While a student at the Interlochen Arts Academy, I attended a guest master class given by Bernard Linden, then a violist in the New York Philharmonic. His daughter Louise was a student at the Academy. In that class, he inspired a journey for me that continues today, that of understanding tonality and intonation. Mr. Linden demonstrated that he would practice the intonation of a passage by determining an appropriate reference tone for the tonality, and then compare the notes in the passage to this tone.
It was many years later that I started to realize that notes even spelled the same way on the page may need intonation adjustment according to the tonality. Even more recently I became aware of the illustrations of Zarlino in the Groves Dictionary, explaining that not all whole steps are the same size and that not all half steps are the same size. Many errors of intonation involve playing sharps too sharp, and flats too flat.
Try these things, preferably with two or more players:
1. Most important for these activities is that the basses (or other instruments) are tuned accurately. I suggest for two players, agreeing on pitch for the open D string. Then one player finds the D on the G string which they both agree is in tune. The D on the G string is sustained while the other player tunes his or her G string until both are satisfied. After the G strings are settled, one person plays the open D while the other finds the A which is one fifth above, and both agree that it is correct. The A is sustained while the other player adjusts his or her A string. After the A strings are settled, find the E which is a fifth above open A. Sustain this E so the other person’s E string can be tuned. Hopefully the instruments are well in tune now.
2. Have one person play his open A while the other finds the E on the D string. Sustain this E while the first person finds the B on the G string which matches. Silently hold this B while the other person finds the B on the G string which matches the open D. After both B’s are found, compare. Are they the same? Which is higher?
3. One person finds the F# on the G string which matches the open D; the other find the E flat on the D string which matches the open G. Are they in tune with each other?
4. Find a G# which is in tune with the open E; find an A flat which is in tune with the E flat which is in tune with the G string. Are the G# and A flat the same note?
I could go on for a long time with other examples, but it will be more meaningful for you to discover some of this on your own. Good luck.