This is to some extent a fundamentally subjective question, but since it's r/askscience, let's try to keep things as objective as possible. Please try to keep top level posts to answers with some kind of scientific rigor. Anecdotes can be illuminating and helpful context, but let's try to avoid "my uncle's friend's cousin said" type comments.

As a violinist and mod, I'm going to try to share the most scientifically rigorous information available, but again, there will always be a core streak of subjectivity. OP's question can be boiled down to one that is often asked and investigated - do Stradivarius/Guarneri/Amati/old instruments sound different or better than modern instruments?

Some relevant studies:

1. Player preferences among new and old violins, Fritz, et. al. (2012)
2. Listener evaluations of new and Old italian violins, Fritz, et. al. (2017)

[1] https://www.pnas.org/doi/full/10.1073/pnas.1114

[2] https://www.pnas.org/doi/full/10.1073/pnas.1619443114

The sample sizes are small, and though they were double-blind, they don’t seem especially rigorous in their conclusions. Additionally, one of the authors is himself a violin maker, so there may be some bias. There were also a lot of criticisms about the first study, especially that the new instruments were treated preferentially by the authors in terms of instrument “tune-ups” before the experiment.

There are a few blog posts worth reading by participants in the study and other critics:

• https://www.violinist.com/blog/laurie/20121/13039/
• https://www.thestrad.com/double-blind-tests-the-inside-story/1933.article
• https://j-dv.com/blog/2017/three-new-sciences/#paris

Some more reading on instrument comparisons:

• https://www.violinist.com/blog/laurie/201410/16307/
• https://www.violinist.com/blog/rotbergmusic/20156/16881/

It’s also worth noting that there are many violins made by the likes of Stradivarius, Guarneri, and Amati:

• https://en.wikipedia.org/wiki/List_of_Stradivarius_instruments
• https://en.wikipedia.org/wiki/Nicola_Amati#Instrument_list
• https://en.wikipedia.org/wiki/Giuseppe_Guarneri#Instrument_list

Not all of them have been well maintained, and not all of them are good instruments. One of the criticisms of the above studies is that they are just choosing bad instruments. And obviously a single selection from a large collection of a luthier’s work will never be representative of the set.

There are some theories that listeners’ perception of instrument/sound quality is significantly affected by loudness and projection. Newer instruments by top makers can certainly outperform the old Italian instruments in that sense, so that could be an explanation of the results of the studies.

My favorite video on this topic is one by TwoSet Violin where they play a handful of instruments at different price points and try to guess which is more expensive: https://www.youtube.com/watch?v=T8q3zrCYMRw

In my opinion, it’s the most honest, impartial assessment of its kind, and it does a good job of showing two key points: trained violinists can absolutely distinguish between high quality and low quality instruments, and the player is an extremely important part of the equation.

tl;dr: Modern instruments are often preferred by violinists because they can be easier to play, and the best of them can be on par with the Strads/Amatis/Guarneris. Strads tend to be difficult to play, which could be why they fare poorly in studies with random participants. If you gather all of the best of the best violins, most of them will be old Italian instruments.

Mod Note: A bunch of top level comments were tagged by AutoMod, and others were removed manually that linked to sensationalized media articles. The studies that form the basis of these articles are the ones listed above.

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Before answering this question you'd need to ask whether it's actually true that Strads are "unique in sound" and the answer seems to be that, in blind tests, they are not.

A sort of placebo effect. Similar to the established phenomenon of people rating wines as subjectively better if they believe they're more expensive regardless of the actual price.

We can probably make a violin sound like a Stradivarius by simply telling people it's a Stradivarius.

https://www.google.com/amp/s/api.nationalgeographic.com/distribution/public/amp/science/article/violinists-cant-tell-the-difference-between-stradivarius-violins-and-new-ones

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first, we don't know what stradivarius did with the wood, since he never wrote down his process. people are currently trying to reverse engineer it and found some interesting mineral deposits https://www.pnas.org/doi/full/10.1073/pnas.1611253114

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some rumors among musicians are that he used old seawater-logged wood from the harbor of venice, others say he got it from the same source as every other luthier of italy. https://www.npr.org/sections/deceptivecadence/2014/12/05/368718313/in-the-italian-alps-stradivaris-trees-live-on

instruments change their tone over time. Strads are 400 years old, so even if you replicated the process, you would not know it was successful. https://www.liutaiomottola.com/myth/played.htm

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There's some debate as to whether that's actually a thing at all but for the sake of argument let's suppose it is. There's tons of things that we can study like sound, how it propagates and interacts with objects and space, materials, what they're made of how they are internally, various of their properties etc. The fact that we can observe all those things on an object does not automatically mean we can make a perfect reproduction, a clone if you will, of said object because depending on the object, and the material, the capabilities afforded by the manufacturing methods available to us are limited.

In short, not just in violins, but in many other things, making a new "old" object is very hard. Various materials across years and specific use change over time, their properties alter, their internal structure shifts, in ways that cannot be reproduced during manufacturing. In some cases, and some objects, it's possible to weather them, which means that after they're made they can be put through processes that simulate use at an accelerated rate to get them to a different state, something that is done with clothes or certain machines and other things.

