Notes 85-86-87-88

[Robert Scott]

Jim Coleman Sr. wrote:

>The Accutuner has only a 25 Hz range on either side of the note you are
>tuning.  If you get the dots to rotate no less a quarter revolution, you
>are doing well.  You are within a half beat.  Most of us aural tuners do
>not tune any more accurately than that in the top few notes. When you
>consider that the tone of the last few notes only lasts from 1 to 2
>seconds, that's not bad.

  This is a problem that I had to deal with in the design of the TuneLab
program too.  The top octave has two problems.  First, the beat rate is
too high to "see" clearly in any phase display unless you are very
close.  (The SAT lights are a phase display.)  The other problem is false
beats.   One solution to the problem of a fast-moving phase display is to
synthesize a "slowed down" phase display.  This is what is done by the
TuneLab and by the CyberTuner in cents mode.  In order to do this the
device must be able to make consecutive phase readings and tie them
together in a meaningful way.  For example, if a VTD is reading the phase
of an input sound 20 times per second and gets phase readings (in degrees
where 360 degrees = 1 cycle) of:

  30  60 90 120 150 180 210 240 270 330 0 30, etc.

then it is easy to see that phase will go through about 1.7 complete
cycles every second.  (i.e. 1.7 beats per second).  But what
if the phase readings are:

 30 180  330  120  270  60  210  0, etc.

This could be interpreted as a phase advance of 150 degrees for each
sample.  Since we are assuming 20 samples per second, this would mean
that the note is sharp by 8.3 beats per second.  But it could also be
interpreted
as a phase retard of 210 degrees for each sample.  That would mean that
the note is flat by 11.7 beats per second.  This ambiguity would have to be
resolved before any VTD could synthesize a "slowed down" phase display.
One solution would be to sample the phase more often.  Do it 50 times
per second instead of 20.  But then you would run into another limitation.
The shorter time span that is allowed for making a phase measurement
the less precise that measurement will be.  I found in the TuneLab that
the practical limit seems to be 20 phase samples per second.

So this brings me to what I believe is a better solution.  Instead of trying
to measure phase in an octave 7 note that doesn't last very long and may
have false beats, just compute the complete frequency spectrum distribution
using what engineers call the Fast Fourier Transform.  In the TuneLab I
compute a Fast Fourier Transform about 5 times per second.  Each
time the frequency spectrum is computed, I display a graph of the signal
amplitude as a function of frequency.  This graph is in addition to the normal
phase display.  There is a zoomed-in mode where the frequency specturm
display can be made to display only the region within +/- 200 cents around
the desired pitch.  When the graph is in this mode, the tuning error is
observed as a peak in the graph which is not centered on the red line which
denotes the desired pitch.  Instead of stopping a moving display, you just
tune in order to push the peak of the graph over towards the red line.  I have
found that using this display in octave 7 is easier than trying to read a
phase display and I believe in practice it is just as accurate.  In fact, if
there
are serious false beats, the frequency spectrum display actually shows
several distinct peaks.  You can tune to the highest peak or you can center
the several peaks around the red line.  In any case, it is easier that trying
to read a phase display which is based on the assumption that the note
you are listening to is pure.


Bob Scott
Ann Arbor, Michigan

P.S. To try the TuneLab 97 software on Windows 95, download it
from  http://www.wwnet.com/~rscott