Recently, I remembered a small feature I noticed in "Hey Jude" a number of years ago (via Wilson Pickett's version, actually) but neglected to write about: in the line "Take a sad song and make it better," "better" is sung with a melisma (D C Bb A), and although the pitches descend, this articulation provides some sense of the comparative nature of the adjective (more notes for a greater degree).
I also had a new realization: during the line "Then you begin to make it better, better, better, better, better, better, ah" at ~2:57, the repeated "better"s and final "ah" are sung to a steadily ascending phrase that spans just over two octaves (E F | G A | Bb C | E F | G A | Bb C | F). This ascent - particularly its scope - also gives a sense of the increase of "better."