Music sheets saved as PDF documents can be converted and transcribed as .midi files using conversion programs like PDFtoMusic or perhaps similar. It won't work on any .pdf document though, only on those that contain saved music sheets.
Convert Adobe Portable document format to MIDI audio.
We have found 2 software records in our database eligible for .pdf to .mid file format conversion.
Microsoft Windows software - convert pdf to mid on Windows
A PDF sheet to music converter
Convert from pdf file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned pdf to mid. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert pdf to mid on OS X
A music scanning and notation program