In the early days of the guitar it had tied gut frets, it was microtonal by nature and you could move the frets for different temperaments. Then in the 19th century things changed and the guitar got fixed metal frets, ever since people have been trying to figure out how to have the benefits of both. 1852 is the first attempt that I know of.
It is still worth noting that the microtones used by Angine de Poitrine are usually just transient notes, and could instead be played portamento with smooth transitions between the notes (eg on a fretless board) in most situations. It still sounds really cool, though, and certainly a technical and musical accomplishment. But the music itself still follows the usual patterns closely.
I'm a bit late on the reply, so to add to what has been said by AlecSchueler consider the piece I linked above being played on that guitar slung mini harp.
It's a cover of an English prog rock piece, the titular Discipline from 1981 by the band King Crimson with the then line up of a drummer's drummer, Bill Bruford, and three top form guitarists, Robert Fripp (sitting on chair), Tony Levin (Chapman stick), and Adrian Belew [0].
One comment on the linked performance is simply: 3+2/4 vs 2+3/4 vs 9+8/16 vs 4+4+4+5/16 INSANE
So, ... it's an instrument that allowed for a credible attempt at covering three "insane" polymeter prog rhythms by a single performer.
I'm old enough to have got the album when it first came out- looking for a live performance I stumbled over a recent breakdown look back at a peer album track: Frame by Frame [1]
A harp can have more than 6 notes ringing out at a time. It's also a different instrument and if you've trained to play harp then a guitar is useless for you.
You only have to put your finger somewhere in between two frets to get a particular note, so you can play more than the tiny handful of chords that can be played on something like a violin.
There are non-fretted guitars but they are rare, and I think early banjos were not fretted.
I can play chords on a violin or viola and strum them. Keeping a four-finger chord perfectly in tune in rapid changes is really hard (near impossible) without frets.
There are those who say it isn't a chord until you have 3 notes. I'm going to skip the complex music theory behind the arguments (I haven't studied them enough to understand much less form an opinion).
Of course in most music contexts there is more than one instrument playing and so the others can fill in the missing note making a full chord. Only a "one-man-band" really feels the loss.
Every jazz player knows you can drop the fifth, and the root too if the bass is filling it in. That gives your fingers room to add even crazier extensions
in college a good friend was a very good Oud player (plucked, some number of strings.... more than 8? I forget), and it definitely sounds different from guitar due to less sustain. Clearer notes and chords, but they don't linger as long or loud.
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