This is delightful. I replaced the battery on my 2011 MBA some years ago, but it's been sitting (replaced for family use by a Framework). You're inspiring me to do something with it.
Kyle Gann's Arithmetic of Listening goes deeply into this. Given an infinite number of ways of dividing the range from f to 2f, some other equal-division temperaments (31 or 53, for example) get closer than 12TET to maintaining low-integer ratios across key centers, but each additional pitch adds complexity. I'd recommend that book in particular. https://www.kylegann.com/Gannbooks.html