iOS Touches Began susequent touches only arrive if first touch moved

Question

I'm overriding the touches methods in a UIView for a piano app.

If I touch with one finger the iPhone or iPad I get -as expected- the touchesBegan callabck. And if I touch with a second finger I get that event in the touchesMoved callback. This is all fine, BUT I get the second (and third etc) callback ONLY if the first finger moves while I touch with the second one.

For a piano app this is a problem since I need to be able to touch really quickly.

Does anybody know a workarround for this? Is there an alternative than using touchesBegan/Moved/Ended methods?