Thinking on the 1-bit SuperSaw on ZX and messing up with assembly code a bit, I tried this thing. The idea behind it is the early electronic orgrans that used frequency dividers to form sound registers. So only one real counter here. Can't remember if we ever used something like this?
ld hl,0
ld de,400
loop
add hl,de
ld a,h
cp #80 ;duty 1
sbc a,a
out (#fe),a
push hl
add hl,hl
ld a,h
cp #80 ;duty 2
sbc a,a
out (#fe),a
add hl,hl
ld a,h
cp #80 ;duty 3
sbc a,a
out (#fe),a
pop hl
jp loop
This is one channel with 16-bit adder, the usual idea with duty cycle control like in Tritone. The trick is to generate a number of octave doubled derivatives (phase synced, though) by multiplying the adder by 2 (adding the adder to itself) a few times, two in this example. It adds octave doubles to the sound. Interesting thing is that the three duty cycles kind of have a limited control on the strength of the octave harmonics.
Another thing is that just applying a few duty checks to single unchanged adder also affects the timbre in a way:
add hl,de
ld a,h
cp #80
sbc a,a
out (#fe),a
ld a,h
cp #08
sbc a,a
out (#fe),a