The Yamaha FB-01 is a bland looking low-cost four operator FM synth which falls into the 'black box' category of late 80s synths. It has been loved and loathed over the years, but from personal experience I can tell you it is a superb machine if you can create your own sounds. All that aside, it also offers microtuning as detailed in this 1989 article from Electronic Musician magazine, written by Jim Johnson. Accessible via three methods, it's possible to create intricate tunings this way.
You'll also find a musical ode to the FB-01 from NoyzeLab, in his release NYZ - NTE GDN which came out in 2018. There's an extensive explanation on MatrixSynth where he details why he's so fond of the digital black box. Here's a brief excerpt:
So why am I interested in the strange and esoteric Yamaha FB-01, and what are these secret sysex codes? Well, first up its a nice little 8 voice FM synth, and I'm well known for being a bit obsessed with FM [see the NYZ - DRN4 Declassified article]. Secondly, its a kind of in-between synth, arriving after the first 4 operator synths, such the DX21, but before the TX81Z which featured a full microtonal tuning table. Its this inbetweeness that really interested me, and its really the only first gen sine wave only 4op that can be micro-tuned, albeit in a very roundabout way via some secret sysex codes.
A fantastic resource for FB-01 owners is http://llamamusic.com/fb01/ - packed with mods, articles, info, and patches.
There are a number of editors for the FB-01, including my own Max4Live device - which was in development for 9 years believe it or not! Other editors are also available, but none (as yet) have implemented this secret feature!
New desktop from Moog
Shimmer reverb and MIDI out too
And more - from back in the day