You can find programs that can process a PDF with music sheets or other audio elements and export or save them to something else. So with programs like PDFtoMusic you should be able to convert PDF to MIDI. Only works with .pdf documents that contain music data. Alternative to this would be to use some Musical OCR (OMR) solutions that can processes scanned music sheets in .pdf files and generate a sheet / music score from it.
Convert Adobe Portable document format to MIDI-sequention sound.
We have found 2 software records in our database eligible for .pdf to .midi file format conversion.
Microsoft Windows software - convert pdf to midi 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 midi. 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 midi on OS X
A music scanning and notation program