Unison coupling

[Ron Nossaman]

>> >>The frequency of vibrating piano strings is not stable, but
>tends to 
>> >>lower as the string continues to sound.
>I would like to see a reference to support this.   

* Don't need one, you can verify it for yourself. I seem to remember you
saying you had a SAT, is that right? If you do, try it out at your next
tuning. Note the pitch in the first half second or so of the attack, and
the drop in pitch as the note continues to sound. The pitch drop isn't at
the same rate through he duration of the sound, but is most rapid
immediately after attack, and continues at a diminishing rate until it
stabilizes, or is dropping too gradually for you to tell. I don't know if
the pitch drop is logarithmic, exponential, polynomial, or just faster at
the beginning, but it's certainly progressive. I haven't tried it in
different areas of the scale, so I don't know how the timing differs with
different string length and mass.



>Studies done in
>1943 as reprinted in _Piano Technician's Journal_ Jan. 1964 
>studied the "measurement of the frequencies of the partials and
>their amplitudes as functions of time."  They did not report a
>lowering of freq as the string continued to sound ( ie function of
>time.) 

* When I see articles like this, it is usually mentioned in the text that
the measurements are taken a couple of seconds into the sound envelope,
after everything has stabilized. Any mention of this in the article? Also,
they would be concerned with measured partial frequencies relative to the
measured fundamental at any given point, wouldn't they. The pitch drop most
likely just wasn't mentioned so it wouldn't confuse the intent of the
article.  


 
>An interesting observation that goes contrary to what some say
>today was that the method of striking the key did not influence the
>frequencies of the partials, "as it was found that variations in
>the strength of the blow produced negligible effects on the modal
>frequencies, the key was struck manually."  

* I don't have a clue one way or another. As an aural tuner, it hasn't come up.


>  If the frequency
>really does lower in time, a strobe light should tell beyond all
>doubt. 

* Or a SAT, RCT, Tunelab, Peterson, Conn, etc.



>What is the need for a mathematical formula to predict
>inharmonicity.? 
>     
>---ric
	
* Designing string scales. As a means to compare theoretical inharmonicity
of one string to another, or a whole scale, it provides a common standard
for comparison. It beats reading tea leaves or flipping coins. In the real
world, you're right that measured inharmonicity is suspect because the ETD
users report that it changes from measurement to measurement.

Ron N