[CAUT] coupled motion and other myths

[Richard Brekne]

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