I was once told that an ensemble that plays in just intonation will always go sharp, and I'm wondering if that's actually true.
The easiest way to disprove this claim is to find an instance where the pitch doesn't go sharp. In this case, let's imagine a descending circle of fifths. If we begin with octave
Cs in the ensemble and move down to an F-major triad, it seems we would keep the common-tone
C in tune, and the expansion of the perfect fifth required by just intonation would then lower the
F by almost 2 cents. If we continue through this descending circle of fifths, the widening of the perfect fifth would continue, and we'd find all the expected commas, resulting in a pitch center moving lower and lower.
With all that said, there are two caveats:
As much as I want to think that my opening premise is false, I really respect the individual that told it to me. He's a college music professor, and one that I would normally expect to always cite his sources (so to speak), so I'd be shocked if he just pulled this out of thin air; I expect he read it somewhere. (Unfortunately, he's not around anymore for me to ask him.) If anyone knows of any source that makes this claim, I'd love to hear it.
Thanks to Pat Muchmore's terrific answer to a recent question, we see that true just intonation is, for all intents and purposes, an impossibility. Nevertheless, there is a "watered-down" version of just intonation that focuses on tuning major and minor triads and connecting common tones, which is what I used in my second paragraph.
So, to repeat: Is it true that a just-intonation ensemble will always go sharp?