Cents vs. beats

[Robert Scott]

Regarding TuneLab's choice of beats vs. cents, Don Rose wrote:

>Cents are a *finer* division in the bass than beats and above
>A6 beats are a *finer* divsion than cents.

You are correct, Don.  And it may seem backwards that TuneLab
avoids the *finer* method at both extremes.  But here is the
reasoning.  Although beats are a finer measure than cents
the higher up the scale you go, you soon reach a point where
beats are just too sensitive, as the SAT demonstrates.  If
you use an SAT to tune C8, you know how hard it is to see any 
pattern at all until the note is almost perfectly tuned.  And even
if you do see a pattern, don't you lower your standards considerably
when judging if the lights are "stopped" at C8?  When tuning A4
you require the lights to be stopped a lot better for a lot
longer time.  Using a pattern speed proportional to the cents
error makes for a pattern that is a lot easier to see.  There
is still plenty of resolution if you use a high-resolution
phase display, which TuneLab does.  (Compare this to only
four lights for one complete cycle in the SAT).

So why not use cents throughout, including down into the bass?
Well, another factor comes into play here.  TuneLab measures the
phase about 8 times per second.  When measuring the phase of a 
lower frequency signal, the fewer cycles you have to
work with the less accurate the phase measurement is.  This
lack of phase accuracy shows up as jitter in the phase display.
I could have countered the jitter by sampling the phase less
often as the frequency goes down.  But that would result in
a phase display that was not as responsive to pitch changes
and that would be frustrating to the user.  Instead, I chose
to use a pattern speed that was proportional to beats below
440 Hz.  That way, what would have been a lot of jitter in the
cents display is much less jitter in the beats display.  Of 
course, to get the same cents accuracy from a beat display you
have to wait longer when measuring lower notes.  But isn't
that what aural tuning does?  You listen to low notes for
a much longer time than you listen to higher notes.  By using
beats in the bass, TuneLab merely copies this characteristic
of aural tuning.

Actually, the fact that TuneLab uses beats below 440 Hz 
doesn't really matter much.  As you tune notes below A4,
you begin switching to higher partials, so you never
get to tune much below 200 Hz anyway.

Robert Scott
author of TuneLab 97