I wanted to create a setup, where I can generate a full score as well as each part and separate registers using lilypond. For the most part, my setup works fine, however I have some issues transposing the midi output for the different instruments correctly.

Here is the setup:

• In my source material I always have the instrument pitch available for each part (meaning the notes the person playing a certain instrument sees)
• The full score in my source material also displays the same notes, so not the concert pitch

I think it woud be relatively easy to transpose everything to concert pitch (= c), but I want to output the sheet music as is since I will probably need this setup in the future.

So the question now is, how to transpose each part in a register output or the full score output according to the instrument?
Here is what I tried so far (example with a part of the clarinet register).

version "2.24.3"
include "_global_definitions.ly"
include "clarinet_eb.ly"
include "clarinet_1.ly"
include "clarinet_2.ly"

header {
  instrument = "Clarinets"
}


book {
  bookOutputName "register_clarinets"
  score {
    midi {
      context Staff = "pitch_es" {
        transposition es 
      }
      context Staff = "pitch_bes"{
         transposition bes 
      }
     }
    <<
      new StaffGroup = "StaffGroup_clarinets" <<
        new Staff="pitch_es" {
          set Staff.midiInstrument = "clarinet"
          clarinet_eb
        }
        new Staff="pitch_bes" {
          set Staff.midiInstrument = "clarinet"
          clarinet_two
        }
      >>
    >>
  }
}

This does transpose something (i have tested this with A-B sound tests), but sounds horrible so my guess is something with the context references is wrong. The actual notes in clarinet_eb and clarinet_two should be correct, I have checked those multiple times now.