"Average Pitch" of an HT

[Billbrpt]

In a message dated 98-03-17 10:28:37 EST, you write:

<< Bill's seems to be coming from the direction of compensating for the pitch
 shift due to coupling of multiple strings. >>

No, sorry, the coupled motion effect is only part of it.  When you have an HT
such as a WT, VT, MT or MMT, there are a certain number of notes tuned sharp
of theoretical ET and a certain number tuned flat.  While the A is not exactly
at the half way point, it is close to it.  

Because of inharmonicity, A4 tuned exactly at 0.0 on its fundamental will read
a positive number when read on octave 5, usually between 1¢ and 2¢.  Setting
A3 at 0.0 and reading it on octave 5 throws it slightly flat of where it would
need to be at Standard Pitch in a theoretical ET.  It also will throw A4
slightly flat of Standard pitch but still within a reasonable tolerance.  The
coupled motion of strings effect will throw it still flatter but still within
that reasonable tolerance.

   At this slightly flat of Standard pitch (but within a reasonable tolerance
of it), the A now is in a position to be almost exactly at the mean point of
all notes which have a deviation to the sharp or flat side of theoretical ET.
Therefore, each note will be the closest to theoretical ET as it possibly can
be and therefore the temperament will be the most compatible that it can be
with other fixed pitch instruments tuned at A-440.

This has worked very well for me.  I can tune a Yamaha Diskclavier in a VT for
example and have the piano be perfectly compatible with the MIDI Orchestra
software.  It also works when a church wants the piano "tuned to the organ".
There has never been any problem with incompatibility.  It will also work in a
situation where there is an acoustic piano and synthesizers or other
electronic keyboards.

Bill Bremmer RPT
Madison, Wisconsin