Check first to see if yours really needs adjustment. Mouthpiece position may not be what you expect. Some brands like a Selmer S-80 fit well down on the cork to play in tune. The Selmer SS fits farther up (maybe 1/8 inch). The Runyon fits farther up yet (1/4 above the S-80). If you do not find the right position, lower notes will be in tune and upper notes will be out of tune. The best thing to do is to tune for good intonation high and low on the concert A. Take your favorite mouthpiece and a good tuner and check it carefully.
It is very common for people starting out to find intonation difficult because of the mouthpiece position.
If there still is a serious problem, a tech should be consulted. I have not had to do that, but I find I can get all notes close to in tune high and low. I have pulled the neck piece out just a bit (about 1/16 inch). This moves out the octave key a little. I have had to move the mouthpiece in a slight compensating amount on the cork. This removed intonation difficulties for two of my mouthpieces except for the high palm key notes. The Runyon is exactly on tune for all notes including palm key notes which pop out strongly, including F# and G. Maybe my chops have deformed to make this happen but it works great.
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