Woah, so cool when a topic I was going into in depth gets to HN.

I'm a relatively new adult beginner on the violin, and one of the fascinating (and extremely difficult) things about un-fretted string instruments is the player has the freedom to shift the tuning around to fit the context. On the violin, we normally play melodies and scales using Pythagorean tuning (which is actually a misnomer as Pythagoras didn't invent it, the ancient Mesopotamians did), which is based on the circle of fifths and leads to wider whole steps and narrower half steps than equal temperment tuning. But then for double stops (i.e. chords), and especially when playing in a string quartet, just intonation, which is based on the harmonic series, is used so the notes sound concordant. This page describes all the different tuning systems a violinist may use, also including 12 TET when trying to match a piano: https://www.violinmasterclass.com/posts/152.

This video shows how challenging it can be when trying to adjust intonation when playing in a string quartet: https://youtu.be/Q7yMAAGeAS4 . Interestingly, the very beginning of that video talks about what TFA discussed that when you tune all your strings as perfect fifths your major thirds will be out of tune.

I'll also put in a plug for light note, an online music theory training tool that was mentioned on HN a decade ago: https://news.ycombinator.com/item?id=12792063 . I'm not related to the owner in any way, I just bought access a few years ago and think it was the first time I really understood Western music theory. The problem with music theory is that the notation is pretty fucked up because it includes all this historical baggage, and lots of music theory courses start with what we've got today and work backwards, while I think it's a lot easier to start with first principles about frequency ratios and go from there.

Other notes (pun intended!): The violin is great for learning music theory because you can actually see on the string how much you're subdividing it - go one third of the way, that's a perfect fifth, go halfway, that's an octave, etc. Harmonics (where you lightly touch a string) are also used all the time in violin repertoire. Finally, the article mentions Harry Patch, but you should also check out Ben Johnston, a composer who worked with Patch and was famous for using just intonation. Here is is Amazing Grace string quartet, and you can really hear the difference using just intonation: https://youtu.be/VJ8Bg9m5l50