>There are only 8 possible valve combinations. How do you play the full 12 notes with sharps and flats? The lips are a variable that can change the note values for a combination, but I thought only by an octave.
>
>000
>100
>020
>003
>120
>023
>123
>103

As you get to the higher ranges the space between notes played with all open valves decreases. It's been a while but I seem to recall the progression as (on a trumpet)

C G C E G

I couldn't get any higher so I never learned them.

I also don't recall any notes played with just the third valve closed (but there might have been alternated fingerings that allowed it).

IIRC the fingerings for the first octave were


C ooo
C# ccc
D coc
Ef occ
E cco
F coo
F# oco
G ooo
Af occ
A cco
Bf coo
B oco
C ooo