That sort of confidence has been earned by the way Strads have continued to generate their glorious sound through the centuries. It can also, however, be learned, as players observe and appreciate the way their predecessors and teachers have loved their own instruments. And that is one reason why the Joachim-Ma is such a fascinating violin to study: it forms a link in the great chain of virtuosi and pupils.

The superiority of Stradivari’s violins was, famously, first established in one series of concerts, given by Giovanni Battista Viotti at the Concert Spirituel in Paris in 1782, nearly 50 years after Stradivari’s death. Every violinist in Viotti’s audience wanted to play like him. That meant a number of things – he would have many followers – but one of them was that they wanted, like Viotti, to play on a Stradivarius violin (in his case, a particularly glorious example from 1709 now owned by the Royal Academy of Music in London).

One of Viotti’s disciples, Pierre Rode, whose name is associated with at least three Strads, taught Joseph Böhm, a Hungarian violinist who by the 1820s was playing his 1733 Khevenhüller Stradivarius in Vienna. Böhm led some of the first successful performances of Beethoven’s late quartets, but later concentrated on teaching. So it was that, around 1850, the 9-year-old Joseph Joachim, another Hungarian, came not just to study with Böhm, but also to live with him. It was with Böhm that Joachim learned to love chamber music; he surely learned to love Strads too. He bought the Joachim-Ma when he was only 18, six years after leaving Böhm’s care, and played it for over 30 years.

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Joachim passed on his love for Stradivari. An 1899 concert to celebrate the diamond jubilee of his first appearance, with much of the orchestra comprised of former pupils, has passed into legend: 44 Stradivarius violins playing together in one performance. Richard Burgin was not a member of that orchestra – he would have been only 6 – but he did go on to study with Joachim and – yes – went on to own his own Strad, the 1705 Joest, while concertmaster of the Boston Symphony Orchestra. His pupil Si-Hon Ma, another violinist and teacher, bought the Joachim-Ma in 1967, generously leaving it to New England Conservatory, which is now selling it to establish a scholarship; his is the second name associated with this great violin.

It is a wonderful chain, and there is one final link that I can’t resist highlighting. Joachim is probably most famous now as the friend and champion of Johannes Brahms, giving the first performances of many of his great works. Among them is the 1887 Double Concerto for violin and cello, composed by Brahms specifically as an olive branch to Joachim, after they had fallen out during the latter’s divorce. That piece was itself inspired by a concerto written by Viotti, the Italian violinist with whom this lineage of teachers began. The connection is not perfect, however. Although Joachim almost certainly used the Strad headed to auction at the premiere of Brahms’s earlier concerto for solo violin, by 1887 he had probably exchanged that for one made the following year.

It can’t be all in the minds of violinists. Luthiers have searched for Stradivari’s secrets for almost as long as they have copied his violins. Once Viotti and his successors established the supremacy of Stradivari’s model – in particular the greater tone produced by its flatter belly – it was natural that every maker would follow his lead. They produced violins that perfectly copied the dimensions of Stradivari’s violins – and which could even be mistaken for Strads by all except the most expert – but the instruments that resulted could not, in the end, compete with Strads for tone.

Was it just that the copies needed to age? Even in the 18th century writers were proclaiming that violins needed a period of 50 or 100 years before they reached full maturity. That is one of the reasons why Stradivari’s violins were valued rather lower than the older Amatis in the years immediately after his death. Those 19th-century copies of Strads are now, however, fully mature and they still can’t match the originals. There is clearly more to their maker’s inimitability than that.

Soon attention turned to the aspects of a violin’s construction that could not be so easily reverse-engineered, most famously Stradivari’s varnish. More ink has been wasted on Stradivari’s supposed secret formula for varnish than on any other aspect of the violin-maker’s craft. Yes: it is possible that a poor varnish might stiffen the wood of a violin to the point where it spoils the tone. It is also possible that makers without an innate understanding of their materials could gravitate to such a varnish, simply because it might be quicker-drying or harder-wearing. The reverse, however – the idea that good varnish can somehow magically enhance the tone of a violin – is much harder to credit. A more recent version of this theory is at least based on scientific analysis. Scanning electron microscopes appear to show that Stradivari used volcanic ash as a sizing agent on his bare wood before applying his varnish. To some modern violin-makers, this is the answer; to others, it is a total red herring.

So what about the wood? Englishmen in the 19th century were keen on a theory ultimately blaming Napoleon for the tonal deficiencies of newer violins. They held that Stradivari had used wood rejected by Venetian shipbuilders: spruce and maple that had been felled in the Alps, floated down the Po to the Venetian Lagoon, left soaking in seawater for a while and then, for whatever reason, not used in the Arsenale but instead carted back inland to Cremona for violin-making. Somehow that seawater bath had given Stradivari’s wood inexplicable acoustic properties. Why could subsequent failure be blamed upon Napoleon? Because he had built roads into the Alps that meant the wood remained dry. Nowadays, researchers are more likely to say that Stradivari’s wood had clearly been treated with some kind of preservative, with a similar supposed effect. Another almost diametrically opposed theory holds that Stradivari’s wood had been attacked by some sort of fungus, one that again gave it almost supernatural characteristics.

Then we have historical fact. Europe went through a mini-Ice Age in the 16th and 17th centuries. Trees grew less strongly, their rings are closer together, and they provided the denser wood Stradivari used in his instruments. You can see it in the grain of their bellies. That is certainly the sort of thing you can imagine affecting a violin’s acoustics. It can’t be the only answer, however. Many of Stradivari’s copyists have used wood from that era as part of their attempts to match him.