As a woodwind doubler, you have to be ready at any moment to pick up one of your secondary instruments and nail those notes. Easier said than done... 😉
If you’re starting out as a doubler, it is my recommendation to be fairly proficient in your main instrument. The reason for this is the possible confusion between different fingerings and embouchure. This isn’t so much a problem if you’re playing alto and tenor saxophone of course. But even then I wouldn’t recommend doubling too early. It can be demotivating, but it is just an advice. Do as you please! And have fun! 🎷
I experienced a lot of problems in switching from clarinet to saxophone. The problem wasn’t so much the switch, but more the decision to keep playing clarinet. 🤣 No, just kidding… The problems started when I changed my embouchure to a lower pressure jazz embouchure. When studying jazz saxophone I was searching for a more “open” sound and needed to change. But my wish was to keep a more classical sound on the clarinet. I didn’t want to play saxophone on my clarinet or the other way around.
The solution was simple and logical. But… I wouldn’t call it easy. I switch up my embouchure when playing clarinet. At first it seems undoable and it feels really strange. But in my experience if you want to preserve a credible clarinet tone it is the only way.
Confusion between different fingerings is of course inevitable, don’t be discouraged by the countless mistakes you will make. It is part of the learning process. One of my own favorites is the switch up between bass clarinet and tenorsax. Somehow the feel of the bass clarinet makes me believe I’m holding a tenorsax and therefore I would play the wrong fingerings.