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I'm just not seeing how it's capable of that with so few circuitry.Exactly what I thought.
But it does.

Signal grounded for simplicity, supplies are +/-5V. (This won't interface nice with some logic, but that can be fixed.)
Input V2 is a 0.5V peak sine wave. On the plot I multiply by 18 so it can be seen among the larger outputs: green line V(V2:+)*18
Bits A B C go up and down. I've offset a trice so they don't overlap.
The proof of our ADCs is a DAC: do we get back what we put in? The "V(BitC) + V(BitB)/2 + V(BitA)/4" is of course the function of a 3-bit binary DAC. Orange line.
The orange line "matches" the green line as good as possible with 3 bits, 8 steps. And there are no glitches at the transitions.
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TL074, which (according to the datasheet) isn't happy driving loads less than 10k.?? Errors are near-zero for 2K load. I used 1K:56 cuz I'm too lazy for math, but (ummm) 2K and 112 or 2K2/123 is the same ratio and 112--123 is far less than the 230K divider.
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big ratios are arbitrary, but they keep the thresholds near AGND, which I thought would be useful for the small signals coming from a passive guitar.In general, when doing decisions on small signals, you first bump them up to substantial level. Dwarfs offset errors, speeds switching response. Gain of 10 simple analog amplifier.
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to avoid phase inversion problems.Simulated LF411 (granddaddy of TL07x) showed that effect. Turn it down a trace.
At 3 bits you probably DO have a compromise between no-output below -18dB, and whatever overload artifacts your chip has. You can clamp, you can use another chip.... leave that for later.
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It might actually be a ratio of the two ratios that mattersOh, surely the two ratios must track. I suspect numbers like 2:1 and 1.5:1 work for large inputs, but I too am too lazy to work the numbers.