It looks like the official track name is Wasteland, but I've also seen it called Desert Shrine Theme or Gerudo Canyon Theme. It's this one: https://www.youtube.com/watch?v=sVge8Cw5MfY
I can't believe I've been having so much trouble finding it, so if it's already out there, please link it!
Actually, I think there's another version of the piece without the guitar/stringed instrument that plays in other parts of Hyrule, but I haven't been able to figure out what that one is called. It's not a similar track, it's melodically identical.
Okay I need to know if your username is scarbo because of Ravel's piece from Gaspard de la nuit, or the poem it's based on, or something else completely
Ravel's piece primarily, but the poem really solidified it
OK in case it helps, I converted the mp3 file to a midi and uploaded to Musescore. Hopefully someone who's better at the program than I am (so, almost anyone) can clean it up.
https://www.dropbox.com/s/gvea0ecprjsu78m/Wasteland.mscz?dl=0