Unison coupling

[Roger Jolly]

Hi Ron,
           What I think is happening, each partial takes time to develop,
and is added to the fundamental to for a progressively more complex wave
form. The negative inharmonicity of the partials aids in lowering the pitch.
The inharmonicty increases with a more powerful blow, and is there for mor
noticable with a firm blow.
I'm convincinced that many factors conspire, damping or impedence of the
board, the wire, the hardness of the hammer, the velocity, the regulation,
and so the list goes on.
Just some half baked musings.
Roger




At 09:46 AM 22/01/00 -0600, you wrote:
>>> >>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
> 
Roger Jolly
Saskatoon, Canada.
306-665-0213
Fax 652-0505