third down, diatonically

[Stefan Thomas]

Dear Lilypond-users,
I would like to transpose this melody diatonically one third down:
\relative c' {
    \clef G
    \key a \minor 
    \time 4/4 
    \partial 2. 
                       
    \ e4 a b  | c2.( a4 )|   % 3
    c2.( a4 )| g  e b' c   % 5
    d e,( d' c) | c( b) b( a) |   % 7
    a ( g) f-. g-. | a4*3 }
the transposed melody should  be: 
\relative c' {
    \clef G
    \key c \major 
    \time 4/4 
    \partial 2. 
                       
    g4 c d  | e2.( c4 )|   % 3
    e2.( c4 )| g  g d' e  |   % 5
    f g,( f' e) | e ( d) d( c) |   % 7
    c ( b) a-. b-. | c4*3 }

Is there any way to do this automatically, maybee in other keys than c-major a-minor?
Thanks,
and have a nice day, it's may 1st!