\transposition question

[Menu Jacques]

Hello folks,

I’m trying to understand how \transposition works with enharmony. 

In the following, what key should be chosen (instead of D major) in the fourth score for a soon-to-be-created Trumpet in A#?

%%%%%%%%%%%%

\version "2.19.65"

\layout {
  indent = 3\cm
}

PartPOneVoiceOne =  \relative d' {
  \transposition bes \clef "treble" \key d \major \time 4/4 | % 1
  d4 e4 fis4 g4 | % 2
  a4 b4 cis4 d4 \bar "|."
}

PartPTwoVoiceOne =  \relative a' {
  \transposition es \clef "treble" \key a \major \time 4/4 | % 1
  a4 b4 cis4 d4 | % 2
  e4 fis4 gis4 a4 \bar "|."
}

PartPThreeVoiceOne =  \relative c' {
  \clef "treble" \key c \major \time 4/4 | % 1
  c4 d4 e4 f4 | % 2
  g4 a4 b4 c4 \bar "|."
}

PartPFourVoiceOne =  \relative d' {
  \transposition ais \clef "treble" \key d \major \time 4/4 | % 1
  d4 e4 fis4 g4 | % 2
  a4 b4 cis4 d4 \bar "|."
}


% The score definition
\score {
  <<

    \new Staff
    <<
      \set Staff.instrumentName = "Trumpet in Bb"
      \set Staff.shortInstrumentName = "Bb Tpt."

      \context Staff <<
        \context Voice = "PartPOneVoiceOne" {  \PartPOneVoiceOne }
      >>
    >>
    \new Staff
    <<
      \set Staff.instrumentName = "Horn in Eb"
      \set Staff.shortInstrumentName = "Hn."

      \context Staff <<
        \context Voice = "PartPTwoVoiceOne" {  \PartPTwoVoiceOne }
      >>
    >>
    \new Staff
    <<
      \set Staff.instrumentName = "Piano"

      \context Staff <<
        \context Voice = "PartPThreeVoiceOne" {  \PartPThreeVoiceOne }
      >>
    >>
    \new Staff
    <<
      \set Staff.instrumentName = "Trumpet in A#"

      \context Staff <<
        \context Voice = "PartPFourVoiceOne" {  \PartPFourVoiceOne }
      >>
    >>

  >>
  \layout {}
}

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