source file: mills3.txt
Date: Mon, 2 Feb 1998 23:42:16 +0100

Subject: Defining pitch bend resolution

From: wcooper@socrates.berkeley.edu

Does anyone know of an authoritative definition of pitch bend
resolution?  I used to think it was obvious.  I used to think that if
a sound module had a pitch bend resolution of, say, 8 bits, that meant
that whenever it received a 14-bit pitch bend signal it used only the
leading 8 bits and ignored the remaining 6.  But then I did some
experimentation and discovered that this is far from the case.

     The experiment is straightforward and anybody can repeat it.  I
tested a couple of synths with similar results, but I'll describe here
only the results obtained with a lowly Roland Sound Canvas.  First I
created a little program (in Max) to make it easy to transmit one at a
time a series of 14-bit pitch bend signals increasing by increments of
one.  By repeatedly clicking the mouse I could send, say, the series
8192, 8193, 8194, . . . from the computer to the sound module.  Next I
set the Sound Canvas' pitch bend range to its maximum value of +/- 24
semitones.  Then I started a note playing in a sawtooth wave timbre,
chosen because it has lots of overtones.  By listening intently for
subtle overtone changes as I clicked away with the mouse, I could tell
when the shifts in pitch were taking place.  Why a minute change in
pitch should cause a discernable change in the overtone spectrum I
don't know, but it does.

     The pitch changes came frequently, about every 4 or 5 mouse
clicks.  To distinguish among that many different pitches, the Sound
Canvas must be extracting something over eleven bits of information
from the pitch bend numbers.  Not bad, I thought, for a unit that is
considered the MacDonald's hamburger of the synthesizer world.

     But wait.  The pitch changes occurred sometimes on an even
number, sometimes on an odd.  This was a surprise.  There is no way of
explaining it unless the sound module was somehow taking into account
even the very lowest-order bit of the pitch bend signal.  The usual
concept of pitch bend resolution, based on how many lower-order bits
are ignored, went out the window.  Even a Sound Canvas looks at all 14
bits!

     I repeated the experiment for other pitch bend ranges.  The
narrower the range, the more mouse clicks it took to get from one
pitch change to the next.  Pitch bend ranges that are powers of two
are special.  They produce uniformly spaced pitch changes.  For
example, for a range of +/- 16 semitones the pitch changes came
regularly at every 8th mouse click.  Here is a summary of how far
apart the pitch changes occurred in response to various range settings
that are powers of 2.  The theoretically implied number of high-order
bits needed is also given:

   ---------------------------------------------------
                    PB increments       Theoretical
    PB Range        between changes     bits required
   ===================================================
   +/-  1 semis    128                  7  bits
   +/-  2   "       64                  8   "
   +/-  4   "       32                  9   "
   +/-  8   "       16                 10   "
   +/- 16   "        8                 11   "