Well, I beg to differ. In fact, I know I am not even the slightest bit
confused. Tho perhaps we are talking a bit past each other here.
For the first, no one questions that string at lower tension... and I
well suppose that means lower BPP as well will react more to a string
length change then a string at a higher one. I simply reacted to claims
that you could calculate change in pitch directly from change in
length.. which you still seem to hold on to. You can not. You are also
incorrect as to the point on strings of same length, same pitch, but
different diameter. They will indeed react identically pitchwise to the
same amount of change in length. Run the numbers in that spreadsheet I
posted and see for yourself. I assume since you see this in terms of
BPP you can look closer at the matter and find the reason from that
perspective. It is correct however that different length same pitch
strings will change pitch differently for same change in length. In any
case... I still see nothing that you have posted that shows you
calculating changes in pitches for changes in length...
As for my spreadsheet needing a bit more work... it does exactly what it
was meant to do... and if you find it lacking... please do take contact
with Dr. Galembo and argue the points. Or perhaps ask Askenfelt . I am
sure either will be more then willing to entertain your criticisms.
Strikes me tho, that as a straight forward way of calculating pitch
change for length change.... its quite easy indeed. A bit of easy
standard trig, and Hooks law.
And David...
You started your last post with a plea to stay away from being
antagonist. I would ask you if you think your little ending statement
in your second paragraph is in that spirit.
Cheers
RicB
I believe you are the one confused. Did you do the problem as I
outlined?
For BPP to change between two notes targeting the same frequency, the
speaking lengths must be different. To see whether a change in
frequency
between two strings will be different with a change in length as a
function
of BPP you must start with two strings that have a different BPP.
If the
strings are equal speaking length then no matter how you change the
string
diameter altering the tension and hold the frequency constant, the
BPPs will
change together. A change in length will not result in a difference
in the
change in frequency between the two. However, if you start with two
strings
of unequal speaking length with the same starting frequency, the
tension (a
in the first example) will be different, but the BPP's will not be
equal.
Now when you impose a similar change in length there will be a
difference in
the change in frequency between the two.
The more complicated calculation comes because we comparing just two
different notes on the same piano. You then must do the
calculations and
convert the change on each note to cents deviation so that you can see
whether as the percentage of a semitone, one changes more than the
other.
In other words, does the high bass go "out of tune" more or less
than the
low tenor. The relative BPPs of the respective notes will give an
indication of which will go out of tune more and it is the one with the
lower BPP that will go out of tune more. Namely, the BPP of the low
tenor
on a Steinway B, for example is around 22%. The first note of the
high bass
is around 60%. I have my own spreadsheet, thank you, perhaps yours
needs a
bit more work.
That's the best I can do with the explanation for now-I gotta go to
woik.
David Love
davidlovepianos at comcast.net
www.davidlovepianos.com
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