At 12:06 -0700 7/1/10, Nick Gravagne wrote:
>....W = 46 mm – 2 mm = 44 mm)
>S = (10 – aftertouch)
>
>Note that of the four factors given here at the outset, only the
>aftertouch is unknown.
>
>H Rear Key = 126 V Front Key = 245
>Rs Resistance whip = 94 Ra Effort Whip = 67
>K Resistance Shank = 141 N Effort Shank = 18.50
>(Jack to knuckle contact taken at half stroke)
>
>The Action Ratio works out to 5.50.....
I have been glancing at the posts in this thread and only responded
to one particular erroneous notion. I now find that such ideas are
widespread and have had a moment to look at the "literature" as well.
My experience is not only in working hands on with piano actions for
36 years but also, more recently to creating from pure numbers movie
representations of the piano action, which require the script that
creates them to perform thousands of exact trigonometrical
calculations.
Pfeiffer claims (The Piano Key and Wippen) that Siegfried Hansing
tells us that "The length of the front lever arm is to that of the
back lever arm as the key dip is to the height of travel of the
action -- v:h = s:sa". Hansing's definitions of these two lengths,
as I remark below, may not be the same as Pfeiffer's, but in any case
Pfeiffer is wrong.
In the example below I will show, far more succinctly and clearly, I
hope, than Pfeiffer's laborious pseudo-proof of his theory, precisely
how much the top of the capstan moves upwards for a given key dip in
a given key.
Note that the measurements I use are not those I have seen used in
this thread, but that makes no difference. Exactly the same result
will occur whichever lines I measure. I have left the numbers
precise in case anyone want to check them.
_______________________________________
DEFINITIONS:
The BASE LINE is a horizontal line parallel with the key drawn
through the balance point of the key.
KEY DIP: An arbitrary figure of 8mm is taken as the (perpendicular)
downward travel of the front of the (natural) key. (8mm of arc would
make a really tiny difference)
KEY RISE is defined as the perpendicular distance moved by the
contacting profiles (lever heel and capstan top).
The KEY FRONT LENGTH is the distance along the base line between the
balance point and a perpendicular drawn from the key front.
The KEY BACK LENGTH is the distance along the base line from the
balance to a perpendicular drawn from the midpoint of the profile
(the top of the capstan).
The PROFILE HEIGHT is the perpendicular distance from the mid-point
of the profile to the base line.
_______________________________________
As an example, take the following key:
KEY FRONT LENGTH : 253
KEY BACK LENGTH : 142
PROFILE HEIGHT : 36
(Distance from profile to balance 146.49232061784)
The diameter of the front circle of the key (round which the front of
the key moves is 253 * 2 * pi = 1589.645882716435
The angle described by the key in executing the KEY DIP of 8mm is therefore
1.812026301 degrees [ asin (8/146.49232061784)].
The profiles at rest are elevated from the balance point
14.225963898748 degrees [atan (36/142)] and when the key is depressed
8 mm will be at an elevation of 16.037990199748 degrees [0.279915734
radians] and the PROFILE HEIGHT will be 40.471374397093
[sin(16.037990199748) * 146.49232061784
The KEY RISE is therefore 4.47211661 mm for a key dip of 8 mm
If Hansing's rule (used by Pfeiffer) says that "the ratio of KEY
FRONT LENGTH to KEY BACK LENGTH (as defined above) is equal to the
ratio of KEY DIP to KEY RISE". Now I read Hansing's book many years
ago and hoped to inherit it, but I've not been able to see it since
and can't be sure how he defines the KEY FRONT LENGTH and the KEY
BACK LENGTH, but if he defines them as Pfeiffer does, then they are
both very wrong, and if not, only Pfeiffer is _very_ wrong and
Hansing is more or less wrong depending on the action.
For the above example (142 ÷ 253 x 8) the Hansing's rule would give
4.490118577075 against correct result of 4.471374397093, so an almost
negligeable difference, you might say, of 2/100 millimetre. To this
I would say:
First : that the PROFILE HEIGHT in the above example is particularly
small, and typical, incidentally, of a Steinway grand of Hansing's
day with a minimal entrance height. The greater the PROFILE HEIGHT
the more Hansings rule will err; on an upright with tall soldiers the
error would be far greater, as I could show by another example if
anybody cares to see it.
Second : This error of 0.02 in a PROFILE RISE of 4.4 millimetres
will be multiplied ten times at the hammer, supposing that the hammer
rises 44 millimetres for the 8 mm KEY DIP.
Now let us come to Pfeiffer.
In the example above, his "key front length" is not as defined above
but the distance from the balance to the top front of the key, which,
supposing a key depth of 25 mm becomes 254.23217734976 mm. His "key
back length" becomes the distance from profile to balance, as
calculated above, which is 146.49232061784.
According to Pfeiffer, therefore, the PROFILE RISE will be
4.609717688609 instead of the actual 4.471374397093 mm, an error of
0.138343291516 mm. Apply the multiplication above to this error and
it is clear that the error is huge.
If the same false notions are then used to calculate the rise of the
jack, the hammer etc. it is obvious that the errors will accumulate
and it will be impossible to base any practical work on the results
so obtained
JD
--
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