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It couldn't add a quarter tone between each semitone on the guitar, it looks like it's just duplicating the lowest 2 or 3 frets on the bridge side.
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Right, but I'm thinking if you added a quarter-tone fret on the palm side, if you hold that down and also fret a different note, you'd get a string shortened to one quarter-tone above the fretted note, right?
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It doesn't work, because the length you need to shorten to achieve a quarter-tone changes depending on which fret is is use (specifically, it would be 24th root of the length starting from the current fret). So if you were fretting in first position, the palm fret would give you roughly a semi-tone (slightly more), and if you were fretting in higher positions, it would be more than that. With some very careful planning, you could maybe use the spots that give you 3/4 or 5/4 tones.
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Ah, shucks, that makes sense. I guess I should have remembered that's why the frets get closer together as you go up the neck!
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