Getting A Real Book?

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Transposing instruments make sense once you’re familiar with them. Both trumpets and saxophones do come in C variants, and C trumpets are pretty common in Orchestras. The difference between the C and Bb trumpets is the tone, so not much different from when you would choose to use a Les Paul vs a Strat. But because they’re transposing instruments, the fingerings are the same as you’re reading the music for both horns. So a written C will use the same fingerings on both horns (open, no valves pressed down) but will sound like a C when played on a C trumpet, but a Bb on a Bb horn.

You can also use the same fingerings for the other valved brass instruments, and the same fingerings on an Eb alto sax and a Bb tenor sax. There’s a few semantics with alternate fingerings having better intonation for certain notes, but if these weren’t transposing instruments then it would be a lot more difficult to go from one instrument to a second very similar one.

Really, it’s not any difference from putting a capo on but still describing the chord shapes as the same as it would with no capo in standard tuning.