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

```Chen-Gia,

I believe that your observations may be well explained by Terhardt's
virtual pitch theory, which is explained at
http://www.mmk.ei.tum.de/persons/ter.html (go to the Virtual Pitch
link).  Many related pitch references are also given on this site,
including definitions of several different pitch concepts.

Very much simplified, this theory looks for submultiples of the partial
frequencies that are grouped close to each other (i.e. that could be
considered as an approximate fundamental frequency F0 of the observed
partials).  This process results in a list of candidates for F0, and the
correct one is then chosen according to criteria given by Terhardt.  You
will have to go to some of his original references to get the details.

Harvey Holmes
H.Holmes@unsw.edu.au

__________________
You wrote:

Hello everyone,

My study of the timbre of the Chinese flute leads me to find a strange
effect of pitch sensation. I wonder if this effect can be explained by any
model of pitch extraction.
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 inharmonic, some pitches can be heard. As expected, one pitch
is the frequency difference 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+1000, 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 kind of pitch sensation appears to be a function of the frequency of
the lowest components e.
I get an empirical equation f = e*0.25 for 300 Hz < d < 1000 Hz and certain
range of e.
I also synthesized files for d = 700 Hz and d = 300 Hz. The empirical
equation seems to fail for d = 300 Hz (the last two tones).
http://server37.hypermart.net/berlin-music/ex/a_700.wav
http://server37.hypermart.net/berlin-music/ex/a_300.wav

I cannot explain this unexpected pitch sensation and the empirical
equation. There are some papers dealing with the effect of grouping by
spectral regularity, but I have not found studies on the pitch evoked by
spectral regularity. It would be wonderful to have some literature to refer
to this strange effect of pitch sensation, or some other ideas. Many thanks
for any help!

All best,

Chen-Gia Tsai
gia@snafu.de
PhD Student (Musicology)
```