Deepest apologies to both Christines! I found the original post
which was from Sally Collyer, should have checked before posting :-(
Sally would like to add this with your permission.
Cheers
Tracey
http://www.vocalist.org.uk
Message: 8
Date: Thu, 08 Nov 2001 16:47:45 +1100
From: Sally Collyer <scol8413@m...>
Subject: Re: Your opinions - techie note on vibrato and spectral
analysis
>>In the singing voice, the overtones are harmonics; that gives the
game away, because it means their frequencies are integer (whole-
number) multiples of the fundamental frequency (fo). Fo rises,
harmonics rise; Fo falls, harmonics fall.
Extent of oscillation in singing is expressed as a percentage or in
semitones (1ST~= 5.9%). Take the A below Middle C (A3 = 220Hz).
Fo=220, 1st harmonic=440(ie 2x), 2nd harmonic=660(ie 3x) etc. If we
take the example of modulation of 5% (ie 2.5% above and 2.5% below
the Fo), then each vibrato cycle starts at Fo=220, then Fo rises to
225.5 (220+2.5%), then turns downward to 220, then continues downward
to 214.5 (220-2.5%), then rises back to 220 - total range, 11Hz.
Meanwhile, the 4th harmonic is also modulating at 5%: 1100Hz
(5x220Hz), up to 1127.5Hz, back to 1100Hz, on down to 1072.5 (1100-
2.5%), and back to 1100 - total range 55Hz. The 9th harmonic at
2200Hz (220x10) is going 2200Hz, 2255, 2200, 2145, 2200 -
total range, 110Hz (but still 5%).
If the spectral analysis program is set to linear, as most tend to
be, rather than logarithmic (remember that the musical scale is
logarithmic), then the oscillation in the Fo is very hard to see: on
a y-axis scale set to 1-4000Hz, to include the singer's formant
region, you'd be looking for a movement of just 11Hz. If your
harmonics were oscillating, so was your Fo - to get a rough idea of
the vibrato extent, choose any harmonic, subtract the frequency at
the bottom of the cycle from that at the top (your program
should show this information to you when you point your mouse at the
spots), divide it by the average of the two and multiply by 100 to
give a percentage; eg 2255-2145=110; (2255+2145)/2=2200;
110/2200x100=5%. Average the result over a number of consecutive
cycles to get a more reliable estimate.>>
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