Button=Valve (wind instrument)
Component of brass instruments
Valves are used on brass instruments to change the tube length to allow a chromatic play. When the valve is actuated, the air is passed through an additional pipe loop of a certain length, extending (usually) the air column of the instrument.
The first valve lowers the natural tone by two semitones (12.4%),
The second valve lowers the natural tone by one semitone (6.0%),
The third valve lowers the natural tone by three semitones (19.1%),
If two or more valves are used in combination, the intonation of the sound heard does not correspond to the calculated sum of its intervals, but to a tone that is too high. This is because the additional tube length switched by each valve into the resonator body is only calculated to increase the air column of the open instrument by a certain interval, but does not take into account the air column already extended by another valve.
The intonation when using multiple valves at the same time is therefore basically more or less unclean if no compensation takes place in any form. Quintessence from this realization: The fewer valves are needed, the better the tone is right.
There are basically as few valves as possible to use.
With the small differences of the "short" valve combination (1 + 2), the compensation is usually done by ear via the approach.
As you’re supposing:
The use of the clean handle 3 would be desirable, but in practice usually not possible, since in the fingering tables of the instrumental schools and thus in the training, the combination 1 + 2 in the foreground.
For instruments of rather short overall length like the trumpet, the difference in combinations with the third or first valve is usually compensated by simply pulling out the valve train of the third valve. Therefore cornets, wing horns as well as high-quality tubes and euphoniums have often already standard triggers as an additional intonation aid.