David Beard

Sorry to hear this.

I think the main difficulty with improvement through acoustic study is that most of the efforts transform into making measurables more specific. But, it seems 'good violins' embody the opposite of that. They have broader and less specific response.

Round and round again we go...

To give a somewhat flip answer: all parts.

Of course, we don't know if the wooden calipers in the artifacts are older or younger than other tools. I would tend to guess they not from Ceruti's time but earlier. However, we don't know. I made a copy of those years ago. I've found my copy of the calipers very useful. They are simply too flexible. However, I do use them to feel how the thicknesses is changing. I just hold them closed and slide the position around. It gives a very sensitive read of change.

Yes. It is not a simple spiral. The curves consist of a limited number of circle arcs with the centers not arranged in a simple way. As result, the gap from the eye out is never decreasing, proceeding somewhat stepwise. Just as you show.

Phi is a red herring. If you are wanting to find phi, I you will find places where you think you see it. But you won't find any old Cremona features where it appears consistently, where it was actually used. Cremona use of ratios is usually the use of some pattern or range of ratios for a feature. So, for example, the starting circles for the upper and lower sound hole eyes in Cremona examples are always in a ratio that makes the upper eyes 'a part' smaller than lower. From the Amati family through Bergonzi, every Cremona example shows this. The early generations made the sizes closer together, so the ratios are higher numbers like 5 to 6 or 8 to 9. Later generations used lower number ratios like 3 to 4 and 2 to3, making the difference greater. But, the point is that all the generations picked this ratio from the same range of 'a part less' ratios. The used 2:3,3:4,4:5,5:6,6:7,7:8,8:9,... The always could have bit never did use phi for this. Likewise, their ratio range for body width to length was always 'length a part less than double width'.. This gives the range 2:3,3:5,4:7,5:9,6:11. The first two of those happen to correspond to two of the early fibonacci ratios, but the whole of the Cremona series shows they didn't have phi in mind. There's no reason the couldn't have, but they simply didn't. Similar, in no features of Cremona work did I find any of their consistently used overall patterns aim at phi. Their ratio uses appear to just be pragmatic working habits, a way to features and to repeat choices. There does not appear to be any idealism or philosophy lurking in their choices of ratios.

Homemade wood one is easy to make and easy to use. They work very well.

But this is inescapable. The best most people can manage is to follow proxy guidance, since they don't perceive the quality directly for themselves. You can call this 'tricked' if you like. But it remains the best option for most. Price is one of the proxy guides. And of course it's imperfect.

Wine, violins, strings, art These things are fake for most. So are science, logic, and math. Most people can't track the truth of any of these things. At the highest levels of anything, depth of perception comes into play, for some. But for most, that perception is either absent or faked. Majority blindness doesn't the truth of extra perception known only by a few. High price is an imperfect proxy for actual perception. Is a bow a good player's bow? Only good players can answer that. But good dealers have many proxies that enable them to present likely candidates to real players, and the many clueless others. It is intrinsically an elitist scenario. Does Sartory make more good playing bows than most? Yes.

From an historical perspective, it seems to me that the back outlines are more 'chosen' clean designs. The top outlines have a greater aspect of 'following' whatever vagries are introduced by the unsquareness of the sides, which in classical work can be very significant.

There is a theory that he could perhaps have worked from one mould. On the other hand, there is no evidence to support that, only the conjecture that it be a possible thing. We don't know. He might have used twenty moulds. The thing is, we don't have them. We're only guessing.

Sure.

This kind of micro layer analysis is the only way to improve our understanding

Some modern makers use the same front to back. Some folks believe the famous instruments of old Cremona were originally made that way, but changed over time. None of those survivng old instruments currently show equal top and back archings. The tops are quite different, particularly in the long arc along the center line.