As always, thanks Fats Treetop for your inspiration.
A Note About Middle C / C4
This site uses the definition of C4 as Middle C (261.63 Hz).
About the Piano Samples
The piano samples were created individually using the free and open source MuseScore application, and are located here. There's also a .zip file that contains all 88 piano samples.
To create each of the 88 samples, two tied whole notes were used. Given the time signature and tempo, the duration of each sample is 10 seconds.
How the Audio is Generated
Using the samples described above, the free and open source NAudio audio and MIDI library is used to read the samples, combine / mix if necessary (e.g. for melodies / chords), then save to .mp3 files. The resulting .mp3 files are what gets played.
How the Transciptions are Generated
Transcriptions are rendered using VexFlow, an open-source online music notation rendering API.