I was practising the middle register today and made some interesting discoveries for myself. So I’ve uploaded my notes here in case it’s of interest.
My trusty friend “harmonics” taught me that notes like D and Eb are easier to split upwards. As vented fingerings (1st finger left hand), they are designed to cut out the lower partial sound, so by blowing slightly lower, I found there was less chance of these notes splitting up. Eb has more instability as there are more possible outcomes around that pitch so one has to be more precise. Even though it’s a vented fingering, Eb can split down if playing with very slow and soft air, but it’s much easier for it to split up.
E and F natural are effectively harmonic fingerings of E1 and F1. So there is a greater chance of the note splitting down, but it could also split up if the embouchure tightens. Making sure to keep embouchure focussed but not tight, aiming the air higher helps with clarity.
General harmonic practice with middle register fingerings for D and Eb was helpful in finding a more “harmonics in tune” tone.
When all else fails, I’ve included some alternative fingerings that I learnt from Wibb.