Beginning violin making

[HoGo]

Sound is not a tiny object bouncing around inside of violin. If the "sound" reflected back and forth it would never leave the body. No one worth following has so far come with any proof about what is the ideal shape of achings and only prolific makers or ones that are very systematic in their approach get to know what works and build consistent sounding instruments.

The templates on the makingtheviolin.com are for generic Strad style violin based upon the Messiah Strad of 1715. I haven't found anything explicitly wrong with them.

[Torbjörn Zethelius]

6 minutes ago, Dr. Mark said:

So you're saying that a parabolic curve and a catenary are the same?

Yes, sort of. It's a bit of a story.

I had already in 2006 written an article in the Strad about carving inside archings by using a chain. Then I met Andrew Dipper who translated Librum segreti de buttegha. He told me that the inside curves were made to be parabolas.

In Librum segreti de buttegha it is stated that the inside should be made to reflect the sound inside the instrument: 'All of the movement and oscillations of the air contained in the body of the instrument are dependent on the correct formulation and setting out of this geometric scheme.'

I was confused at first because I had by that time already figured out that the old makers carved the insides first with the use of a chain. A chain curve, or 'catenary' is the 'simplest curve derived from nature' as I wrote in my article Inside Information.As I dived more in to this topic I found a passage by Galileo Galilei from his famous 1638 book Discourses and Mathematical Demonstrations Relating to Two New Sciences. Here is the key relevant passage (from the standard English translation by Henry Crew and Alfonso de Salvio, 1914):

"I must tell you something which will both surprise and please you, namely, that a cord stretched more or less tightly assumes a curve which closely approximates a parabola. This similarity is clearly seen if you draw a parabolic curve on a vertical plane and then invert it so that the apex will lie at the bottom and the base remain horizontal; for, on hanging a chain below the base, one end attached to each extremity of the base, you will observe that, on slackening the chain more or less, it bends and fits itself to the parabola; and the coincidence is more exact in proportion as the parabola is drawn with less curvature or, so to speak, more stretched; so that using parabolas described with elevations less than 45°, the chain fits its parabola almost perfectly."

I take it to mean that violinmakers of the time used a chain to approximate parabolas on the inside of the plates. We all know that the inside curvature do not exceed 45 degrees so a catenary coincides well with a parabola.

Bonus note: Galileos' father Vincenzo was a famous lute player who made acoustical experiments together with the son. They must certainly have visited a violinmaker and seen instruments being built.

[Torbjörn Zethelius]

4 hours ago, HoGo said:

Sound is not a tiny object bouncing around inside of violin. If the "sound" reflected back and forth it would never leave the body. No one worth following has so far come with any proof about what is the ideal shape of achings and only prolific makers or ones that are very systematic in their approach get to know what works and build consistent sounding instruments.

Sound is not a tiny object bouncing around inside the violin, that is true. Inside the violin is a body of air that is shaped exactly as the inside of the violin body and which moves in synchronicity with the vibrations of the violin body. The movement of this air body is crucial for the development of the sound. IMO

[HoGo]

1 hour ago, Torbjörn Zethelius said:

Sound is not a tiny object bouncing around inside the violin, that is true. Inside the violin is a body of air that is shaped exactly as the inside of the violin body and which moves in synchronicity with the vibrations of the violin body. The movement of this air body is crucial for the development of the sound. IMO

It's not as simple. The air is springy substance and doesn't exactly follow body, it also acts against the body like water in water bed causing pressure vawes that exit through apertures and spread into surrounding. This is roughly what happens at lower frequencies, the higher frequencies mostly radiate from outer surfaces where arching as "reflective" surface shape gives no sense.

Arching adjusts stiffness of the whole and localized areas of the instrument and thus its vibrational behavior that is infinitely complex and extremely hard to study except for the few lower frequencies that are not as important for quality of tone we hear. The response and perceived quality of instrument may depend on combination of many additional parameters within the whole system of interaction of string/bridge/players hand/bow/bowhair/rosin/ear of player/ear of listener/acoustic space/number of flies in the room etc. that are impossible to measure.

[Bodacious Cowboy]

On 2/10/2026 at 3:04 PM, mendel said:

Thank you all for the feedback. Does anyone know about the website makingtheviolin.com and if the templates over there are good and accurate? This is what I'm up to now it's taking forever

 

Start your rough arching and gouge down the edge thickness to around 6mm before you clean up the outline. That will save you a lot of time.

