moment of inertia in keys

[Jon Page]

At 07:14 PM 10/12/98 -0400, you wrote:
>snip>that a piano is "hard to play".  If the static weights and the
>inertia are all measured, one might be able to either confirm the
>artist's complaint, or else show that he is full of hooey.
>
>Bob Scott

Static touchweight (TW  =  UW/DW) is what we can measure.
Dynamic TW is what the artist feels.

If we center on the BW the TW is determined by the friction for each given
key.

Specs for a S&S concert action are:

bass      tapering to   treble
50 DW	            46 DW
20 UW

BW = 35

Friction = (DW-UW)/2
bass has 15 F

It just so happens that the friction factor is also the distance from
BW to both UW  and  DW. (20+15=35      50-15=35)

By maintaining a BW of 35 across the keyboard and using these
factors we know that UW in the treble is 24. (46-35=11, 35-11=24)
Treble notes by nature have a lower friction factor.

So we can see that a higher friction moves the UW & DW apart.

There are two touchweight aspects to consider. Static and Dynamic.
Static being that which we can measure (UW, DW); Dynamic being
that which the pianist feels.

So if we target the BW and make that uniform, then slight discrepencies
in the UW & DW are negligable. These discrepencies will be the result of
the friction differences from note to note: 
A note with a BW of 35 with a friction of 17 will have an UW of 18.  This
could
pose a problem in repetition on occasions. 
Usually a BW of 38 is light enough for most since the friction averages around
16 bass and 11 treble and will accomodate humidity swings to play a part.

If you weigh off solely by DW, them the UW's will be more irratic.:
50 DW with 15 F = 20 UW    BW 35
50 DW w/ 12 F = 26 UW       BW 38
centered on BW:
35 BW w/ 15 F = 20 UW        DW  50
35 BW w/ 12 F = 23 UW        DW   47

Dynamic weight remains constant at 35gr even though TW differs, negligably.

It is the_feel_we are going for, right?

Balance weight targeting is the best figure to zero-in. From there friction
is your concern.

Of course hammer/strike weight and leverage play  a contributing factor.




Jon Page
Harwich Port, Cape Cod, Mass. (jpage@capecod.net)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~