Key Ratio

[Isaac OLEG]

John,

I appreciate your example, but I had a little grand with an exact 100
mm/50 mm ratio and the same kind 1/2 on sharps WHILE MEASURED UNDER
THE KEY, and they show a clear difference in weight ratio, when
measured at the capstan (with the weight method). The black key had a
higher ratio by some 0.3 - 0.4  difference (0.51 whites 0.54 sharps).
the SWR on this piano is 5.50 on whites and  around 6.20 for sharps.

I'll say it was a very short grand, may be other things came in
consideration, as the height of the sharps vs. the length of the keys
that exacerbate that difference. That was my thought at this time
anyway.

So why the weight should be acting differently ? its downward force is
yet driven by the same lever arms we try to evaluate (while I see you
point in regard of the curve of the move).

With Best Regards.


Isaac OLEG

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> -----Message d'origine-----
> De : pianotech-bounces@ptg.org
> [mailto:pianotech-bounces@ptg.org]De la
> part de John Hartman
> Envoye : mercredi 11 juin 2003 01:13
> A : Pianotech
> Objet : Re: Key Ratio
>
>
> Richard Brekne wrote:
>  > I think it was John Hartman that asked me for a drawing of what I
>  > meant about the key ratio changing depending on the
> starting position
>  > and ending position. Again, here is that exagerated
> example of the
>  > three points on the key. A is the key front, B is the
> capstan, and O
>  > is the fulcrum. And remember we are looking at the
> change in vertical
>  > position for points A and B.
>
> Thanks for the drawing, I see your point. I think the
> contradiction can
> be resolved looking at the lever arms in relation to their arcs of
> motion. Then the ratios will be correct. As I said before how you
> measure the lever arms depends on what aspect of action
> mechanics you
> are interested in working on. If you are investigating the static
> balance of weights it is easier to use lever arm
> measurements that are
> perpendicular to the force of gravity. If you are interested in the
> motion of levers (how far they move) then you should
> measure the lever
> arms diagonally and use arc measurements for the motion.
> The two are
> roughly similar but not the same.
>
> Let me give you some examples. It is true that for a key
> with a front
> lever arm of 100mm and a back lever arm of 50mm (measured along the
> length of the key) a 2 gram weight on the capstan will
> balance a 1 gram
> weigh at the front of the key. It is only roughly true that
> when you
> depress the key 10mm at the front the capstan will rise 5mm (your
> drawing shows this). To measure this motion precisely you need to
> measure the lever arms diagonally and use arc measurements for the
> distances. The two will be very close (In the case of a
> key) but not the
> same.
>
>
> John Hartman RPT
>
> John Hartman Pianos
[link redacted at request of site owner - Jul 25, 2015]
> Rebuilding Steinway and Mason & Hamlin
> Grand Pianos Since 1979
>
> Piano Technicians Journal
> Journal Illustrator/Contributing Editor
[link redacted at request of site owner - Jul 25, 2015]
>
>
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