[Dr. Mark]

On 2/11/2026 at 2:04 PM, Torbjörn Zethelius said:

On 2/11/2026 at 8:55 AM, Dr. Mark said:

So you're saying that a parabolic curve and a catenary are the same?

Yes, sort of. It's a bit of a story.

The curtate cycloid people are going to be very upset.  Not me though - I think the plates should be flat, which is the same as a parabola, sort of.

[Torbjörn Zethelius]

4 hours ago, Dr. Mark said:

The curtate cycloid people are going to be very upset.  Not me though - I think the plates should be flat, which is the same as a parabola, sort of.

You're late to the party. They were very upset. The big debate happened years ago after I published 'Inside Information' in August 2006. Several threads on Maestronet and elsewhere. 

Giordano Bruno (1548-1600) meant that a flat line is just an infinite circle with an infinite radius. Likewise we can argue that a parabola and a catenary are also flat lines if extended into infinity.

[Dr. Mark]

On 2/13/2026 at 6:13 AM, Torbjörn Zethelius said:

Giordano Bruno (1548-1600) meant that a flat line is just an infinite circle with an infinite radius. Likewise we can argue that a parabola and a catenary are also flat lines if extended into infinity.

Lol then you know that the catenary equation is (y - y0) = a*cosh(x/a) where 'a' is your horizontal scale parameter.  The Taylor expansion is a*(1 +[(x/a)^2]/2! + [(x/a)^4]/4! + ...  A catenary is somewhat of a parabola when (x/a)^4 << (x/a)^2, but in that case (x/a)^2 << 1, so sort of a straight line.  If the error between the catenary and the parabola is tolerable for your purposes, then the error between a straight line and a parabola is likely tolerable for your purposes.

So what is it about a parabola that makes it ideal anyway?  Flattening the plates relative to other models is by most accounts what separates the Strads and del Gesus from the Amatis, Stainer, and other Guarneris, and I can quote from people with more experience than I have.  Flattening would tend to reduce, rather than accentuate, the effect of curve shape by a similar argument to that you ascribe to Bruno.  But I'm open - convince me otherwise.

 

[HoGo]

Central part of shallow parabola is also quite close to a circle so why bother at all with such "exotic" curves when everyone and his brother has a compass (or dividers) already in the workshop...

[Marty Kasprzyk]

A drawing bow makes a shallow parabola.  https://www.finewoodworking.com/2017/02/08/shopmade-drawing-bow?srsltid=AfmBOopTOHzEQOxZCiGKqookLmW7Vq50my5FV4cHPgIxTG7Ii2JbAZM3

[Torbjörn Zethelius]

2 hours ago, Dr. Mark said:

So what is it about a parabola that makes it ideal anyway?  Flattening the plates relative to other models is by most accounts is what separates the Strads and del Gesus from the Amatis, Stainer, and other Guarneris, and I can quote from people with more experience than I have.  Flattening would tend to reduce, rather than accentuate, the effect of curve shape by a similar argument to that you ascribe to Bruno.  But I'm open - convince me otherwise

We need to be careful with comparing curves. The difference is not as great as somebody with less experience may think it to be. A flatter curve gives a dark tone in my experience while rounder curve accentuates more the brighter spectrum. But as long as the curves are well made and with good wood, it will make a great instrument.

[Torbjörn Zethelius]

When I started out carving the insides I had a ruler laid across the plate and followed the shadow. It was simple enough. But harder to teach somebody who doesn't know what they're aiming for.

[Torbjörn Zethelius]

19 hours ago, HoGo said:

Central part of shallow parabola is also quite close to a circle so why bother at all with such "exotic" curves when everyone and his brother has a compass (or dividers) already in the workshop...

Yes, visualise a circle when working the outside thicknesses after having finished the inside, since they are practically the same. The shadow from a straight edge is the best tool for this.  Then blend it with the edge. That's how I do it. It's easy and straightforward.

[LCF]

On 2/14/2026 at 6:28 AM, Marty Kasprzyk said:

A drawing bow makes a shallow parabola.  https://www.finewoodworking.com/2017/02/08/shopmade-drawing-bow?srsltid=AfmBOopTOHzEQOxZCiGKqookLmW7Vq50my5FV4cHPgIxTG7Ii2JbAZM3

 

Is that parabolic or elliptical?

