Fundamental (in Hz) to a MIDI note

Working to have audio-to-midi in NetworkEditor (CLAM) I needed to convert a fundamental frequency value to a MIDI note one.

I found some source code related with this in Voice2MIDI app, but was not explained at all, so looking for the reason of that formula I arrived at this:

Knowing about equal-tempered scale (check this) and $latex 2^{\frac{n}{12}}$ relation between frequencies plus the fact that C4 or “middle c” has a MIDI value of 60, it’s easy to conclude that then A4 (which its frequency value is 440Hz, a standard for tunning and is 9 semi-tones more) has a MIDI value of 69.

Then, starting with:

It’s easy to arrive at this:

and then, also taking in account this mathematical relation::

the final formula looks like:

and a final c++ code like:

 
Related post: nictuku’s inverse formula (i.e. from MIDI to Hz) here “Translanting MIDI Notes to frequencies in the diatonic scale using the central A (440hz) as reference“.