Inharmonicity

[Richard Moody]

Hi Jim
	I  have always heard the "zinging" high sound in tuning forks, and in the
beginning was amazed at the tone when put to the bridge.  Just when you
thought I was anti machine ; )  I must confess I don't use a tuning fork
for pitch reference any more. I do carry one in case my old Korg analog
needle type decides to give up the ghost. or I accidently left it on and
drained the batteries, which btw has NEVER happened.  I can't believe
that. Well I left it on overnite in the shop, but it didn't drain the
batteries. But with low batteries, you better check it with a tuning fork.


Regarding the temp strip experiment. I have read it twice and did it in my
minds eye.  Is that like virtual?  I did hold a rubber band in front of
the monitor and snap it to see if I could see the partials.  I did see
upon "restoring" a snake like movement besides the vibrating segment.  I
did not see the seperate segments.  I thought a rubber band would vibrate
longer than it did. I should hold it up to a florescent light. Yes when
doing that I can see three segments briefly.  I think the dying out of
upper partials first causes an  illusion of a "standing wave" moving
across the string length.  Hmm I better try this with a piano wire just to
stay in the same venue. 
	Also what I would like to try to see if piano wire does the same as
rubber bands is the effect of loudness on tension. On first observation
loudness in a rubber band does not seem directly related to amplitute of
vibration.  At lower tensions the amplitude is  higher, but it does not
necessarly sound louder.  There is a point in stretching where it sounds
louder, then less so.  Of course this is plucking.
	Well anyhow demonstartions and experiments can go on and on, with endless
varations and variables.  As long as it seems to aid "understanding" I
will keep doing it. 

Richard

----------
> From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu>
> To: Richard Moody <remoody@easnet.net>
> Subject: Re: Inharmonicity
> Date: Thursday, August 20, 1998 12:34 PM
> 
> Hi Richard:
> 
> In your request for more experiments, I suppose you have already
listened
> to your tuning fork. If you hit the end of something very hard, you will
> hear the second partial which is over 2 octave higher than the
fundamental.
> 
> Did you try the experiment with the temperament strip yet? This shows
that
> there are 2 restoring forces to bring a string to the place of quiet. 
> Tension is the main restoring force, but stiffness controls more at the
> higher partials with tension remaining constant.
> 
> If you have a piano you can play with, you could change one string two 
> sizes higher at
> F3 as an example and tune it carefully to have the same octave
relationship
> which the original string had. This would cause the M3rd F3-A3 to beat
> slower because of the greater inharmonicity and stiffness of the larger
> diameter string. Its 5th partial would be much sharper than the 4th
partial
> which you have matched to the F4 2nd partial. If you used the C#3-F3 to
> C#3-F4 (3rd-10th test) to prove your octave F3-F4, this utilizes the 4th
> partial of F3. The F3-A3 M3rd utilizes the 5th partial of F3 which has
> more inharmonicity than its 4th partial, thereby slowing down the beat
rate
> of the F3-A3 M3rd. You don't need electronic machines to do this
experiment.
> Of course, it would be much easier to see the results.
> 
> Jim Coleman, Sr.
> 
> 
> On Thu, 20 Aug 1998, Richard Moody wrote:
> 
> > 
> > 
> > ----------
> > > From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu>
> > > To: Richard Moody <remoody@easnet.net>
> > > Subject: Re: Inharmonicity
> > > Date: Wednesday, August 19, 1998 12:41 AM
> > 
> > 
> > 
> > 
> > Stiffness has a greater restoring
> > > effect on short segments than on long segments. Is this
understandable?
> > 
> > Yes, explained very well in your 8-18 post. 
> > 
> > Would you like me to detail the
> > > experiments which you can do yourself?
> > 
> > Yes....
> > 
> > 
> > 
> >  McFerrin talks about stiffness not only at the at the ends of the
> > strings, but at the nodes also."effectively shorten the vibrating
halves
> > of the string."  Actually he doesn't use the word "node" in his
> > illustration showing the mid point G, and the two stiff sections EG
and FG
> > "effectively shorten the vibrating halves of the string...." But he is
> > pointing to what I would call the node.  
> > 
> > If the nodes are pivot points and do not take up space, I can  see how
the
> > partial segments with  a thicker wire in proportion to the fundamnetal
> > segment, by the laws vibrating piano wires might vibrate at a higher
freq.
> >   I don't have time to do it now, but it would interesting to use the
> > partial lengths and the tension and diameter, to see if the freq. come
> > out. This must have been done other wise they wouldn't need the
> > complicated formula of Young and Shuck.   
> > 
> > It appears I mis-read both Reblitz and McFerrin. They do not on second
and
> > third and fourth reading state that the string diameter causes the
> > shortened vibrating segments of piano wire. Rather they say, in
McFerrin's
> > words, "this deviation is inharmonicity and its cause is stiffness of
the
> > wire. "  Reblitz comments,  the thicker the wire the stiffer it is"
the 2"
> > portionis thicker in proportion to its length; it is also stiffer".  
> >   
> > I don't know where I got the idea that a segment of vibrating wire is
> > shortened by a distance proportional or equal to its diamenter.
> > 
> > Thanks for your time in explaining these concepts. 
> > 
> > Richard Moody    
> > 
> > 
> > 	
> > > 
> > > Hi Richard:
> > > ...............  .......
> > (McFerrin) Along with all the formulas in his book, he is
> > > missing the point I am making that the node does not take up space,
it
> > > is merely a pivot point. The pivot point has nothing to do with
> > stiffness.
> > .......
> > > It is the stiffness which is the cause of inharmonicity. 
> > > You can do the experiment yourself. Would you like me to detail the
> > > experiments which you can do yourself?
> > > 
> > > Jim Coleman, Sr.
> >