There’s probably a PhD length answer that involves the transition from Renaissance to Baroque music, the plagues of the mid 17th century and the Little Ice Age.

There’s probably a PhD length answer that involves the transition from Renaissance to Baroque music, the plagues of the mid 17th century and the Little Ice Age. Violins have always been identified as being tuned in 5ths to the best of my knowledge, but the features mentioned above helped them out-compete other stringed instruments over a century when the fashion in music favoured those features. Some of them are - the construction favours better projection over the kind of mellow sound of a viol, the rounded bridge allows for better virtuosic playing rather than chords. Music from the late 16th to the time of Monteverdi had a tradition of florid embellishments (diminutions) which favour a more responsive instrument, like cornetto, recorder or violin. The plague of 1630 in Venice is thought to be a major factor in the decline of the cornetto, so the violin had an opportunity to fill that gap then. There’s also a change in the theory of harmony around this time from the Guidonian hand and hexachords to a more complete chromaticism. As someone’s already pointed out, fifths make for a very convenient arrangement of tones and semitones in order to play a scale. I suspect hexachords fit more naturally (!) across strings tuned to fourths - you would have ut-re—mi on the hard, soft and natural hexachords at your fingertips. As music theory moved away from this understanding of harmony, it would have also been more suited to the violin over the similar instruments tuned to fourths and thirds.