If those bows were tillered similarly to a wooden archery bow they would be useful for drawing circles. This is a slightly redundant thing to say in that bows are often tillered to form a smooth circular curve when 'drawn'.

[LCF]

9 hours ago, Torbjörn Zethelius said:

Yes, visualise a circle when working the outside thicknesses after having finished the inside, since they are practically the same. The shadow from a straight edge is the best tool for this.  Then blend it with the edge. That's how I do it. It's easy and straightforward.

For those areas of violin arches which can most closely resemble a curtate cycloid namely in the cross sections near the corners, the inside will often be very close to a cycloid if the plates are smooth. This is a specific example of a more general situation where a curtate cycloid on the outside of a typical violin plate implies a (very nearly) cycloid on the inside.  You might as well start from the inside. 

If that is your inclination 

[Marty Kasprzyk]

20 minutes ago, LCF said:

 

Is that parabolic or elliptical?

If those bows were tillered similarly to a wooden archery bow they would be useful for drawing circles. This is a slightly redundant thing to say in that bows are often tillered to form a smooth circular curve when 'drawn'.

The drawing bow is parabolic. Very similar to a catenary or hanging chain.

 

[Torbjörn Zethelius]

11 hours ago, LCF said:

For those areas of violin arches which can most closely resemble a curtate cycloid namely in the cross sections near the corners, the inside will often be very close to a cycloid if the plates are smooth. This is a specific example of a more general situation where a curtate cycloid on the outside of a typical violin plate implies a (very nearly) cycloid on the inside.  You might as well start from the inside. 

If that is your inclination 

Circles are easy to visualise and they don't require elaborate templates. As far as I know Cremonese makers didn't use arching templates. There is not a single original arching template by Stradivari. Those that exist were made by Guadagnini for count Cozio di Salabue as study material. They were made from original instruments in Cozio's collection.

Count Ignazio Alessandro Cozio di Salabue (1755-1840) experienced the decline in Cremonese violin making and the transition to the modern French practice of making 'artistic copies' of Italian instruments. The new method was called 'La methode Francais' while in contrast the old Italian method was named the 'Amati method'. It was because of the French method – that is still in fashion – that Cozio had the templates made.

Edited February 15 by Torbjörn Zethelius
A note on the French method

[HoGo]

Some time ago I compared old (turn of the century) pic of du DIable and one recent and also compared the long arch to pure circle. The old one virtually copied the circle except the last cm or two, You would be hard pressed to carve it so close to circle even with templates being such large radius. The recent pic shows quite flatter arch more in line with modern arching.

[gorge riam]

 Maybe it is useful for someone to compare the various mathematical arch shapes (circle, chainline, parabola) with an actual example. The first foto shows a cross arching of a violin top plate (Strad-Poster: GGG-Brusilow). A circle and a chainline is fitted to the actual internal arching. Up to the inflection point (maximum gradient) there is little difference between the various shapes.

the diagram shows how much a chainline and a parabola deviates from a circle. 

As I understand the "inside first with curtate" method (revived by Torbjörn?) has the main advantage that the arching in ALL directions can easily be controlled by a chain up to the inflection point. And this is definitely not possible from outside. right?

comparison circle - chainline.pdf circle chainline parabola.pdf

Edited February 15 by gorge riam
...added: STRAD-poster into the text

[HoGo]

Most if tops of Strads have seen arch re-forming after they distorted under tension. MAny of those several times. Each time the restorer reshapes the arch to what HE considers best using hot sandbags that naturally smooth out curves of archings against modified cast. Most of the tops have lost wood in their centers due to bass bar replacements and crack repairs. Strad very likely  used his punch tool to get consistent thicknesses over large areas of tops but they often show thinner centers and especially nearer bass bar posiiton. If you add a tenth or two in the central part the circle easily becomes better match than chain or parabola.

You'd better analyze backs that are much less prone to deformations and arching corrections. The back of the Brusilow shows the inside of back having quite noticeable anomaly (on left upper side) with abrupt inflection point and bump starting halfway from center to edge.

[gorge riam]

@HoGo ... If you add a tenth or two in the central part the circle easily becomes better match than chain or parabola.

