Jump to content
Maestronet Forums

Deciding the arching height


robertdo
 Share

Recommended Posts

Unless one is making a real copy, I was wondering how luthiers will decide the arching height for each plate. Until now I finish the garland, then I use it to trace the outline of the plates. And I have to decide the arching height. So I had a look at the few posters I bought, and just took the measurement I found before adding the average of the rib height at the neck, the average height at the end pin end, the top height (across) and the back height. Of course this calculation has nothing scientific, but it did help me to get an idea.

For the titian I found 90.1. For the viotti 91.1, the arching height for the kruze were missing on the poster (but the addition of both could be about 30-31). the Bett gives 92; Lord Wilton 91.4; Plowden 88.8; Cessole 87.5 and Cannone 94.1 (I don't have the cannone poster but extracted the numbers from old maestronet posts). So when I finish a garland now I will try this.

I would be curious to know how people do, and also if people have poster that are not listed here I would be glad to see if some numbers match.

Link to comment
Share on other sites

  • Replies 50
  • Created
  • Last Reply

Top Posters In This Topic

Distortion of the arching and loss of plate edge thickness can both result in reported maximal arching heights on classic instruments that are less than original. Also, the gluing surface of the rib structure may not be all in a single plane so trying to measure arching height from the archings on posters may be a little confusing as one might get contradictory numbers from the long and short axis tracings, for example. All I'm saying is that if the number you obtain from documentary evidence of historic instruments is extreme you might consider allowing yourself to moderate a bit (especially if your historic model seems to have a surprisingly low arch). There are instances where the original arching heights were unusually high or low, of course (the Messiah Strad top arch is an example of a really low one) so I wouldn't imitate those any more than I'd copy an arch that is obviously distorted.

Link to comment
Share on other sites

I wrote an email to the Strad regarding the arching heights of the Messie, that was published in the June 2011 issue. I post it here since it relates to robertdo's question:

To: the soundpost.

I appreciated the fine poster of the ‘Messiah’ Strad 1716, in the March issue. Calculating the inside arch heights from the measurements given reveals an interesting fact: the relative arching heights are reversed on the inside! Subtract the plate thickness from the given arch height and we get the inside arch.

Belly: 13.8 - 2.1 = 11.7 mm inside arch height.

Back: 15.4 - 4.3 = 11.1 mm inside arch height.

This agrees with a statement by Francesco Griselini in “Dizionario delle arti e de mestieri”‎ (Venice 1770, Volym 8‎) that the back arch of a fine violin is made equal to the belly. From the above it may be speculated that they were originally the same and that the belly has risen by 0.6 mm from the tensioned strings. This well known behavior of wood under stress is called creep. For modern violin makers who practice arching the outside first, Griselinis' statement seems to be a contradiction from what we see in old violins. However, if Griselini’s statement concerned the inside arches, then it is absolutely comprehensible.

If the ‘Messiah’ had been in constant use over the 295 years since its making, I’d speculate that the belly today would be about the same height as the back, from constantly tuning (tensioning) the strings to pitch (with a belly thickness of just over 2 mm), and Stradivari's original intention would be obliterated.

Another unplayed Stradivari in near mint condition is the 1716 ‘Medici’ with similar arching. These two examples of near mint Strads suggests to me (see my article in The Strad, August 2006), that the inside back and belly arches were made to be similar, or even opted to be exactly the same. I suspect that CT scans of the ‘Messiah’ will reveal this to a higher degree.

Torbjörn Zethelius

Stockholm, Sweden

At the time I was hoping that the Ashmolean Book of instruments would include CT scans of the Messie, which it unfortunately does not.

Link to comment
Share on other sites

Here is a comment to the inside arch theory. The black line is equal inside arch heights of a set of del Gesus and Strads. All seem to lie below that line and the regression lines are not paralell to that line. So either there must have been a large and similar distortion making the top arches higher, huge regraduations being done making the tops thinner, or the theory could be wrong.

post-25136-0-81840400-1330728619_thumb.jpg

post-25136-0-80787500-1330728792_thumb.jpg

Link to comment
Share on other sites

Thank you, Anders. I'm not sure what the regression lines are showing?

It's a test I usually do on such samples of data to see trends. It is possible to test if the trend is statistically significant or not by a numerical test involving how many data points there are (degrees of freedom) and the correlation coefficient, R. I suppose the data from the Strads might be significant, which may indicate that there are a sort of rising trend there.

The correlation coeficcient squared, R2, may give an indication of how much of the variation in the back plate inside arch can be exlained by the variation in the inside top plate arch height. For the Strads that may amount to some 35%.

The statistical theory does not take into account if the variables along the x and y axes indeed are dependant on each other or not. The theory will say that they are statistically dependant if there is a significant correlation. To reveal if the statistical dependance are reflecting a real dependance one needs to do experiments or tests varying one of the values to see if the other then will change. I guess for a violin under string tension that test would take some years to accomplish so the arches can move for a while. Another way to test is to do it on an other independant sample of data, if similar correlations appear, it strengthens the hypothesis of a connection between them in some form.

