I am currently making an app that recognizes certain notes and chords and I have been scouting the internet to find really what happens when the computer records sound and I cant seem to find anything. I would really appreciate it if anyone can explain this process to me.
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As mentioned in the comments, the computer is just recording the signal that is present on the microphone or instrument input that is being used. That signal is likely to be in a PCM / WAV format. The software you're using to record the sounds may choose to encode the audio to another format and/or preform some signal processing, before saving it to a file.
If you're inclined to write a little bit of code, plotting a spectrogram in Octave may be illuminating.