I have no clue what i'm seeing in that gif...
X is frequency, Y is dB at that freq.
The blue line is perfect interpolation, how it should look like.
The green line is "no interpolation", and turns into a lot of audible distortion.
The pink line is linear interpolation, which already has a better quality.
The black line is cubic interpolation, and has the lowest distortion.

A perfect interpolation would be using sinc functions, I heard.