polytempi in Lilypond - is it possible?

[Bálint Laczkó]

Hey Everybody,

I would like to engrave a polytempical musical material in LilyPond. I am a newbie to this software so I am still learning the basics, but I saw quite a few mentions in some forum comments here and there, that LilyPond support polymetry and polytempi quite well and folks do it all the time. Now I found many useful tutorials/examples/documentation about polymetry but as for polytempi I am still stuck in the darkness.

What I would like to see is similar to this:

...except for the ending, I would like to to it strictly proportionally.

This is a screenshot from [bach.score], a Max MSP object/package which can do polytempi quite well, but it exports pdf files via LilyPond, and somehow in this case they don't quite understand each other. Anyway, actually I would be more interested in doing it all the way in LilyPond without introducing any weird syntax-conversion from another software.

So the Max package created a .ly file, and inside I found something like this (I only kept two staves for the sake of tinyness):

\version "2.18.2"
\layout {
            \context {
                \Score
                \remove "Timing_translator"
                \remove "Default_bar_line_engraver"
            }
            \context {
                \Staff
                \consists "Timing_translator"
                \consists "Default_bar_line_engraver"
            }
            }
\score {
    <<
        \new Staff {
            \clef treble \time 3/8     \tempo 4 = 120
            c'8 d'8 e'8 | f'8 g'8 a'8 | b'8 c''8 d''8 | e''8 f''8 g''8 | a''8 b''8 c'''8 | d'''8 e'''8f'''8
            \bar "|."
        }
        \new Staff {
            \clef treble \time 3/8    \tempo 4 = 105 %or any other number...
                        c'8 d'8 e'8 | f'8 g'8 a'8 | b'8 c''8 d''8 | e''8 f''8 g''8 | a''8 b''8 c'''8 | d'''8 e'''8f'''8
            \bar "|."
        }
    >>
}

Now ideally I would like to see this engraved in a proportional way, so that the lower staff has a wider spacing, and so the notes are distributed in the two staves illustrating their exact relation to a mutual time-scale (so in short: sort of like on the picture above).

Is there any way I can do this? I only read that some guy did it with giving individual horizontal spacings for each staff, but there were no examples for that, and while it is not quite the thing (ideally it would be like LilyPond understands and calculates the time-differences, and most ideally it would render a coherent MIDI representation of it as well), I can't even do that one.

Please shed some light over this for me!

Thank you all in advance!

Bálint Laczkó