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Francois Denis article in The Strad

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In the Feb. 2010 issue of The Strad, page 47, in the article by Francois Denis, it appears to me that a mistake has been made. I am sorry to not post the figure. If you have this magazine, please look at the figure 2. The omega symbol is used twice on each line segment. The segments cannot possibly be equal. I suggest "omega" and "omega prime" were the intended symbols.

This makes a huge difference in the analysis.

If I have missed something, please tell me.

John

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Are we the only ones who read The Strad?

I guess everyone else is busy making and selling violins.

Francois, can you post a correction here?

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Ok, so I had to dig it up again.

In figure 2, it appears to me that the lower-case omega is representing the mid-point of the nearly semi-diagonals, the sides of those two similar triangles.

But I think figure 5 still has a chi vs 'c' mismatch between the text and the sketch.

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I think it's correct. No mistake.

Torbjörn,

The upper and lower segments, both marked "omega" are NOT the same length. Measure it, please.

Thanks for your interest. Let's get to the bottom of this.

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Shouldn't have gotten into this now, because I do have gluing to do!

Here's a quick sketch of the problem in figure 2

<well, can't seem to upload an image right now>

It's not the same length in either case, but it is halfway.

Edit: quick sketch, approximate. Omega at midpoints.

post-24063-1268860335.jpg

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John,

the line segments you describe are indeed of different length.

The common properties of the points labled omega are that they each lie at the midpoint of their respective line segments and that they mark locations that are half the reference height.

I found the article significant in that it presents an easy and direct shop practice that sets up the long arch without a template and also sets up an overall distribution of height that is aproximately cycloidal. All in all, is very plausible to me and in line with the way I like to do things-- for example quicly shaping a curve by eye to pass through several reference points. The reference points in the article are placed at what I call "powerful" positions.

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... .

The common properties of the points labeled omega are that they each lie at the midpoint of their respective line segments and that they mark locations that are half the reference height.

... .

I too spotted this, but never got around to asking the question. I believe you are correct. Thanks.

Now I have to get my copy of The Strad back.

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John,

the line segments you describe are indeed of different length.

The common properties of the points labled omega are that they each lie at the midpoint of their respective line segments and that they mark locations that are half the reference height.

I found the article significant in that it presents an easy and direct shop practice that sets up the long arch without a template and also sets up an overall distribution of height that is aproximately cycloidal. All in all, is very plausible to me and in line with the way I like to do things-- for example quicly shaping a curve by eye to pass through several reference points. The reference points in the article are placed at what I call "powerful" positions.

Doug,

Ok, I guess I see the point now. Just not the way I am used to seeing labels. I thought omega referred to the length of the segment. They are both midpoints. I would have labeled them differently. Thanks for clarifying.

If I get time, I will try to translate it into my language. Sometimes my brain works differently than it should. And sometimes it just doesn't work at all. :)

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In the Feb. 2010 issue of The Strad, page 47, in the article by Francois Denis, it appears to me that a mistake has been made. I am sorry to not post the figure. If you have this magazine, please look at the figure 2. The omega symbol is used twice on each line segment. The segments cannot possibly be equal. I suggest "omega" and "omega prime" were the intended symbols.

This makes a huge difference in the analysis.

If I have missed something, please tell me.

John

Actually the diagram 2 is right but the caption is a little bit ambiguous. The correct redaction would be at the middle of each segment of the diagonal ("Be" "Bb","Bf" and "Ba").

Note also that the height of "B" the crossing point of the diagonal is the reference for the measurements of the other points but I don't say that is the highest point of the arching

francois denis

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I don't say that is the highest point of the arching

Ah yes, indeed, a subtlety I missed. Makes your concept even more interesting.

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Actually the diagram 2 is right but the caption is a little bit ambiguous. The correct redaction would be at the middle of each segment of the diagonal ("Be" "Bb","Bf" and "Ba").

Note also that the height of "B" the crossing point of the diagonal is the reference for the measurements of the other points but I don't say that is the highest point of the arching

francois denis

Francois,

Thank you.

John

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I was wondering how the fractional arching heights were measured. It is easy to do this today with dial calipers and calculators. Francois hints that maybe metal calipers were for arching heights. Stradivari's wooden caliper with equal arms was used for thickness

post-24376-1268967922.jpg

To measure 1/2 heights one would need calipers with arms in the ratio of 1:2. The central measurement (beta) is taken with the long arms and then compared with "little omega" using the short arms.

