Try a yamaha. If you find it better sounding/feeling go for it.Should I buy a new mouthpiece to get a better sound, even though I'm a beginner, or should I stick to the default right now? I'm eager to get a reasonably priced Yamaha mouthpiece, but am not sure if I need to. Please help, lol.
Try a yamaha. If you find it better sounding/feeling go for it.
Your teacher can probably advice you in your choice.
My advice is not to spend more than the price of a yamaha.
Buying a Yamaha mouthpiece is, I am sure, a good idea. However, before you rush off and buy a 4c, think about the tip opening. Yamaha tip openings are very small - the 4c on tenor is 1.7mm, or 0.67". I think a conservative opening for a new player would be about 2.2mm, or 0.85-0.9". I'd suggest you go for a 6c - even that is only 1.9mm, or 0.74, so still very narrow. Similar sort of proportions apply for alto.
My first sax teacher tried to encourage me to "drop" my jaw when playing the lowest notes, which is similar on trumpet too. Unless there is a slight technical problem it is possible that it is about tight embouchure. It is perfectly possible to play notes an octave above your fingering by tightening your embouchure.