The pitch an instrument sounds for a written note.
The interval decides the letter, so the spelling of the part survives the
conversion: on a clarinet in A a written C sounds A, a written D sounds B,
and a written D# sounds B# — a semitone count alone could answer C natural
for that last one and lose the letter the part is written on. A note carrying
an octave moves register with it — a written C4 sounds A3 — while an
octave-less note stays octave-less, so a pure octave transposer leaves it
alone.
The pitch an instrument sounds for a written note.
The interval decides the letter, so the spelling of the part survives the conversion: on a clarinet in A a written C sounds A, a written D sounds B, and a written D# sounds B# — a semitone count alone could answer C natural for that last one and lose the letter the part is written on. A note carrying an octave moves register with it — a written C4 sounds A3 — while an octave-less note stays octave-less, so a pure octave transposer leaves it alone.