I’ve read here and there claims that just intonation constantly resets itself, back to an equal tempered baseline.   But I don’t think that’s right.   As proof, I offer an acappella version of my Alleluia.    It modulates quite far, following the circle of fifths; it goes almost two Pythagorean thirds away:  Bb to D (up 8 cents) and then D on to B (6 more cents).   The seventh in B major, A#, then is 12 cents lower than the B, while the tonic is 14 cents higher than the original reference pitch: presto:  an enharmonic A#, +14 cents to B and -12 cents to A#, is very nearly the same as the original Bb reference at 0 cents.   The approximately 2 cent difference has a name, too:  a schisma.  

I recorded the Alleluia, tuning every note, and posted on  Fandalism:  http://fandalism.com/williamcopper/cJ1g

and Soundcloud   https://soundcloud.com/williamcopper/alleluia-a-cappella-beginning  

The score is here: Alleluia

And on my Hartenshield Music website:  http://www.hartenshield.com/0580_alleluia.pdf