I have read, I think from one of David B's posts at some time, that arching corrections are easier to do outwards than inwards. It is easier to remove material from molds than adding. So there might be a trend for corrected arches to rise a little over time. I guess tops are corrected more often than backs, so maybe that could have skewed the data from the equal inside arch line?

Edited by Anders Buen
Link to comment
Share on other sites

What are the possible benefits of having a similar inside arch height between the top and back plates?

Is there an assumption that the arch shapes of the tops and backs have been more similar from the beginning, in some form?

The idea is not mine. It is published in Dizionario delle Arti e de Mestieri, Francesco Griselini, Marco Fassadoni, Venezia 1770. Page 196.

I like it because it makes sense to me and adds to my inside first theory as how the old masters were working. The point is that the inside shapes should be made identical to each other.

Link to comment
Share on other sites

Here is a comment to the inside arch theory. The black line is equal inside arch heights of a set of del Gesus and Strads. All seem to lie below that line and the regression lines are not paralell to that line. So either there must have been a large and similar distortion making the top arches higher, huge regraduations being done making the tops thinner, or the theory could be wrong.

Dear Anders,

Your graphs would be little more user friendly if the axis were switched so that the vertical axis was the top arch height and the horizontal axis was the bottom arch height. If a top arch height was greater than the bottom arch height then the point would then appear above the black line instead of below it.

The vertical and horizontal scales should be of equal length so that the black line which gives a 1 to 1 relationship appears as a 45 angle.

Marty

Link to comment
Share on other sites

So there might be a trend for corrected arches to rise a little over time. I guess tops are corrected more often than backs, so maybe that could have skewed the data from the equal inside arch line?

Downforce at the bridge will cause the top arch to fall and push the back arch out higher. Compression longitudinally causes the longitudinal arch of the top to bulge out where it is most curved, usually north and south of the bridge. The back, being far thicker in the center and not having F-holes, is far less likely to distort, and any distortion is more likely to be a less objectionable slight rise in arching.

I don't think correcting arches would be a believable source of "arching rise", unless it was accompained by some rather serious changes in the instrument outline. Higher-than-original arching would cause the outline of the plate to become shorter and narrower, as old plates don't like to stretch very much.

The conclusion I draw is that distortion (even with corrections) would tend to show higher back arching relative to the top, and that the plots showing all back arches less than tops is conclusive evidence that they were never built equal.

What are the possible benefits of having a similar inside arch height between the top and back plates?

Is there an assumption that the arch shapes of the tops and backs have been more similar from the beginning, in some form?

I see no benefits to equal arching, unless you have an emotional attachment to stuff that matches. I DO see some benefits to lower backs:

1. Really fabulous looking maple is far more rare than good spruce, so you'd want to keep the billets as thin as possible to get the most yield from a good log. In other words: it's cheaper to go lower.

2. Acoustically, the top is much more strongly coupled to the bridge, among other differences, and the tone effects of arching will be different. I'm quite convinced at this point that low top arching gives some tonal problems that are far more objectionable than what you'd get from low back arching.

I like it because it makes sense to me and adds to my inside first theory as how the old masters were working.

What about those examples of outside dimpling, showing that the graduation punch was used after the outside arch was completed?

The point is that the inside shapes should be made identical to each other.

Why?

Link to comment
Share on other sites

What are the possible benefits of having a similar inside arch height between the top and back plates?

I don't have the answer to this of course but if really the top arch was really made flatter in the central area and the back plate was initially like a real cycloid, that is really rounded, and if we agree that for structural reason the back plate central region had to be made thicker than the lower and upper bouts, then the similarity of shape and height between both plates is basically a natural consequence of this. there is not even a need to imply this was planned by the makers.

to come back to the relation between ribs heights and arching height, I supposed you are all aware of these article dealing with the inside air volume of violins, that seem to have remain quite constant in the Stradivarius violin tested (while the total weights and densities of the bodies were greatly varying). I supposed there had been several topics dealing with this on Maestronet, and it could simply have been a red herring. But at least it would be a simple rule to follow during the making and provide a goal easier to achieve (For example: lower ribs height would rather go with higher arching, in turn this would allow thinner plates; while higher ribs could go with low arch and subsequently very thick graduation)

Link to comment
Share on other sites

Not familiar with this material, can you provide a link?

Oded

I supposed you are all aware of these article dealing with the inside air volume of violins, that seem to have remain quite constant in the Stradivarius violin tested (while the total weights and densities of the bodies were greatly varying). I supposed there had been several topics dealing with this on Maestronet, and it could simply have been a red herring. But at least it would be a simple rule to follow during the making and provide a goal easier to achieve (For example: lower ribs height would rather go with higher arching, in turn this would allow thinner plates; while higher ribs could go with low arch and subsequently very thick graduation)

Link to comment
Share on other sites

Not familiar with this material, can you provide a link?

