(1) Sharpens pitch control. One's sense of pitch becomes heightened after intense quarter-tone study. Since the semi-tone becomes larger, you have a more nuanced understanding of intervals as a whole.
(2) Widens your timbral understanding of the instrument. Since many of these notes require unorthodox fingerings, you also get introduced to new note timbres, quarter steps below and above conventional notes.
(3) Improves dexterity. There's something about playing these awkward fingerings in succession that leaves the fingers very nimble. I think it's the equivalence to running with ankle weights on. You might be moving slower, but you're working harder.
The MusicThis piece shown below is from a book by Ronald L. Caravan titled Preliminary Exercises & Etudes in Contemporary Techniques for Saxophone. A must-have! This is the first piece in a series of etudes the appear in the section of the book called Quarter-Tone Etudes for Saxophone.
I've included a metronome click with my reading of it. It makes it easier to follow. I also give a universal 4 counts out front.
The recommended tempo is quarter note = 84 -92. But I would say take it at a quarter note = 60, if you have to. The pitches and the fingerings take some getting used to. So take it slow.
Let me know how it works out for you!