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
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