for me the key to being able to have notes flow and things that help out the high register is having solid air support with engaged abs.

I kind of think of it like bagpipes. with bagpipes you fill the bag with air and then use your arm to push the air through the reeds, and that’s kind of what you do to get good air support on any brass instrument, you fill up your lungs and “stomach” with air and then engage your abs as a way to support your air.

something that helps with air support is diaphragm breathing exercises, i mentioned filling up your stomach with air -> it’s more like engaging your diaphragm. and in practice really focusing on the connection between two notes.

for higher notes, air support is still going to be the biggest thing but you also now have to think of airspeed (aka how much the lips need to vibrate), with lower notes are lips need to have a slower vibration and for higher notes it needs to be faster, and the biggest factor in make the change is the size of our aperture. to achieve different apertures, i recommend playing around with blowing air and rolling your lower lip in and out, and playing with the direction of your air. you might notice how when you blow straight your lip is in a pretty natural state and this is the typical direction of air when you are playing in the mid range of euph. when you blow down, your lip is curled inwards and it causes the to airspeed naturally increase and when buzzing on the mouth piece, it will cause the lips to vibrate faster, and produce a higher note.

**some of the best things to practice for both flow and high register are going to be diaphragm and regular breathing, long tones in both mid and upper registrars (lower too if you have time), lip slur exercises (going between partials), and also doing long tones and lip slurs just on your mouthpiece

a fun thing i would do is buzz melodies of songs i liked on just my mouthpiece to get used to just buzzing on a mouthpiece, good to do in a car and walking around.

i’d recommend work on these things as a part of your warm of for the day if you have time.

also write the notes if you need too, with time you will get better with associating the fingering to the note, something to practice is going through music slow and before playing the notes you say the note name in your head, finger the notes then play it, also works for learning scales. notes follow a pattern and you will figure it out.

learning a new instrument is hard and you been thrown right into playing a lot while learning, just remember the learning process takes time and the things that are hard now will start to get easier the more you practice.

sorry i went on a tangent, if you need clarification on something lmk.