Smart fingering. When you change valves, when you don't, and the laziest move between any two notes.
starting note (written)
interval up
the textbook way
Each note in its standard fingering.
valves that move: 0
the smart way
Same harmonic series — no valves move at all. A pure lip slur.
valves that move: 0 · lip slur
When two notes live in the same harmonic series you never touch a valve — that's a lip slur, the smoothest connection on the horn. Otherwise the smart path hunts for alternate fingerings that keep the fingers still.