Beginner saxophone - reed question.?

My reed and ligature both slide loose when I'm playing, no matter how tightly I do up the ligature, (and it is done up as tightly as it will go).

Could it be that it's too high on the mouthpiece? any other suggestions?

I think the tonguing is making it move, and it's very annoying!

There's a very good chance that you have the ligature too high. Try loosening the screws a bit then move the ligature more towards the bottom of the mouthpiece. If you have the screws as tight as they will go, then they are too tight. When your ligature is placed properly, the screws shouldn't be all the way tight. There should be space between. The sound is produced by the reed vibrating so if it too high, you get a stuffy muffled sound. So loosen up those screws a bit. If you try this and it doesn't help then you might have the wrong size ligature for that mouthpiece. They are not all the same size and you can get a new ligature for about $10 - $30 at any music store.

Looking at my mouthpiece there should be about 1/4 of an inch between the bottom shaved part of the reed and the top of the ligature.

That could be the reason. Some reeds, as well as some mouthpieces, have a horizontal line on them. The top of your ligature should be in line with that. I've also seen people with a tenor ligature on an alto. Or a legit ligature on a jazz mouthpiece. But if the tip of the reed is at the tip of the mouthpiece, and you have the ligature right below the cut part of the reed, it should be fine.

Get a Rovner ligature, they are the best in my opinion:

http://www.rovnerproducts.com/

Hey, I play the tenor and also experienced this problem. A friend of mine who happens to be an alto player told me that because of the different brands of mouthpiece and ligature... I actually need a alto ligature to fit correctly on my tenor mouthpiece.. since my mouthpiece is a narrow build that's just how those two brands work together... this may or may not be your problem.... but it is worth looking into... i agree.. its annoying! Good luck!