Compression waves

[John Delacour]

At 9:32 PM -0800 11/19/01, Delwin D Fandrich wrote:

>Let's just say I worked with the concepts some while at Baldwin. The 
>scales I worked on then ended up without SyncroTone scaling. The 
>concepts are perfectly valid. Using Mr Conklin's techniques you are, 
>indeed, able to design bass strings that control the longitudinal 
>mode harmonics of the speaking length and cause them to fall on a 
>harmonic that is not dissident. However, to do so requires making 
>some rather wild note-to-note jumps in both core wire diameter and 
>wrap wire diameter that makes it impossible to maintain a smooth 
>tension, power and inharmonicity curves. The variations in 
>acoustical power and tone color were more noticeable and more 
>objectionable than were the odd longitudinal mode harmonics.
>
>In the side by side tests we did, nearly everybody preferred the 
>tone performance of the bass string scaling that did not use 
>SyncroTone scaling techniques but did maintain smooth tension, 
>power and inharmonicity sweeps.

In a word, then, my "unattainable goal"?  That was what my intuition 
predicted even before I interspersed a few preliminary tests whole I 
was making the double-covered string for a Blüthner grand this 
morning.  These tests give extremely surprising results.

I am taking as given that the compression wave is significant in the 
tone building of a piano string, though I am not at all convinced of 
this and Conklin's paper does not provide adequate data to enable me 
to verify his findings.  What the relative strength is of the sounds 
induced by the compression wave is the key point, since if they are 
so weak as to be virtually inaudible, then the whole book goes out of 
the window.

In his paper he states:

>In longitudinal modes of vibration, energy propagates lengthwise 
>along the string (as periodic compressions of the string material) 
>without sidewise (transverse) motion of the string. Longitudinal and 
>transverse vibrations of a piano string can occur simultaneously. 
>However, the lowest-frequency longitudinal mode of a piano string is 
>always more than ten times the frequency of the lowest-frequency 
>transverse mode.

My tests this morning suggest that this is miles from the facts and 
that it would be a meaningless comparison even if it were close. 
Bear in mind that this extract is in the context of his treatment of 
covered strings.

The strings I used for the test all consisted of a 1.150 mm core to 
be covered with two covers in a ratio of approximately 30:70.  The 
total length between chuck and hook is about 1700 mm and the length 
of the cover round about 1300 mm.  The machine tension (which is 
irrelevant) is about 80 lbf.  The compression wave was produced by 
pulling along the bare steel a piece of doeskin covered in powdered 
resin.

The frequency of the wave before the spinning on of the first cover 
was in the whistle range and is not in consideration here.  I now 
spun on a 0.65 cover and tested the lowest frequency of the wave. 
This was roughly 400 c/s.  So far I had no surprises, accustomed as I 
am to see pitch fall as mass is added.  Under this misapprehension, 
imagine my astonishment when after spinning on a 1.40 top cover, the 
frequency of the compression wave was practically the same as before. 
The only apparent difference in practice was the obtaining of the 
fundamental frequency since the wave was all to ready to break into 
multiple partials like the beginner trying to get a low note on the 
flute.

I tested only six strings and found that the diameter of the 
undercover (owing to its mass or to the frequency of the coils ??) 
caused a change in the frequency of the wave but that the 
overspinning of the top cover caused no change.

Now this raises at least a dozen interesting questions which at the 
moment I'm in no position to answer and it would probably take a 
solid week to gather the necessary data.  Here are some of the 
questions:-

1.  What variables determine the frequency of the compression
     wave in a wire?
2.  Will the use of different covering wire of the same diameter
     have any effect on the frequency of the wave?
3.  Does the tightness of the wire affect the tendency of the wave
     to divide into partials?
4.  Does whipping or the closeness of the covering to the bridges
     in any way affect the compression wave?
5.  What interaction is there between harmonics of the transverse
     wave and of the compression wave?
6.  Are any audible combination tones produced by dissonance between
     transverse harmonics and hramonics of the compression wave?
7.  WIll music wire from different makers give different frequencies?

etc. etc.


You say that Harold Conklin's concepts are "perfectly valid" and yet 
as a practical man and a musical man, you chose not to regard them 
and found more pleasing results in Baldwins' very factory from scales 
that did not take them into account.

HC writes:-

>It has long been known that the strings of pianos and other musical 
>instruments can have longitudinal modes of vibration (Rayleigh 1877, 
>Knoblaugh 1944, Leipp 1969).

All good recent stuff!  Let's get reading.

>My patent simply teaches what the designer should do about it in 
>order to make the best sounding instrument.

Off to the Patent Office to see if they've webbed it yet.

JD