Let's Get Technical: Hysteresis

[Marshall Price]

     According to various dictionaries, this word is
pronounced "hista REE sis," and comes from the Greek
hysteros = later, behind.  The adjectival form is
"hysteretic" ("hista RET ic").  Don't confuse it with words
related to Greek hystera = uterus.

     From the "Concise Science Dictionary," Oxford U. Press:
                         +    +    +
hysteresis -- A phenomenon in which two physical quantities
are related in a manner that depends on whether one is
increasing or decreasing in relation to the other.
     The repeated measurement of stress against strain, with
the stress first increasing and then decreasing, will
produce for some specimens a graph that has the shape of a
closed loop.  This is known as a "hysteresis cycle."  The
most familiar hysteresis cycle, however, is produced by
plotting the magnetic flux density (B) within a
ferromagnetic material against the applied magnetic field
strength (H).

                            B ^
                              |    _  + + +   P
                                 +      +
                            Q |+      +
                             +       +
                            + |     +
                         R +       +              H
          -   -   -   -   *   O   *   -   -   -   >
                         +       + T
                        +     | +
                       +       +
                      +      +|
                    +      +
               S  + + +  "    |

     If the material is initially unmagnetized at O it will
reach saturation at P as H is increased.  As the field is
reduced and again increased the loop PQRSTP is formed (see
graph).  The area of this loop is proportional to the energy
loss ("hysteresis loss") occurring during the cycle.  The
value of B equal to OQ is called the "remanance" (or
retentivity) and is the magnetic flux density remaining in
the material after the saturating field has been reduced to
zero.  This is a measure of the tendency of the magnetic
domain patterns (see "magnetism") to remain distorted even
after the distorting field has been removed.  The
value of H equal to OR is called the "coercive force" (or
coercivity) and is the field strength required to reduce the
remaining flux density to zero.  It is a measure of the
difficulty of restoring the symmetry of the domain patterns.
                         +    +    +
     Note the generality of the first three lines here, and
how, in tuning pianos, we are directly manipulating our
tuning wrenches, but only indirectly controlling other
things.
     Imagine sitting at a table with a bullseye target on
it.  Put an aspirin on the table.  Then invert half a
walnut shell over it, and a lowball glass over that.
Finally, invert a colander over the lowball glass.  Your
mission (should you choose to accept it) is to center the
aspirin, the walnut shell, and the glass, on the bullseye.
And there you have it: tuning in a nutshell.
     The colander of course, is your tuning wrench; the
lowball glass is the tuning pin; the walnut shell is the
tension on the string; and the aspirin is the tension on
the tail end of the string.
     In one way, we have it easy, because in real life we
are only working in one dimension, not two; but then again,
we can only observe the "nutshell," (I'm assuming we know
what pitch we want!), and we do that by hearing beats,
which gets increasingly difficult as we get closer.
     But there's an important point here which many
beginners overlook, and I've known more than one otherwise
promising tyro who changed careers over such things.
     It's not good enough to get the walnut where you want
it.  You've got to center the tablet inside it.  In other
words, if you leave the tension on the tail end higher or
lower than the tension on the speaking length, you haven't
done the job right.
     How can you do that?  Well, there's only one way: by
going past the pitch over and over, a little bit less each
time.  Remember, you can't see the pill, but that's what
you're really "tuning."  It's time consuming and tedious,
and (unless -- like Ben McIlveen, who indirectly convinced
me of the necessity of this approach -- you're a concert
tuner) the rewards are usually far away, perhaps when some
one leaves the windows open overnight, or turns up the heat
on a cold winter day.
     So if you're just beginning to get pretty good at
tuning, and hope to reach a new plateau, don't waste your
time as I did, struggling for a very pretty tuning that
will fail on the first real "test blow," but take the time,
and put in the work, to do it right: the hysteretic way.

--
Marshall Price
Miami, FL
d021317c@dcfreenet.seflin.lib.fl.us