[pianotech] Tuning the duplex sections

[Delwin D Fandrich]

Most of my work was with the front duplex. A piano was modified so I could easily vary the lengths of the duplex string segment. When the duplex string segment length was such that it vibrated as some specific harmonic of the fundamental--i.e., it became an aliquot part of the speaking length--the decay rate (as measured at the bridge) increased and the overall sustain time of the notes decreased. My only explanation was that by providing an inefficient termination to the speaking string and by coupling some significant amount of vibrating energy from the speaking string to the aliquot string segment more energy was being lost to the gray iron frame (or plate). It is the nature of gray iron--with its high damping factor--to readily absorb and dissipate vibrating energy and it seemed to be doing this quite effectively.

For these things to work as their proponents claim the string deflection angle has to be relatively shallow. There does not seem to be any standard in place but to work as claimed the deflection angle has to be something less than about 12˚ to 15˚. I'm not sure if there is an "optimum" deflection angle; if there is it is going to vary somewhat with the frequency of the fundamental and with the length of the duplex string segment. In general, the deflection angle needs to be low enough to allow energy to easily bleed across the termination point yet high enough to terminate the speaking length and provide some minimum amount of rendering friction as the string is tuned. (Certain models of Steinway verticals have had so little rendering friction across the V-bar as to make stable tuning virtually impossible. I remember one piano from the 1970s that I could force out of tune using just finger force against the tuning pin.) 

I haven't looked at these things lately but when I took an informal survey a few years back of the so-called "aliquot" systems some newfound devotees had put in place I found that many of the string deflection angles used were sufficiently higher than 15˚ to ensure that the speaking lengths were efficiently terminated and there would be no appreciable energy bleed across the V-bars. That is, even if the duplex string length was tuned to an aliquot part of the speaking length there would be no appreciable vibrating energy transfer across the V-bar. This, I suppose, should be the best of both worlds; an efficient string termination system--i.e., one that does not have the accompanying string noises and loss of sustain of the true tuned duplex system --that the marketing department can still make all kinds of wild--albeit misleading--claims about and virtually nobody, certainly not the beleaguered customer, will be the wiser. 

I have personally done very little work with tuned backscale systems. I have, however, discussed them with many advocates and have read whatever literature I can find; yet I remain unconvinced. I have also attended various presentations put on by those who have claimed all sorts of nearly miraculous results yet when the string segments are tuned to spec the acoustical differences have been--to me, at least--minimal if, indeed, there were any at all. It is important, even in the treble, that the backscale not be so short as to restrict the mobility of the bridge(s). I have found some systems that are at least borderline on this. Increasing the backscale length on these designs results in noticeable improvements but I don't know if there is some "optimum" length we should be settling on. As of now I'm not convinced that tuning the backscale to some aliquot part of the speaking length will make any difference. I remain willing to be convinced but I'd like the results to be measurable--or at least audible--and not just suppositious.

ddf 


Delwin D Fandrich
Piano Design & Fabrication

Centralia, Washington 98531 USA
del at fandrichpiano.com
ddfandrich at gmail.com
Phone  360.736.7563


-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf Of David Love
Sent: Wednesday, March 09, 2011 11:22 PM
To: pianotech at ptg.org
Subject: Re: [pianotech] Tuning the duplex sections

Hopefully Del Fandrich will comment on this as I believe he is either aware of or has himself conducted tests on the effects of the tuned duplex on the tuning pin side in terms of its contribution to energy loss from the speaking length of the string.  According to a discussion we had the effective loss of energy from the speaking length is quite pronounced.  Ron Overs may also have done some research in this area.

Whether the duplex scale contributes audibly on the other end (back side of the bridge) I can't say for sure.  I can say that braiding the untuned backscale in the high tenor does seem to impact the tone (or at least the effective shut off) whether the rear duplex is tuned or not.  But it is interesting that while the idea of the duplex scale has been widely copied, the way in which it manifests itself varies considerably when you measure the relative speaking lengths of duplex scales on different pianos.  For example, Steinway's are quite short relative to the actual speaking length.
Yamaha, on the other hand, are relatively long.  I haven't really carefully examined to what interval they are actually intended to be tuned.  What difference that makes in actual practice, I don't know, but it does appear that some copycat manufacturers weren't convinced of the effectiveness of those original relationships enough to modify the approach FWIW.

David Love
www.davidlovepianos.com


-----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