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viullame formula

 
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Nick Walker
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Joined: 17 Sep 2014
Posts: 43

PostPosted: Fri Nov 21, 2014 12:58 pm    Post subject: viullame formula Reply with quote

WWIT,

You mentioned the formulas for graduation in crash's thread.
Can you discuss its application?

When I run the formulas I get numbers that appear irrelevant to my graduation. Are these multipliers or dividers? What to do with them?

Also, what about the adjustments necessary on the side?
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whatwasithinking
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Joined: 26 Jan 2013
Posts: 209
Location: Washington State

PostPosted: Fri Nov 21, 2014 10:17 pm    Post subject: Reply with quote

Nick,

Okay, but before I spout off, please consider the source...

You're probably already familiar with the history--that Fetis measured many Tourte bows and found the taper to follow a mathematical formula. IIRC, Fetis and/or Vuillaume seemed to infer that Tourte used scientific principles to arrive at the taper they observed in his bows. But maybe I was reading something into Fetis' findings. Anyway, the diameters of most of his bows do seem to increase as a logarithmic function of the distance behind the head. Did Tourte actually use a logarithmic formula? Probably not.

I've been told that this isn't a bad way to arrive at an acceptable taper, if I'm not sure how to proceed. Clearly, the masters taper their sticks with much more subtlety, adjusting for inconsistencies in the elasticity of the wood. I like to look at finished bows, to see if I can sense how well the tapering was done. Sometimes, it's obvious that it wasn't done well. There are stiff spots, or spots that are too soft.

As an aid in working on new sticks, I decided to measure several bows I liked, and record their dimensions at intervals that correspond with increases in diameter of 0.5mm. I based this on the Woolhouse variation of Fetis' formula. I traced the outlines of these sticks on foam-core poster board, and wrote down the two dimensions of the stick at each point. I'm not sure if that's exactly the same thing that others do, but it seemed to make sense to do it that way. And that's how my compas is calibrated, so the measurements correspond to the tool.

I put these formulas into a spreadsheet, and played a bit with the starting points, until the diameters looked about right. I only had to do this for the viola and cello; the published formula handles violin bows perfectly.

I'm not sure there's a uniform concensus about width vs. height. Many of the French bows I've looked at are a bit fat at the middle, and a little tall just behind the head. We're talking tenths of mm--maybe .2 to .4mm fat, but sometimes .5mm tall just behind the head. I really don't know how common this is--I haven't measured hundreds of bows. Andreas Gruetter wrote an article for The Strad, I believe, about a Maire bow he especially admired. It was like this, and I think he said that the extra width in the middle helped limit the bow's lateral deflection, while the extra height kept the bow from feeling too soft. I think you can find something about this bow at his site.

You can find an article by Colin Gough about taper and camber, via a link in the resources thread.

Well, this was probably TMI, but you asked! Now perhaps a real bow maker would be kind enough to enlighten us with how they achieve final graduations. I know it's not simply by a formula.

How did you decide on the taper for the sticks you've finished?

Bob
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Nick Walker
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Joined: 17 Sep 2014
Posts: 43

PostPosted: Sat Nov 22, 2014 9:33 am    Post subject: Reply with quote

Thanks. I've read st. George and I think fetis. The paper by Gough is very detailed. I think it will be helpful once I have my scientist wife explain the mathematics.
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