Here:
Should be self-explanatory. I tuned f-a-e'-b via pure 3rds and 5ths,
the resulting tritone beats enthusiastically and I can't detect any
kind of mystery root or even difference tone to it. (Not that the
presence or absence of extra tones has much to do with purity IMO.)
Then I took up the tuning hammer and adjusted the b downwards to give
an audibly pure 7/5 tritone (or aug4, they are equivalent... just as a
'ditone' is a major 3rds). For an encore this is shown in a perfect
cadence g7->c within a meantone framework (g, c', the low e).
~~~T~~~