Oded

Hi Oded

Here is one link air volume You can read the full pdf at the end of the article

I simply used "air volume violin" keywords (since it was what I had in mind when asking about ribs heights and arching) and got several other entries more or less interesting but not really comprehensible by me. I know that few words were said about this on maestronet but couldn't really find the complete topic. I am pretty sure Anders and Don have been dealing with that before.

Link to comment
Share on other sites

Your graphs would be little more user friendly if the axis were switched so that the vertical axis was the top arch height and the horizontal axis was the bottom arch height.

I agree, much more intuitive to interpret too, so here they are with switched axes and closer to 1:1 size of the axes. Thanks for pointing this out, Marty!

post-25136-0-30754300-1330794452_thumb.jpg

post-25136-0-99945800-1330794458_thumb.jpg

Edited by Anders Buen
Link to comment
Share on other sites

I agree, much more intuitive to interpret too, so here they are with switched axes and closer to 1:1 size of the axes.

Although it shows that there is not a identity, clearly the Stradivari are much more homogenous and not that far off when compared with the Guarnerius. Maybe this doesn't come as a surprise given the temperament of these 2 makers... :)

Anders, could you do the same but instead of using the inside graduation for the top plate, you would use the outside graduation. In other words you would compare the inside of the back with the outside of the top.

Link to comment
Share on other sites

Downforce at the bridge will cause the top arch to fall and push the back arch out higher. Compression longitudinally causes the longitudinal arch of the top to bulge out where it is most curved, usually north and south of the bridge. The back, being far thicker in the center and not having F-holes, is far less likely to distort, and any distortion is more likely to be a less objectionable slight rise in arching.

From my own observations, the back arch doesn't tend to rise. It is under longitudinal tension, which would be a force tending to reduce height. The soundpost, pushing the other way, might increase total height if it was in the center. However, it is off center, so it's major contribution doesn't seem to be to increase total height, but to move the highest point of the cross-arch in the direction of the post. This distortion is usually easily seen on CT scan "cross-slices" of the soundpost area. It can also be seen by comparing original cross-arching templates with the back arching after an instrument has been strung up for a few years. The soundpost side will be pushed out, and the opposite side will be flatter.

Also, total top arching height doesn't necessarily go down. It seems to depend on the original height and shape (higher archings can actually go up), and can also depend on soundpost tension.

I don't think correcting arches would be a believable source of "arching rise", unless it was accompained by some rather serious changes in the instrument outline. Higher-than-original arching would cause the outline of the plate to become shorter and narrower, as old plates don't like to stretch very much.

In practice, when correcting archings with moisture and heat and adequate time, the wood of the top is plastic enough to change arching height in either direction without changing the outline. However, going through 5 sets of Strad measurements just now, four tops were shorter than the backs (one was the same). Four tops were narrower at both the upper and lower bouts than the backs (one was greater). I don't know how useful that is though, because we can't assume that the top and back length and width started out the same, if they were traced from the rib assembly. I also don't know to what extent these variations might be due to greater wear on the edges of the top, since the measurements weren't taken "purfling to purfling".

Link to comment
Share on other sites

I don't have much experience with old violins but treating the violin as a moment diagram, the top will be under compression, and the back under tension. This would ordinarily make the top push upward and the back flatten out.Is this what has been observed?

I tend to design my fiddles with this in mind.

Link to comment
Share on other sites

What about those examples of outside dimpling, showing that the graduation punch was used after the outside arch was completed?

Have you seen more than one example (in Mr. Darnton's blog)? There are spike holes in the outside tops of 90 % of old fiddles that I've seen.

Why?

For symmetry I guess. I guess they tried it and it worked. Have you?

Link to comment
Share on other sites

For symmetry I guess. I guess they tried it and it worked. Have you?

Nope... most of the good fiddles I've seen have had very different top and back arches, so that's what I've done... and it worked, too. :)

Have you seen more than one example (in Mr. Darnton's blog)? There are spike holes in the outside tops of 90 % of old fiddles that I've seen.

Nope to that too... I couldn't find it... do you have a link?

Roger Hargrave's article on DelGesu's method seems pretty convincing to me... outside arch first.

link to article

Link to comment
Share on other sites

Nope... most of the good fiddles I've seen have had very different top and back arches, so that's what I've done... and it worked, too. :)

Anything works when you put strings on....

Nope to that too... I couldn't find it... do you have a link?

Roger Hargrave's article on DelGesu's method seems pretty convincing to me... outside arch first.

link to article

Link to Darnton's blog.

Don, I thought that you were an investigator. But I guess everybody has their limits.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.



×
×
  • Create New...