Why do some players place the ligature screws on top of the mouthpiece while others have them below ? Does it make any difference ?

Only thing I can think of you talking about, is screws on the front or back of mouthpiece. (On the reed, or on the mouthpiece itself)

Personally, I play with the screws on the reed. (Facing me when I play) I've tried the opposite, and noticed no difference. I don't think it matters. Go with what you are comfortable with.

it does matter, actaully. ligatures are designed to be one way or the other. standard ligatures have the screws on the bottom by the reed, and inverted ligatures have htem opposite, on the top. you can tell if you are using yours right because the screws are supposed to point right regardless, so they can be tightened/loosened with teh right hand.

My ligature have little "cannal" type area (i can't think of any other way to describe it) by the screws to guide where the reed and the ligature are soposed to sit.

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My ligature has a little "cannal" type area (I can't think of any other way to describe it) in between the screws to guide where the reed and the ligature are soposed to site.

Mine's got the same "canal" type thing, but I will be getting a cloth/leather/non-metal ligature soon, which are actually rather a lot better than the metal ones because they allow more vibrations through the entire reed. My private teacher highly recommends them over metal ligatures. They typically run about $20 or so, but well worth the investmet. They screw on the top of the mouthpiece. (Wow that sounded REALLY bad, but you know what I meant.)