[pianotech] Tuning the duplex sections

[Don Mannino]

Nice post, George.

Another important factor which is, if I recall correctly, mentioned in the
old patents is the benefit to the tone and longevity of the string from
changing the wire movement at the capo from a bending action to a pivoting
action.  When the duplex length is short or the angle very steep, the wire
is effectively locked down against the capo.  When the angle is lower and
the length is longer, the wire can rock or pivot slightly on the capo,
reducing stress on the wire.

The envelope of the attack and sustain certainly is affected by the duplex
and it's tuning.  Whether the change to the envelope is better or worse is,
to a certain degree, a matter of taste.  This is why a lot of debate can
take place on this type of subject.

But I will weigh in your side that the duplex scale by the capo has a
positive benefit to tone, and to longevity of the wire.  The duplex lengths,
angle, and hardness of the capo surface can be balanced to give the tone
desired.

Don Mannino

-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of George F Emerson
Sent: Wednesday, March 09, 2011 10:58 PM
To: pianotech at ptg.org
Subject: Re: [pianotech] Tuning the duplex sections

In Steinway's patent, US000126848, he makes repeated reference to the
effects of the longitudinal mode partials, but what he describes in the
further text sounds less like longitudinal partials than transverse.  I
suspect that, at that time, they did not have an adequate understanding of
the effects of longitudinal mode partials, or how to calculate their 
frequencies.   It is correct the longitudinal mode is not affected by 
tension.

This patent also suggests that the problem area being address by this patent
is for notes above C5.  Ironically, it is at this point, or the note just
below it, B4, that the frequencies of the longitudinal mode partials exceed
the human ear's range of hearing.  Most resources give 20 KHz as the maximum
frequency that the human ear can detect.  It is commonly acknowledged that
there is a fair amount of variation in the top detectible frequencies among
human subjects, but that variation is usually on the low side of the 20 KHz
limit.  That being the case, how can it be that longitudinal partials are so
significant in that range of the piano's scale, where they are inaudible to
the human ear?  This is not to discount the phenomena of what is called a
whistling sound in the upper range of the piano, but rather to attribute it
to the transverse modes of vibration in the non-speaking segments of the
strings, not the longitudinal modes of these segments.  The longitudinal
mode is of more significance in the bass range of the piano, but that is
another subject.

Most "modern" thinking is that duplex scaling does more harm than good. 
There is a finite amount of energy delivered from the hammer to the speaking
length of the string.  If that energy is dissipated too quickly, being used
up in exciting the vibration of the duplex segments, it robs the speaking
length of the energy required for a desired longer sustain-time.  At risk of
raising the ire and ridicule of the disciples of this logic, I must
disagree.

Every piano technician has encountered, at one time or another, the
frustration of sympathetic  vibrations as much as 2 or 3 meters remote from
the piano, not to mention components of the piano itself causing an
obnoxious buzz from a sympathetic vibration.  Annoying as these sounds are,
they do not rob the soundboard of any energy.  The duplex string segments,
being well within 3-4 cm of the vibrating soundboard, are certain to readily
pick up a sympathetic vibration from the soundboard if its length is
consistent with a frequency being produced by the soundboard, assuming the
diameter and tension of the duplex segment to be the same as the speaking
length.  For this reason, my argument would be that the vibrations of the
duplex string segments do not rob the speaking lengths of energy required
for sustain, but they recapture energy already lost to the system by means 
of sympathetic vibrations, derived from the air vibrating around them.   For

this reason, I have to agree, in part, with the claims of the Steinway
patent that duplex scaling bolsters the harmonic structure of the speaking
length, and not only enriches the sound, but contributes to a greater
sustain, by producing a more efficient system of recapturing already spent
energy from the soundboard.  Those who would disagree with this would
question if I have object measures from testing to verify this.  The answer
is that I do not.  All I can offer is subjective observation that the tone
is noticeably weakened when duplex segments are muted out.

With regard to the secondary agraffe at the tuning pin end, these are more
remote from the soundboard, and I would question the effectiveness of making
these segments match the length of a speaking length partial.  Even so,
muting these segments has a negative impact on the brilliance of the tone of
their respective speaking lengths.

For the desired effect, it is, of course, critical that the duplex segments
match the frequencies of the harmonic partials of the speaking lengths.  It
is not good enough to rely on measurements of lengths.  One must tune the
duplex segment, moving the duplexer in or out to match the musical interval
defined by the mathematical relationship.  With a continuous duplexer, the
best that can be done is to tune the first and last duplex segments of each
continuous duplexer.  If the design of the duplexer is accurate, the
intervening notes should be in tune with their respective speaking lengths,
as well.

Frank Emerson