Once the pitch contour of the melody is extracted, the next (non-trivial!) step is to segment it into notes and quantize the pitch of each note, producing a discrete series of notes that can then be exported into a any symbolic format such as MIDI or JAMS.
Quantizing a continuous pitch sequence into a series of notes is an active area of research and remains and open problem. Still, we can obtain fairly decent results using a series of heuristics:
1. Convert the pitch sequence from Hertz to (fractional) MIDI note numbers
2. Round each value to the nearest integer MIDI note number
3. Optionally apply a median filter to smooth out short jumps in pitch (e.g. due to vibrato)
4. Iterate over the sequence and whenever the pitch changes start a new note
Here's an example:
The script is open source and available on GitHub: https://github.com/justinsalamon/audio_to_midi_melodia