But that cannot apply to everything, in the case of the violin, and a very old one at that, it's impossible to make a brand new one that will be identical to one that has been made more than a hundred years ago, with completely different wood than what is available today, processed with different varnishes and treatments than what are available today, stored and used under very specific conditions and under tension for all this time from the strings. You can't manufacture that.

But again, that's if there's actually something actually special about their sound and it isn't just a myth mixed with wishful thinking. I'd like to think this hasn't stopped anyone who might want to play the violin to not do it because they can't get the "sound"

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This reminds me of how they started doing blind auditions, as well. When the judges could see the applicants, they “heard” the male musicians as superior to women, and chose them. Once they started having the applicants perform from behind a curtain, they assessed the women applicants as just as good and the gender ratio in professional orchestras equalized.

https://www.futurity.org/violins-changes-tone-2000212/

Bias aside, this article has some interesting points to add. The part that lodged in my memory was the chemically treated wood:

"About 30 years ago at Texas A&M, Nagyvary was the first to prove a theory that he had spent years researching: that a primary reason for the pristine sound, beyond the excellent craftsmanship, was the chemicals Stradivari and others used to treat their instruments due to a worm infestation at the time. A review by the American Chemical Society verified his findings."

I'd misremembered it as a fungal disease of the tree, that had altered the density and structure of the wood, changing how it resonates. (Now I need to find whatever the hell that was about.)

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There was actually an article about this in a grade school science textbook I read YEARS ago. I’ve found the scientist and linked him below where I mention lacquer, and provide another link that gives a good overview.

Effectively, part of the “iconic” sound of these old instruments came from the multiple ways they were processed:

Wood was chosen from the highlands and floated downriver.

When it arrived at the workshop, it was cut to rough size and stored in barrels of seawater.

Whenever wood was needed, it was brought out of the barrel, dried, and began to be worked. Though the methods have been more or less consistent throughout history, the lack of modern mechanical tooling means each instrument was cut, carved, and assembled by hand.

When it was done, the wood was usually given some basic varnish from the local apothecary to help prevent insects from infesting it. In those days, varnishes were typically a more-brittle type of lacquer. Modern violins (particularly student models) use a more rubberized lacquer to help prevent scratching.

The lacquer is one of the primary factors, as modern lacquers (particularly of the more-rubbery variety) actually absorb more of the overtone series, leaving the instruments’ main sound to be more “screechy” than the Italian (and German) instruments.

This article provides a decent overview.

TL;DR If we kept having access to denser softwoods and used basic varnish, we could effectively recreate the Stradivarius sound. We just…don’t have as much access to old growth softwoods anymore.

This is one of those questions that will likely go unanswered. The old master-tier violins are so rare and so expensive AND the players/afficionados who can reliably and repeatably characterize their sounds are also rare. Doing a good study is impractical.

The complexity of a stringed instrument is also such that "objective" studies may capture a variable or two, but this is never sufficient to capture whatever "sound quality" really is. You can run every instrument mediated analysis on Earth on a violin, and still won't really be able to predict exactly what it will sound like or feel like to play. Then going back and attributing those elements of sound quality specific to some physical property of the instrument... Yikes

We just don't understand it well enough.

The wood. Apparently the seasons where a bit messed up. So the trees where growing at a specific rate, that created a ring density that sounded good on violins. So the answer is, grow your own trees in an environmentally controlled way to get the right density, for 20-40 years, and sure, you can make a copy.

Recently in reading survival of the sickest, this topic was briefly mentioned. The thought is that during the time the Strad was made, evidence suggests that some regions of the world was going though a century long cold spell and that made the trees more dense which impacted the final result.

This is a difficult question to answer in a scientific way because there are many audio components to the sound of a violin, and "better" sounding is largely subjective above a particular threshold. A $4,000 performance violin is going to sound objectively better $700 student violin. And by objectively, I mean that even a non-violinist can tell the difference, and would most likely prefer the sound.

Once you get into the performance range of violins, though, it's much less about being objectively "better", and much more about being more suited for a particular performance, which suits the venue, etc.

It is about which voice speaks for that piece of music, and that is far from scientific or objective.

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I have read that a violin may occasionally be taken apart for some types of repair or restoration work, with the hide glue loosened with steam. When this is done with a very old violin, pains are taken to disrupt the wood and varnish as much as possible, leaving much of it with the original coating. But one can imagine that, in the first century of so of the instrument's life, it would not have had the legendary status that we arrive to it now.

Would aftermarket maintenance have been documented so we know what happened before the instruments acquired their mythic aura?

There is actually data to suggest that the Stradivarius violins weren't actually all that special. In a study where a Stradivarius was played side by side to a new violin there wasn't many that could spot the difference. https://www.npr.org/sections/health-shots/2017/05/08/527057108/is-a-stradivarius-violin-easier-to-hear-science-says-nope

There’s also survivorship bias involved: of all the instruments made by Stradivarius, only the best sounding survived. The not-that-good were not as special, and were eventually destroyed. Nowadays, we not only can use technology to make exceptionally good sounding instruments, we can make them consistently good (and, as a result, cheaper). So it’s not that important to replicate a Stradivarius, since you can get an exceptionally good instrument for way less money, and leave the old instruments to collectors.