This message was posted by Gus Pratt on the Onelist TUBAEUPH discussion list several years ago. It is still a good discussion.

When tuning the valves the most critical thing is that you think about whats going on with the horn from a techincal aspect. If you tune the first valve first, then when you adjust your main tuning slide the note you tuned with the first valve is now out. Here's the order that I would use, some of which will need a tuner.
  1. Tune to concert Bb main slide.
  2. Tune 2nd valve slide to concert A according to tuner
  3. Tune 1st valve to concert Ab
  4. Check tuning of G (1 and 2), if G is sharp adjust first valve, then recheck your Ab. You may have to settle for Ab being a tad bit flat and G being a tad bit sharp. Neither will be noticeable. That's just the nature of using multiple valves.
  5. Tune the 3rd valve slide. I tune Gb to be in tune adjusting the 3rd valve slide (playing 2 and 3). That's because I rarely use the third valve by itself, but use it alot in conjunction with the 2nd valve so I tune it how I'm going to use it.
    (Note: more recently I've enjoyed using 3 by itself for G, so I may adjust my tuning accordingly.)

    Now you're ready to tune the 4th valve and all the compensating valve slides.

  6. Tune the 4th valve slide by matching the fourth line F pitch playing back and forth between open F and 4th valve F. The last 2 slides depend mostly on what notes you plan on playing the most.
  7. If you play low Eb then tune the 1rst valve compesator by matching Eb 1rst valve (third space) with Eb 1 and 4. If you play low D then tune the first valve compensator by matching 3rd line D (1 and 2) with 1,2 and 4.
  8. For the 3rd valve compensator it depends on whether you play low Db or low C most. Match the pitch of Db 2 and 3 with 2,3 and 4. For C match the pitch of 4th valve only to tune 1,3, and 4. Depending on what notes you are playing you may want to adjust the slides to make settle for some notes being less in tune and other being more in tune. Any of the notes using multiple valves you'll need to make choices. Others may tell of a better way to tune, but this way gets the job done.