There are basically three problems with notes on the trumpet: One is that the instrument resonates to the natural harmonics, which do not comply in pitch (tssk tssk) with the equally tempered scale. The big example of this is the 5th harmonic (4th space open E, Eb, D etc). These notes are not as sharp as the equally tempered scale requires them to be. Two is that the length of the tubing needs to be increased by a proportionate amount to lower the pitch, not by a set amount. So, although 1st slide is long enough to lower an open note by one step, it is not long enough to lower a 3rd valve note by one step. Blaikley designed a compensating system for Besson in the 1890s(?) which solved this one. We have to make do with thumb hooks and triggers. Three is that the upper octave contains 9 open notes to cover an octave. That means that none of the notes can be in tune when played open. Yes, many players find that one note or the other is best in tune open, but this is more a factor of out-of-tuneness of their horn or chops. Four (I can't count); the longer the tube is, the less secure the high notes are. This explains the instability of, for example, the G# fingered 2nd and 3rd above the stave.