Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!wuarchive!mit-eddie!uw-beaver!ubc-cs!fs1!fs1.ee.ubc.ca!jthornto
From: jthornto@fs1.ee.ubc.ca (THORNTON JOHAN A)
Newsgroups: comp.music
Subject: Re: Frequency shifting
Message-ID: <1337@fs1.ee.ubc.ca>
Date: 25 Jul 90 07:13:06 GMT
References: <3956@rodan.acs.syr.edu> <110260001@hpcvlx.cv.hp.com>
Sender: root@fs1.ee.ubc.ca
Reply-To: jthornto@fs1.ee.ubc.ca (THORNTON JOHAN A)
Organization: Dept. of Electrical Engineering University of B.C.
Lines: 72

In article <110260001@hpcvlx.cv.hp.com> bw@hpcvlx.cv.hp.com (Bill Wilhelmi) writes:
>/ hpcvlx:comp.music / davisonj@ecn.purdue.edu (John M Davison) /  7:53 am  Jul 20, 1990 /
> >Pitch shifting = frequency scaling
> >freq(new) = freq(old) * factor
> >
> >Frequency shifting:
> >freq(new) = freq(old) + factor
>
>Being on the fringe of this sort of stuff, I can't help but notice an
>oddity.  If factor = (2 * freq(old)), then
>
>   freq(new) = freq(old) + factor    [ Freq Shift ]
>	     = freq(old) + 2 * freq(old)
>             = freq(old) * 3         [ Pitch Shift ]
>
>
>For Pitch Shifting and Frequency Shifting to have any differentiation of
>meaning, severe constraints must be placed "factor".   The point is that
>according to the definition above, the value of "factor" doesn't seem
>to give enough information about whether the shift is a Pitch or Frequency
>shift.  The only difference seems to be that pitch shifts are large-scale
>frequency shifts.  But they still both modify the frequency.  Am I missing
>some big point?
>
>Bill Wilhelmi    

Well, yes.  Let's look at a signal that contains a 100Hz, a 200Hz and a 
300Hz sine.  The spectrum of this signal is:

A|
 |   |   |   | 
 |   |   |   |
 ---------------------
 0   1   2   3   4   5  (x 100Hz) 

If we do a pitch shift on this, say a factor of 1.5, we do
       f = f(old) * 1.5  

and get  frequencies of 150, 300 and 450 Hz.  This new signal will sound
like the old one but a perfect fifth higher.  The new spectrum is:

A|
 |     |     |     | 
 |     |     |     |
 ---------------------
 0   1   2   3   4   5

If we do a frequency shift on the original signal, say by 50Hz, we do

       f =  f(old) + 50

and get 150, 250 and 350 Hz.  Note that these no longer have the same
harmonic relationship.  The spectrum now looks like:

A|
 |     |   |   |
 |     |   |   |
 ---------------------
 0   1   2   3   4   5

A pitch change stretches the spectrum while a frequency shift slides it.
A frequency shift will generally change a  harmonic sound into an 
inharmonic sound.


 -------  _/__/   -----------------------------------------------------
        _|  ___|    E l e c t r i c a l      |  Johan Thornton, Esq.
       | | |_/     E n g i n E E r i n g     |-------------------------
       |/|  __|     U n i v e r s i t y      |  jthornto@fs1.ee.ubc.ca
       |-| |/__     o f   B r i t i s h      |-------------------------
       | |_____|      C o l u m b i a        |   This space for rent
 ----  |__|/_|   ------------------------------------------------------