequencies and phases have
strong influence.

For example:

Please calculate with high resolution the following three compositions,
using five sinusoids:

1.	10,000 / 10,002 / 10,004 / 10,006 / 10,008 Hz. All sine
contributions.

In that case you will hear the high tone that corresponds with 10,004 Hz but
with a strong beat of 2 Hz.

2.	10,000 / 10,004 / 10,008  Hz. All three sine contributions.
10,002 / 10,006 Hz.  Both cosine contributions. So a 90 degree phase shift.

In that case you will hear the high tone that corresponds again with 10,004
Hz but now with a strong 4 Hz beat.

3.	10,000 / 10,002.0333 / 10,004 / 10,006.0333 / 10,008 Hz. All sine
contributions.

In that case you will hear the high tone of 10,004 Hz again, but within a
period of 30 seconds and starting with a 2 Hz beat after 7.5 seconds the
beat will gradually change into a 4 Hz beat. After 15 seconds the beat is
back again at 2 Hz. At 22.5 seconds again at 4 Hz and after 30 seconds the
composition ends with a 2 Hz beat in the 10,004 Hz tone.

If you change the sine contributions of 10,002.0333 and 10,006.0333 Hz into
cosine the composition starts with a beat of 4 Hz, 2 Hz at 7.5 sec, 4 Hz at
15 sec, 2 Hz at 22.5 sec and finally 4 Hz at 30 sec.

For noise filtered by a narrow band-pass around 10 kHz it is known that we
will hear just a 10 kHz tone. Nothing more.

For example, do we perceive a difference between a few sinusoids around
10kHz and a band-pass filtered noise around the same frequency?

The answer is clear:  Although, according to existing perception theory, the
different frequency contributions in the composition are entirely unresolved
we can hear differences related to different phase and frequency settings.

Anybody have some references or links for this subject ?

In this context I also want to repeat August Seebeck?s statement that he
published in the year 1844:

?How else can the question as to what makes out a tone be decided but by the
ear??

It was part of his answer to the erroneous hypotheses of Ohm about pitch
perception in the famous Ohm-Seebeck dispute.

And I want to add the following to it:

The above described sound experiments with indisputable results are entirely
based on the hearing theory I have described together with J. A. de Ru in
the booklet:

Applying Physics Makes Auditory Sense

Based on the concept in this booklet that our hearing sense is
differentiating and squaring the incoming sound pressure stimulus, this
mechanism evokes in front of the basilar membrane the sound energy frequency
spectrum.

In that case Fourier series calculations show exactly the frequency spectrum
including the 2, 4, 6 and 8 Hz difference frequency contributions. Of which
the 2 and 4 Hz frequencies are responsible for the beat phenomena.

Kind regards

Willem C. Heerens

On Thu, 19 Jul 2012 19:08:30 +0300, Gilles Degottex
<gilles.degottex@xxxxxxxx> wrote:

>Hi all,
>
>At high frequencies, it is "often said" that we do not perceive
>differences between random and deterministic components.
>For example, do we perceive a difference between a few sinusoids
>around 10kHz and a band-pass filtered noise around the same frequency
>?
>Anybody have some references or links for this subject ?
>
>Bests,
>Gilles
>--
>ICS - FORTH
>Vasilika Vouton, P.O. Box 1385
>GR 71110 Heraklion, Crete, Greece
>Mobile: +30 6942 207403
>Work:   +30 2810 391580

```