> The modern piano mitigates this by having the hammers strike strings at a position that avoids exciting the 5th harmonic... I think it's actually the 7th har

> The modern piano mitigates this by having the hammers strike strings at a position that avoids exciting the 5th harmonic... I think it's actually the 7th harmonic that pianos avoid, if I remember correctly. (I guess one could verify this by measuring the hammer position on a piano string and figure out if it's hitting the node at 1/5 of the string length or 1/7th). This random google result agrees with me: https://pages.mtu.edu/~suits/badnote.html https://pages.mtu.edu/~suits/badnote.html I have a theory that pianos and guitars have become the dominant musical instruments of the last hundred years or so simply because you can get away with mis-tuning them and they still sound pretty good. (I once had the opportunity to play a 15-tone equal tempered guitar, and it still sounded good, which led me to believe that you can get away with almost anything with a guitar.) Which isn't to say that guitars don't sound better in just intonation, they do. On the other hand organs and accordions, for instance, sound amazing in just intonation but not nearly so good in 12-tone equal temperament. The notes (especially thirds and sixths) clash with each other too much. It's tolerable, but not great. I've been working with a group of people converting guitars to 41 tone equal temperament; they have a nicer third (off by about 5 cents instead of about 15) and a closer 4th and 5th (off by about half a cent instead of 2) and can approximate 7-limit just intonation intervals pretty closely. The trick to make it playable is to omit half the frets, so it's fretted for 20.5-tone equal temperament, and any notes not available on one string are available on the string next to it. It sounds like it shouldn't work, but it does. https://kiteguitar.com/ https://kiteguitar.com/