Is there some inherent quality in the frequencies that make them notes, or is it just an arbitrary human construct?
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It’s ultimately arbitrary (kind of). Looking at a music note frequency chart will help understand.
Each octave is divided into 12 notes. The notes are (sort of) evenly distributed in that octave. The difference in frequency between each successive note is not equal, but the ratios between the frequencies of successive notes are equal.
When you go up an octave you double the frequency of whatever note you’re playing.
This is all done because notes whose frequencies have simple ratios sound good together, and this system allows for a lot of different notes that have nice ratios. Playing A1 and A0 (2:1) sounds good. Playing C2 and A2 (3:2) sounds good. For reasons.
That said you could tune your guitar to a slightly higher frequency, and as long as the ratios between each string were the same it would still sound good. But we standardize the exact frequency so multiple instruments can be played in unison.
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