you need to understand the physics behind the speed of air flow.
when you speed the flow of air up, you to raise the pitch, slow down the speed of air and the pitch falls.

The best example when a kettle starts to boil you hear the pitch rising to a high pitch whistle, turn the gas off and the pitch falls.

the samething happens when you blow air on the reed, if you speed up or slow down the speed of air you will alter the pitch. A lot of people fail to grasp this, and end up playing the higher register slightly out of key.

Whats happening is when you use a stronger reed you are having to apply more air to get a sound out of the reed, and in doing so you are having to increase the air speed, so for the first couple of days/weeks until you get the right air support – you will sound different to how you play on your normal reed. The same thing happens when you go from tenor to alto – another reason why when you play your main sax, the main sax sounds more in tune thsn the other sax’s you tinker around.

another example is try whistling – high pitch whistles you blow faster, low pitch whistles you blow slower. Same thing happens with a reed.