There are a few ways to figure out if you’re in tune on the saxophone.
You can either tune it with another instrument or use a tuner.
To tune with another instrument, you play the same note as another person playing the other instrument. The piano can be a good choice. Basically, the piano should be in tune and even if it’s not, if you’re going to be playing with the piano, you want to be in tune with it.
You’ll hear something called ‘beats’ if the instruments are out of tune
You can also use a tuner, in that case you read what the tuner outputs, how flat or sharp you are.
You can use a smart phone app for tuning.
You can also use a recording that you know is in tune to play with and listen to whether your note seems in tune. In that case, you probably want to figure out a note that is in the key and see if it seems to fit with the music or seems dissonant.
In Mark Salzman’s book ‘Iron and Silk’, I read about how he tuned a piano using a cassette of Michael Jackson’s music.
Tuning the saxophone
If you play one note in tune, it does not necessarily mean all your notes will be in tune on saxophone, but it is a start.
You basically pull the mouthpiece out on the cork or push it on farther to make adjustments.