[pianotech] Tuning the duplex sections

[George F Emerson]

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