Circle, chain and parabola are quite the same for the area up to the inflection point, see diagram "circle chainline parabola".

circle chainline parabola.pdf

[Torbjörn Zethelius]

19 hours ago, gorge riam said:

 Maybe it is useful for someone to compare the various mathematical arch shapes (circle, chainline, parabola) with an actual example. The first foto shows a cross arching of a violin top plate (Strad-Poster: GGG-Brusilow). A circle and a chainline is fitted to the actual internal arching. Up to the inflection point (maximum gradient) there is little difference between the various shapes.

the diagram shows how much a chainline and a parabola deviates from a circle. 

As I understand the "inside first with curtate" method (revived by Torbjörn?) has the main advantage that the arching in ALL directions can easily be controlled by a chain up to the inflection point. And this is definitely not possible from outside. right?

comparison circle - chainline.pdf 38.69 kB · 13 downloads circle chainline parabola.pdf 30.69 kB · 11 downloads

I don't do the "inside first with curtate", I don't know what you mean by that? I don't use curtate cycloids at all to be clear. They're not necessary for the way I work. I prefer using a chain for the internal arch as your image illustrates perfectly.

The delta diagram I don't understand so I can't comment on it. Perhaps you can explain it a little more? The other image is more clear. Had you fitted a parabola to the internal arch instead of a circle it would have shown the close resemblance between the catenary and a parabola. Only when I work on the thicknesses (on the outside of the plates) I tend to visualise a circle because it's easier to visualise than a curtate cycloid. In my method focus is mainly about creating an acoustically designed internal space. The external as I said are the thicknesses. That's the difference between the inside first versus outside first. I hope that is clear.

[gorge riam]

@Torbjörn Zethelius... I don't do the "inside first with curtate", I don't know what you mean by that?

Sorry I meant to say "inside first with chainline"

@Torbjörn Zethelius...Had you fitted a parabola to the internal arch instead of a circle it would have shown the close resemblance between the catenary and a parabola....

Exactly this is shown in the diagram:

The blue curve shows how much a fitted parabola differs from a fitted circle. And the red curve shows how much a fitted chainline differs from a fitted circle. The horizontal axis represents the distance from the centerline of the top plate. The vertical axis does not represent directly the chainline or parabola, but rather the DIFFERENCE (delta) between chainline and circle, parabola and circle.

E.g. in 30 mm distance from the center (cross arch middlebout GGG-Brusilow top) the parabola differs delta=0.07 mm and the chainline delta=0.16 mm respectively from the circle. Distance 30 mm is about the inflection point for this example.

[Michael Richwine]

.

[David Beard]

Oops.  I thought this these was about beginning making?

Looks like folks got sidetracked into designing arching, without templates.  Not such a simple beginner thing.

 

Approach the channels as having a bottom, in set a determined amount through each bout.  The distance is constant through the main part of each bout, but can be different and usually is in the upper, center and lower bouts.  At the end blocks, the distance can be chosen differently if desire.  But then, a smooth transition must be made.   Through the corners, these  bottom lines are joined smoothly and minimally.  (Bent spline version of smooth no matter how actually worked).

Use radii with diameter proportioned for the rib height to guide the curves from the bottom of the channel toward the edge, and later toward the center.  These two radii most necessarily the same.

Both the channels and the long arch 'bound' the arching and must be settled ahead of the arching they bound.

Approach the long arching like the hull of a ship.  Mark off even distances along the length and set guide heights at these, or at least in relation to them.  I use 9ths, but the choice is largely arbitrary.  This method can be used to set any long arching profile desired.  I prefer what I believe was classical practice.  So I give the top a long flatish region that just barely crowns, extending around the bridge and toward or even through the corners.  For the back, I use a much shorter flatish area just in front of the bridge.

If you like, classical plate heights can be interpreted as a portion of side heights.

The curvature of classical arching is mostly NOT simply circular.  Though, there are some examples of Amati instruments and perhaps other like Peter of Mantua perhaps at times using circle arcs to guide fixed curvature (or fixed in parts) for the arching.   More generally, the curvatures are smoothly changing through the arching, and the curvatures tighten as the decent -- until they flatten and transition into the channels via a recurve.

These changing curvatures are again 'spline smooth' (which Marty likes to see in all things).

However, that does not mean free.  Like traditional boat building, I use controlled points, joined and connected into a smooth surface by the artisan's traditional spline smoothness.   

I use '1/2 fall in 2/3 run' to set my control points.  This applies with long arch, and with cross arches at the main bout lines.  

I've demonstrated, defended, and explained these methods elsewhere, so will not repeat now.

These methods readily provide very good modeling of the full range of classical examples.