Overpull

[Robert Scott]

When we speak of calculating overpull using 25% or 30% or whatever, it
is important to consider what the 25% or 30% applies to.  Nearby notes
have a larger effect than notes that are slightly farther away.
Therefore the correct overpull depends on how much pitch change there
will be in the notes we are going to tune after the current note.
Ideally, we would like to look ahead and learn how flat are the notes
we have not tuned yet, because they will affect the settling of the
current note.  But that is not practical.  Instead we use the recent
history of flatness as a predictor of how flat the upcoming notes will
be.  Here is where the various tuning devices use different methods.

RCT, as far as I know, uses a moving "boxcar" average.  That is, the
history of the last N notes is averaged to arrive at the estimate of
how flat the piano is in the region of the current note.  As you move
up the scale, the contribution from the most distant note drops out
of the average as a new note is added in.  But all notes in the
average participate to the same extent.  This gives equal weighting
to the most recent note and the most distant note in the average.

TuneLab, on the other hand, uses a declining weight average.  The
most recent N notes are combined in a weighted average.  The
weighting given to each note is the most for the most recent note
and it declines linearly to zero for the most distant note.  In
this way the notes participate in the average in proportion to
how recent they are.  The most recent notes have the greatest
effect.  This is done to develop an average that responds
more quickly to changes in flatness as you move up the scale.

Both TuneLab and RCT allow adjustment of the number of notes
that are used to form the average.  Then the overpull percentage
is applied to this average to calculate the overpull amount in cents.

Perhaps Dave would like to enlighten us on how the VT forms its
average in pitch raise mode?

And Bradley, you have been asking some very interesting questions
lately - about arcane aspects of inharmonicity and overpull.
One might suspect you are developing a tuning program of your own?

-Robert Scott
  Real-Time Specialties