Doug Rhodes asked about the question of partials and their
positions along a string.  Such a phenomenon doesn't have to be seen
(although it has been).  Let me put it this way, Doug: A large, heavy
string is able to vibrate at many different frequencies, all at
once.  The only way this can happen is if some of those partial
frequencies (and sub-partials) overlap.  It isn't hard for a string to
do that, actually.  But the errors come in due to the "imperfect" shear
characteristics of the wire, and the thicker the wire, the more space
the shear  requires.  An air column has almost perfect shear
characteristics.  That means, its nodes are "cut" at precisely the
right places to give you perfect partials, and they are zero length.
Therefore their spacing is perfect.  Not so with string.

    But not only do partials overlap during a steady state vibration,
but the real effect comes during the playing of the wire by a hammer.
It is the decay of a string that really defines the pleasing or
not-so-pleasing quality of a piano, in my opinion.  And it is the
continual moving about and changing partials on a string as it loses
energy that determines the piano's overall tone to discriminating
ears.  That is when they HAVE TO OVERLAP if they are going to exist at
all, and since you can hear them,  we do not require a mathematical
model.  Since they have to overlap, then their spacing is going to vary
by necessity, due to the physical length of each node and the
constantly changing makeup as the energy is expended.  As far as the
precisely arranged even order harmonics are concerned, that is a fact
of life that can be measured in db and cents inharmonicity.  It is not
an opinion.  Different scales have a different set of partials
predominating.  The Mason&Hamlin has very strong even order partials, in
my opinion.  And they are pretty clean as well.

   How many other people can hear this decay effect, I don't really
know.  But If you will concentrate and get into a string's real speaking
sound, try this test: Play A3, holding down the key as it decays.
Listen for the vowel tones it emanates as it diminishes.  It might sound
something like this; "AErOmnIIUuuuu.  (Hmm.  That's hard to describe
without pronunciation marks).  So let me just say that on different
pianos you will hear different combinations of vowel tones as the
string decays.  That means, the momentarily dominant partials are
traveling into others which are losing power at the same time.

    Now try another test.  Do the same thing, but this time, raise the
dampers.  Notice how the character changes.  The reason the bass section
is called the foundation is because it plays sympathetically with the
string just played.  The vowel tones now are different, but the
important thing is how they "end." For example, if the decay ends in a
higher vowel tone, i.e. a sound that one would make with a smile on his
face, that is more pleasing to the ear than a "lower" vowel tone, ie.
one that you might sound by pursing your lips.  You think about that,
and then go to your most unfavorite piano and experiment for awhile.
You might find that this has merit.

    All strings finish in a somewhat lower vowel tone.  So I am asking
you to understand something more sublime.  I am asking you to realize
that every time we compare things, we are speaking relatively.  And with
that in mind, listen and compare the differences.  Some pianos decay in
a vowel tone pronunciation that is higher than others.  It is like a
signature.  I have never heard it fail.  But then again, likes and
dislikes are personal preferences.

    As far as "evenly spaced harmonics" are concerned, that is a
physical necessity but a very short description.  Whether I say "evenly
spaced" or "more perfectly harmonic" is immaterial.  To the degree that
you have inharmonicity is the same degree that your harmonics are NOT
evenly distributed along the string.  The inharmonicity is measurable.
I don't think it was a stupid comment.  It is provable.  The "raised
eyebrow" comment is a little scornful-- for which I can see no purpose.
We are just chatting here as friends.  Sometimes we speak better than
other times.  And sometimes, what may seem ridiculous to us one week
begins to have merit the next.  I think the best policy for all
concerned is to give the other guy the benefit of the doubt, and if you
don't agree, say so directly and politely (like I am doing right now).
Either we try to be the consummate gentleman, or we are sometimes less,
right? {;-)

    Don't worry if this idea doesn't make any sense right off the bat.
Sometimes, the better way to get over a new concept is to ask a
challenging question.  And while you're still thinking about this ask
yourself, "Why does a tuner have to stretch octaves when tuning a
piano, but does not stretch octaves when tuning an organ? " In other
words, why do perfectly tuned treble strings sound flat?  Could it be
because of an effect recognized by the ear that is not recognized by
looking only at the fundamental pitch? Also ask yourself, "What affect
to both pitch and dissonance would the length of nodes on a wire have
as they subtract a greater and greater percentage from the total length
of the vibrating string, but are still counted as mass?" (Remember,
they cannot be counted in the total length because they do not
constitute part of the partial they are in, but they add to the total
mass).  So you can think about it.  I think you will eventually answer
your own question.

    Regarding the manufacture of bass strings, all manufacturers have
the original (or at least accepted equivalent) scale sticks for major
makes of pianos.  If you want a 5'8" M&H scale, you don't even have to
send them in, actually, although they still like to see them and may
request them just the same, especially if they haven't dealt with you
before, or don't have confidence that you know what you want.  They are
also able to tell if what was on the piano was not original, and was
changed at some time.  Then they may call you and ask about the plate
designation, and what you wish to do, if they know you.  You can also
specify an exact scaling.  Just ask them what information they need, or
what they go by.  I have done this with a Chickering and greatly
improved its tone, by the way.

Craig B.

craig_brougher@msn.com