It's easy in a simulation but I was going to test it in real life with only 4 bits to start because I don't own that many good resistors.
Fun fact; this kind of thing, binary counters in discrete logic and DACs, is how 70's "string machines" (string synths) worked.
You'd have a "top octave generator" that gave you 12 square waves spaced around an octave, then divide those by two for each octave further down, and then add octaves up just like you have done to get ramp waveforms.
In fact I wanted to do this to get bleepy low bit sounds anyway
As someone who started out in the 8-bit era, I feel the need to point out that jagged edges on ramp waveforms had nothing to do with the sound in that particular period. :-)
But then perhaps that's not what you're going for anyway.
(Most of the "8-bit sound" is just squarewaves and PWM. The 6581 SID, which is what I grew up with, had something like 20-bit counters for the ramp and triangle waveforms IIRC.)