The trumpet doesn't seem logical.  We need a way to think about it to make it sensible for the students who don't play piano.  There is an underlying logic to the instrument: each valve combination plays, in sequence, the same series of notes (the overtones or the harmonic series).  As we get higher on the instrument, there are greater and greater overlaps, and many possible fingerings.  Above high C (two ledger lines above the staff) most notes can be played with almost every fingering (with a little help from your embouchure)!

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if you find these ideas valuable.