Hi Ric The article is a bit longer then the one side in the link you have below of course... but this page is easy enough to explain I suppose. Basically he starts off by saying that two strings can either vibrate in phase or out of phase with each other. In the latter, which he refers to as the antisymmetric mode, the two strings vibrations will have a tendancy to cancel each other out... which causes the support (bridge in the case of the piano) to behave as if it was very stiff... unwilling to vibrate easily. This otherwise known as a high imedance condition and results in a long sustain.. He notes that he is looking at the Vertical vibration of the string(s) only... for simplicity. The rest of the page is pretty much experimental data that back up this opening statement. The measurement you take issue below with... at 12 seconds after the initial sound, is of course from a long string with a sustain time long enough to demonstrate the principle. The amount of decay is going to be relative to the length of the string... so what it says about the first three seconds needs to be seen in terms of what percentage of the ring time the string has you want to know about. In the example string, three seconds is perhaps within the time frame that one sees the initial effect of the coupling take place. Figures 3 and 4 show the comparitive decay rate for vertical vibration modes between one string vibrating alone and two strings vibrating together. The coupled string shows an initial peak followed by a steep drop and rise in amplitude (I think in another place in the 5 lectures it is claimed this is because of the antisymetric mode kicking in.. somebody may correct me if I am wrong here.). The uncoupled string does not show this. The decay afterwards is at a higher amplitude for a longer period of time for the coupled string then the non coupled string. Which is to be expected since the coupled string as stated initially forces the support to tend towards being stiffer... hence increasing acceptance impedance (resistance). Figures 5 and 6 show two strings vibrating (again only the vertical mode is being looked at here) The 12 second bit is just to emphasize the point. When the mute is inserted the antisymetric coupling is stopped and one observes a quick 20 db increase in sound and vibration followed by a much quicker decay rate then in figure 5 where no mute is inserted at 12 seconds. This is just to more or less prove the point that coupling strings increases the decay time. In the quote you take below, there is some said on this subject by another author in the 5 lectures unless I am mistaken. I will see if I can hunt it down. More interesting tho is the questions that follow this quote and the subsequent page which provides in some part an answer to these. It took my unschooled mind several readings, lots of pondering, and a good deal of discussion with many other techs and piano physics friends to begin to digest and understand. So if you are at that same point... its just to keep on keeping on. Finally, Ed Sutton suggests Jim Ellis' article from early 80s on the subject matter... which I alluded to in my last. By all means read this... it is very easy to get the basic idea of coupled motion in his pendulum based illustrations and examples. Cheers RicB To understand this article I would to hear from technicians who do understand it. http://www.speech.kth.se/music/5_lectures/weinreic/strings.html "It is interesting to note parenthetically the rather complicated beat structure in Figs. 5 and 6, which is not precisely the same for the vibration and the sound. Presumably, the discrepancy comes from the horizontal modes, which contribute to the sound but not to the vertical motion." One glaring issue with the graphs in above, the data he presents comes 10 seconds after the note sounds. If a mention of coupled motion in the above article could you point me to it? What does it say about the first 3 seconds of sound? My first impression of the articles was it was an inquiry and suggestion about how someone might think about how to muddle about trying to synthesize a piano sound for electronic keyboards. ---rmoody
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