[ofalkaed]

Try the wikipedia pages for Equal Temperament and Musical Temperament, they explain all of this.

Here is a 1688 Stradivari[1] guitar with fixed frets and a EDO octave, they were reasonably common by that point. Much of the information regarding this is looking at the fixed frets that many lutes and guitars had applied to their soundboard and comparing that to how composers used those fixed frets, either the tied frets adhere to the scale of the fixed frets or they are out of tune. The history of EDO/ET in fretted instruments goes back to at least Vincenzo Galilei[2] (father of Galileo) who developed the rule of 18 for fret spacing. If memory serves we have a few early steel string instrument (cittern, bandora, orpharion) from around ~1600 with equal spaced frets and this orpharion[3] looks it but it is difficult to tell from that photo. Going back earlier things get more difficult since we have so few intact and unaltered instruments but we do have a fair amount of ingravings and art plus writing on the topic such as Galilei's.

There is a paper going into great depth on all this that is just out of reach in my memory and I can't seem to trick the search engines to give it to me, I will post it if I remember/find it. No time to dig more right now.

[1]https://lsaguitarshop.substack.com/p/gear-27-the-stradivariu...

[2]https://en.wikipedia.org/wiki/Vincenzo_Galilei#Acoustics_and...

[3]https://i0.wp.com/earlymusicmuse.com/wp-content/uploads/2017...

[moefh]

> I will post it if I remember/find it

If you remember and have the time, please do! (And thank you for the links you already posted).

I see now that everything I read about this was way too focused on keyboard and violin, since I had never heard any of this about fretted instruments. I'm glad I get to correct a bit of my understanding, so thank you. Now I'm left wondering about wind instruments.

[ofalkaed]

Western theory is focused on the keyboard with violin as second fiddle, the rest of the instruments do their own thing unless they are forced to kowtow to a piano or violin. Each instrument is ultimately tuned to the physics which dictate how it makes sound and this is part of why our tempered 12TET works and why we see the rise of the big orchestras of unlike instruments with the move away from meantone, it provides a compromise which works quite well for all instruments with the exception of the brass (with the exception of the trombone) who are forever out of tune (sort of).

Part of the reason beginners sound bad is because most instruments have to bend notes to be "in tune," I can teach anyone to play a chord on the guitar and get them having each note sounding clearly in a couple of minutes but my DMaj will sound better than theirs simply because I have played that DMaj thousands of times and my fingers have learned to adjust the pressure on each string in just the right way to make it sound "right" just as the woodwinds learn to bend certain notes and the brass learns to live with being out of tune.

Also part of why the lute became such a dominant instrument is that it could retune in ways other instruments can not, which was a major advantage for the working musician back in the days when every city had its own idea about tuning; nudge a few frets, retune a few strings and accept that certain notes were now out of bounds and you could play with anyone like you were playing in your native tongue. As tuning became more standard the lute started to die.

Meantone Temperaments on Lutes and Viols might be of interest to you, it is aimed towards lutenists and violists but has some more general stuff as well and I think does a good job of showing the compromises the lute (and viol) had to make in moving away from equal temperament.

I don't really think brass is forever out of tune, I love the brass and used to play trumpet but the brass section is more under the influence of the physics of its instrument than anyone but the pianist but the pianist is "in tune" because western theory is built around the keyboard.