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Perfect fourth could be achieved via natural harmonics at 5th and 7th frets, double octave is just the 5th fret and voila you can get the standard tuning. Inapplicable for necks without a precise position of frets, good luck compensating height differences from nut and gauges with intonation tuners.

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Oh yeah, I should've mentioned fretting the lower strings for a unison (1:1) to the higher adjacent open string. No beating in this unison yields equal temperament, due to frets scaled accordingly, so it avoids the problem I mentioned... but introduces likelihood of intonation issues (or simply bending the pitch) as you say.

I had been thinking about listening for beating in the 5:4 and 4:3 intervals using open strings, which does present the just temperament problem, and harmonics on open strings to make a unison unfortunately shares this problem 100%.

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