I am not going to go into the millimetres of each gap and what mouthpiece number correlates with which millimetre opening because each manufacturer does it differently, the Americans do it in the imperial system instead of metric and it becomes an absolute nightmare. When you start playing the saxophone, most players will start on a Yamaha 4C mouthpiece which is a tip opening 4. This is very narrow and makes blowing down the saxophone a lot easier. It also gives the saxophone a much more focused sound, as well as makes articulation such as sharp and precise staccato notes easier to perform. This is why classical saxophone players often stick with a very narrow tip opening. 

When you increase the space between the reed and the mouthpiece, you allow yourself the ability to put more air through the mouthpiece and into the horn. Getting more air through the horn will immediately give you more projection overall, whilst also broadening the tonal shape of your sound. Your tone will be much more spread, with overtones adding colour to your sound. This is perfect for those jazz heads or R&B players looking to cut a bit more. It’s worth noting that when you increase the tip opening, it will make the saxophone more difficult to play particularly at the bottom register. It’s entirely your choice whether you want to persevere with this difficulty and get past it, or play something a little closer and more comfortable. 

What difference does this make? The speed at which the air travels through a horn affects how loud and bright your overall tone will be. Think about this like water through a hose. When you let water flow through a hose without obstruction, the stream is lovely and thick but doesn’t travel very far. If you were to cover the edge of the hose with your thumb, you would restrict the amount of space the water can travel through, therefor the water has to move faster through this smaller space. This, in turn, means the water moves further but with a much thinner stream.

Let’s then apply this logic to the airflow of a mouthpiece. The less of a baffle there is, the bigger the space the air travels through. It moves slower through that space and gives the overall tone a lovely fullness, however, it has very little attack or cut. The more of a baffle you have, or the bigger step within the baffle, the less space the air has to travel through, so the faster the air has to get through that space. This will give you plenty of cut and attack, with a big and bright sound, but will have less body and thickness to the overall tone.