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From:  Sally Collyer <scol8413@m...>
Date:  Thu Nov 8, 2001  5:47 am
Subject:  Re: [vocalist] Your opinions - techie note on vibrato and spectral analysis


><< Is it possible in naturally occurring sounds for the
> overtones to varytheir frequency but not the fundamental? >>
>
> i guess so. i tried to get that oscillation to stop and i couldn't do
>it but, i can increase it without oscillating (visibly) the fundamental.
>(this is using a spectral analysis program.)

Mike, fiddle with your program a little.

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.

There's research on vibrato vs wobble vs tremolo, but it's been hampered by
the challenge of finding two 'expert listeners' who'll agree on what
they're hearing.

Cheers

Sally




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