Ask Augustin 11 - About Intonation Part 2

In this installment I continue talking about different aspects of intonation. As I mentioned in the first installment, intonation is relative and there are different ways to hear intervals and leading tones. In fact, depending on how you are listening and which intervals you are prioritizing, you could end up with very different results.
The intervals we can be certain about are perfect fourths and fifths. As string players we should prioritize making sure those intervals are in tune. However, there is a funny phenomenon: fifths ring perfectly in tune when they are quite wide -- if you started on a low note and kept going up infinitely in intervals of perfect fifths, you would get sharper and sharper, and eventually end up a half-tone sharp compared to how you started!
Even in a string quartet, the E string of the violins will sound a bit sharp when played together with the open C string of the cello. So we need to be aware of the low voices and adjust so that the intonation gap between highs and lows doesn't become too wide. (It is generally the top voices that need to adjust to the low ones)