Hi Matthieu, thanks for using WindWorks. There are a couple of instant concerns I have in regards to your post:
1. Practising with a mute most of the time is quite destructive for several reasons including sound development and simply the feel of what of what it should be like to play; you could be encouraging negative tension and over-blowing.
2. The psychology of “blowing harder” can really suggest that you are already working too hard. When playing, you are displacing the air that is already in the pipe – and that is NOT HARD to do; you can make a MASSIVE SOUND using Passive Reduction (as demonstrated repeatedly in the course) in the low register. Yes, as you get higher, the air support muscles work a little more to support the greater “displacement” of air as you ascend in range BUT the idea of “blowing harder” means you are forcing against either the resistance of the pipe/instrument or against lips that are impeding the airflow/oscillation of the air column.

I know this may all sound a little complex but it is a very deep conversation and there is a very fine line between the right amount of support and over-blowing.

Remember, if you have watched the lessons closely, blowing harder tightens the body and reduces resonance and projection. The need to open up the “The Body’s Concert Hall” and let it sing. Remember the Sound Equation – Sound = Flow + Tension If the flow is too forced or the tension in the lips too pinched, sound is reduced.

Remember also the 1% Rule (please watch all of these videos again), can you make 1% more sound by relaxing the body by 1%.

You are not blowing through the instrument, you are energising an air column and it takes less work that what you think. Back Off, Open Up and let your body sing!!!
Cheers,
Greg