This idea would require a different caliper for each fraction. Is there another way to measure fractional thickness??

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Mr catnip,

Maybe you were thinking of this item?

Oded

Yes, that is it ! ... proportional calipers. Did Strad have a tool like this? I was going to make one using the golden ratio, but having read Francois articles I think simple fractions are more useful.

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I remember reading somewhere that Bergonzi borrowed a proportional compass from the estate of Stradivari. I interpreted it as the X type of proportional compass. But it could also have been what you are asking about, I guess?. I don't know if it was returned, but it's not in the collection now.

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Hans Weisshaar had a set of proportional dividers like this for investigating some of the proportion ideas. I think his had a geared rack and pinion for changing the pivot point quickly and precisely by turning a knob attached to the gears.

zoom_1101-157.jpg

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That's interesting David!

Euro Pelluzzi, in a book called Tecnica Costruttiva Degli Antichi Liutai Italiani (sold out) mentions proportional dividers, and I think proportional dividers are also mentioned in the 1795 Cremonese manuscript "LIBRUM SEGRETI DE BUTTEGHA - Regule et Formule Phoniche per Liutaro et Violinaro" (that I would translate as "Workshop's Secret Book - Phonic Rules and Formulas for instrument and violin makers"). This manuscript was once in the library of the Schollar Patetta Federico and now in the Vatican Library.

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That's interesting David!

Euro Pelluzzi, in a book called Tecnica Costruttiva Degli Antichi Liutai Italiani (sold out) mentions proportional dividers, and I think proportional dividers are also mentioned in the 1795 Cremonese manuscript "LIBRUM SEGRETI DE BUTTEGHA - Regule et Formule Phoniche per Liutaro et Violinaro" (that I would translate as "Workshop's Secret Book - Phonic Rules and Formulas for instrument and violin makers"). This manuscript was once in the library of the Schollar Patetta Federico and now in the Vatican Library.

Euro Pelluzzi

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I was wondering how the fractional arching heights were measured. It is easy to do this today with dial calipers and calculators. Francois hints that maybe metal calipers were for arching heights. Stradivari's wooden caliper with equal arms was used for thickness

post-24376-1268967922.jpg

To measure 1/2 heights one would need calipers with arms in the ratio of 1:2. The central measurement (beta) is taken with the long arms and then compared with "little omega" using the short arms.

This idea would require a different caliper for each fraction. Is there another way to measure fractional thickness??

Hi Mr catnip

You can find fractions with the triangles. The well-known 3-4-5 triangle provide fractions are 3-4 ; 4-5 and 3-5 . As they used few of them you cab find any measurement with a simple geometrical drawing . Personnaly I use a "pige" (a kind of triangle template ) with a compas.

francois

post-29143-1269108442.jpg

post-29143-1269108428.jpg

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A little bit more...

About compass. There is this interesting similitude between the set of compass used by Stradivari and the set illustrated by the Diderot d'Alembert encyclopedia . Note that only the wooden caliper is said to be a thickness compass both the metal compas are called "arching compass"....

About the pointing technic, I add two illustrations of this type of compas from the Middle Age (Villard de Honnecourt booklet XIII° century and a sculptor at work XVIII° century).

François

PS: I have to say that I found the type of proportionnel compass showed by David is easy to use but.... it takes time to adjust. Too much time I think for the ancient instrument makers.

post-29143-1269109565.jpg

post-29143-1269109606.jpg

post-29143-1269109646.jpg

post-29143-1269109536.jpg

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A little bit more...

About compass. There is this interesting similitude between the set of compass used by Stradivari and the set illustrated by the Diderot d'Alembert encyclopedia . Note that only the wooden caliper is said to be a thickness compass both the metal compas are called "arching compass"....

About the pointing technic, I add two illustrations of this type of compas from the Middle Age (Villard de Honnecourt booklet XIII° century and a sculptor at work XVIII° century).

François

PS: I have to say that I found the type of proportionnel compass showed by David is easy to use but.... it takes time to adjust. Too much time I think for the ancient instrument makers.

Hi François:

Thoroughly enjoyed the Strad article. Anything you would care to add about how the old masters reached their final arching shape would be of great interest here. Of course, we have beaten catenaries, curtate cycloids, circles, etc. to death but tell us more of what you think if you will. If is a research topic for your next book, we'll understand if you don't want to.

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