# Re: Pitch evoked by spectral regularity (inharmonic components) (beauchamp james w )

```Subject: Re: Pitch evoked by spectral regularity (inharmonic components)
From:    beauchamp james w  <j-beauch(at)UX1.CSO.UIUC.EDU>
Date:    Wed, 19 Feb 2003 10:53:25 -0600

Chen-Gia,

Have you checked the possibility that f might be heard as the fundamental
of approximate harmonics e, e+d, e+2d, ... ? I.e., that f is the virtual
pitch frequency?

There is a demo similar to this on the ASA/Phillips Auditory Demonstration
CD -- Demonstration 21, "Shift of Virtual Pitch", which uses three
frequencies, 800+d, 1000+d, 1200+d. The virtual pitch frequency heard
is approximately (1/3)*((800+d)/n + (1000+d)/(n+1) + (1200+d)/(n+2)),
where n = 4 or 5. Reference is:

Schouten et al, "Pitch of the residue", JASA 34, 1418-1424 (1962).

My question always is "what is the pitch of a square wave with a missing
fundamental?".

Jim Beauchamp
j-beauch(at)uiuc.edu

You wrote (in part):
>In my experiment, all complex tones contain five components with
>frequencies {e, e+d, e+2d, e+3d, e+4d}. Although these spectral components
>are generally inharm onic, some pitches can be heard. As expected, one
>pitch is the frequency differe nce between the adjacent components; d. It
>may be evoked by DPOAEs.
>
>Strangely enough, there is another pitch f.
>
>For instance, a complex tone consisting of frequencies {1344, 1344+500,
>1344+100 0, 1344+1500, 1344+2000} evokes a pitch f = 336 Hz. Similarly, I
>found
>
>{1680, 1680+500, 1680+1000, 1680+1500, 1680+2000} , f = 420 Hz
>{2016, 2016+500, 2016+1000, 2016+1500, 2016+2000} , f = 504 Hz
>{2285, 2285+500, 2285+1000, 2285+1500, 2285+2000} , f = 571.2 Hz
>
>These four tones can be heard in the file
>http://server37.hypermart.net/berlin- music/ex/a_500.wav. In this file I
>demonstrate the pitch sensation f by pitch matching.
```

This message came from the mail archive
http://www.auditory.org/postings/2003/
maintained by:
DAn Ellis <dpwe@ee.columbia.edu>
Electrical Engineering Dept., Columbia University