So my fault, I misspoke. I said the ratio of ribs to body when I should have said ratio of sides to body. What is correct is " the old tradition was to make the side height 1/9th the body length in violins and violas, 1/6th in cellos. Variations when found will be based on including or excluding the plate edges in the calculations."
As noted, different instruments might use a different ratio, or variations using the same ratio could be achieved by including or excluding the edge thicknesses.
With Cremona violins, we overwhelming see a 1 to 9 ratio, calculated including both edges. The example of Lady Blunt above is clean and straightforward. The back lies pretty well in a straight line, and the rib height and edge thicknesses seem pretty much fully intact. We see the expected full height at the bottom block and corner blocks, with the expected reduction heading to the neck.
The concept of edge height is complicated by wear damage and repairs, but also by the notion of a 'working edge' that was higher than the 'final edge' in Cremona work, and further by the possibility that Cremona makers didn't always work the edges to the same plan choices.
However, to make a rough calculation for violins, edges are about 1/8 the rib height or equivalently 1/10 the side height. So, given a body of 354mm, the normal Cremona choice of (1 to 9, including both edges) predicts the sides to be ~39.33mm, with the edges ~3.93 and ribs ~31.47. Of course, using ratios and dividers as the primary measure in the workshop is not going to exactly match these numbers.
It's valuable to recognize that modern methods using standardized rulers and numeric precision calipers will produce different kinds of characteristic errors compared to a workshop relying primarily on ratios between parts, calculated mechanically by dividers and related tools.
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I examine these sides to body ratios using software to overlay a scalable graphic of the ratio onto the example instruments.
The overwhelming majority of Cremona violin examples show the maker choosing a 1 to 9 ratio, and including both edges in the calculation.
Even with his otherwise experimental 'long violins' we still see Strad using the common (1 to 9 ratio, including both edges) choice.
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For violins, we can see that a ratio choice of 1 to 9 for (Sides including both Edges) to (Body) was 'normal' in the Cremona tradition. It also wouldn't have been normal for them not to experiment some with this choice. And indeed, we can see some examples of that in the Sides to Body choice.
To be consistent with their practices with other features, we would expect to see Cremona makers experiment more often and more readily with the specific application of the ratio first, and then later resort to change the actual choice of ratio used only if needed. But we would not expect to see them ever abandon the basic principals and range of choices traditionally used in a feature.
Notice, that including/excluding the edges leads to three distinct options in applying a ratio for the sides and ribs. You can 'include' both edges. You can 'include' only one edge. Or, You can 'exclude' both.
'Including' edges in the calculation will give a shorter rib from the same ratio compared to 'excluding' edges. So the 'normal' Cremona choice of including both edges in a 1 to 9 ratio for violins gives ribs on the short side of what's possible using a 1 to 9 ratio.
To experiment with taller ribs, a maker could choose a different ratio like 1 to 8, or 1 to 7. But, we don't actually find examples of this. Observing the broader practices in Cremona making, we can see a preference to first experiment by varying the specific application of a ratio, rather than the ratio itself. So in example, a maker could stay with the 1 to 9 ratio choice, but experiment with taller ribs by excluding one or both edges from the calculation.
And in fact, in the later Cremona generations we see some experimenting with a taller violin rib created by choosing the 1 to 9 ratio, but excluding one edge when applying the ratio.
Did they also experiment with shorter ribs?? This turns out to be a bit less secure turf for us to examine. After all, repair work and damage can end up shortening ribs. So when we see abnormally shorter ribs, how can we tell if it was made that way intentionally, or arrived at a lower height by some accident? One thing that might suggest ribs purposefully made shorter is if we found a group of shorter rib instruments that we can also see as distinguished or grouped together in additional ways.
Unfortunately, I haven't yet identified any clear cut case of purposefully shorter ribs in Cremona work. But there are some Ruggieri example that I suspect might represent an experimentation with a shorter rib choice. However, consistent with Davide Sora's concerns, these same instruments tend to also show more distortions of the sides and the line of the plates, making them less certain as clean examples of anything.
The normal Cremona choice for violin ribs includes both sides, and therefore is the shortest choice you can get from the traditional 1 to 9 ratio. Thus, to experiment with shorter ribs while staying within the traditional framework of ratio choices, a Cremona maker would need to resort to a different ratio, namely 1 to 10. Here is one of the several Ruggieris I suspect might represent an experimentation with choosing a 1 to 10 ratio.
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With violas, we of course see freer diversity in the ratio and inclusion/exclusion choices, but still a 1 to 9 ratio is clearly the normal choice.
( 1 to 9, including one edge)
( 1 to 9, including one edge)
( 1 to 9, including both edges)
(1 to 10, including both edges)
( 1 to 9, including both edges)
( 1 to 9, including both edges)
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With cellos, we see a 1 to 6 ratio, and compete freedom about inclusion/exclusion.
( 1 to 6, excluding both edges)
( 1 to 6, including one edge)
( 1 to 6, including one edge)
( 1 to 6, excluding both edges)
Andreas,
I know this is a bit tangential to your quest. However, it illustrates how you could if you wish conduct your experiment with the traditional Cremona framework of choices. You could for example choose a higher ratio like 1 to 10, 1 to 11, or 1 to 12. Then narrow that down by your choice of inclusion/exclusion of edges.
It does look like choices shorter than the normal 1 to 9 might well need some kind of compensating reinforcement for stability.