# Re: harmonic vs. inharmonic sounds (coming full circle)

Readers might be interested to note that the appropriate reference for Al Bregman's take on the perception of the missing fundamental is Helmholtz (1875). If memory serves, you will find that on the first or second page of Chapter 1 (after the introduction), Helmholtz begins the discussion of pitch by saying that pitch corresponds to the repetition rate of the waveform. All of the spectral modelling of Helmholtz was to explain how you extract the repetition rate from the sound. He did not know that auditory fibres phase lock to membrane motion. So the question is not what we hear but how you extract it from the sound.

The tricky bit comes when you shift all the components up, say, 10 Hz. Then the true periodicity drops to 10 Hz, but you hear the pitch move up to about 101 Hz. The phenomenon is referred to as the pitch shift of the residue (Schouten, 1940; de Boer, 1956; Schouten, Ritsma and Cardozo, 1962, Patterson, 1973). The auditory system understands quasi-periodicity as well as periodicity.

`Regards Roy P`

`On Mar 16 2007, Al Bregman wrote:`

`Dear Kevin and list,`

```Here's my take on the "perception of the missing fundamental". I'm
going to frame it in terms of periodicity because it's easier to
explain that way.```

```Whenever a repetitive waveform is played (i.e. one whose partials are
all harmonics), we hear the pitch that is characteristic of that
repetition rate.  For a tone having the partials 200, 300, 400, 500,
600, 700, the same exact waveform repeats 100 times per second.  This
gives rise to the pitch, "100 Hz RR", i.e., the subjective pitch
associated with a 100-Hz repetition rate.  Note that a pure tone of
100 Hz also repeats 100 times per second, and therefore, like your
complex tone, it has the pitch of 100 Hz RR..  However, it has a
different timbre.  The repetition rate of the wave determines its
pitch but its harmonic structure influences its timbre.```

```Therefore, we shouldn't think of your complex tone as containing a
100-Hz pure tone.  It is just that they both have the same pitch.```

```I have framed the explanation in terms of repetition rate because it
was easy to do, but it might not be correct.  For example a "harmonic
sieve" or template, might derive pitch.  To be more general, we can
say that whatever method is used to compute pitch, the relation
between your complex tone and a 100-Hz tone is that they have the same
pitch, not that you hear the simpler tone as part of the more complex
one..```

`Cheers,`

```Al
-------------------------------------------------------------------
Albert S. Bregman, Emeritus Professor
Psychology Department, McGill University
1205 Docteur Penfield Avenue
Montreal, QC, Canada H3A 1B1.
Tel: (514) 484-2592, (514) 398-6103
Fax: (514) 484-2592
www.psych.mcgill.ca/labs/auditory/Home.html
-------------------------------------------------------------------```

On 3/15/07, Kevin Austin <kevin.austin@xxxxxxxxxxxx> wrote:
`On reconsideration, I would reframe the question something as:`

```When hearing the partials 200, 300, 400, 500, 600, 700, do you
perceive the fundamental to be 100 Hz? Do you hear a 100 Hz component?```

`Best`

`Kevin`

`--`