two strings flatter than one,

[Richard Moody]

> 
> Richard,
> 
> Tune the middle strings of F3-A3 to approx 7 bps.  Then tune one outer
> string of A3 to the middle.  You will then have a 2-string unison.  If
you
> have a perfect unison, the beat rate for F3-A3 will be just a bit slower
> with the unison with two strings than just the middle string and F3. If
this difference is not perceptible, then tune the middle string of A4 to
the
perfect 2-string A3 unison.  Make F3-A4 beat exactly the same as F3-A3.
Exactly.  Then tune one outer string of A4 to make a perfect unison.  You
will notice a "big" difference in beat rates from just the middle string
alone.  The F3-A4 beat rate will now be slower.  To verify this, put your
mute back on the outer A4 string, allowing just the middle to sound.
Compare F3-A4 beat rates, then remove the mute, and listen to the 2-string
A4 with F3.  You should hear a pretty good difference in the beat rates
then.

>	>John Formsma



Upon trying this experiment, I could not hear an appreciable diff between
the beat rates, Closer to the truth is that I am not sure if I can hear a
difference or not. 
	  In the A4 -A3 octave, single strings, the tenth ended up beating a
little faster than the F4-A3 third.  With two strings (on A4) it seemed to
beat just as fast if not a little faster, even though it was suggested
that I would hear it slower. If two strings made it beat slower then it
should have come down toward the rate of the third. The rates of single
strings in the third vs  double strings were not noticeably different.  
	But this is one piano and one set of ears, and one set of notes.   It
would be interesting to see what a room full of technicians come up with
in a blind test.  If you are told to expect a slower beat in a tenth from
the third, chances are you will hear it.  If you are asked straight out if
the beat between the third and  tenth is...A, The same;  B, Faster;  C,
Slower;  D Can't tell; I would be surprised if a group technicians would
show even a statistical agreement execpt for answer D.  

Now what about listening to the other side? Suppose you tune a F--A third
in single strings.   If adding a second string causes the unison to go
flat, then if you added a second string to F but left  A single, 
shouldn't  the rate of the third now speed up. ? 

At any rate the, beat rate should return to normal when  two strings of F3
are  compared to the two strings of A3.  In that way this phenomenon
whether
it exists or not is taken care of aurally just as inharmonicity is.
---ric  

ps On second try an hour later I thought I heard a slower third, but it
turned out I had a bad unison.  I didn't bother setting the pin.  The
other thing to watch out for is if the single string itself has a slow
beat in it. 
 Listen to the single  string as carefully as to a two string unison.  I
am always surprised at how many single strings have a slow "roll" or
actual beat if I take the time to listen. This could cause two strings to
"go flat" ??