Going up a half-step is one of the most common modulations of all. Two good reasons: it is close enough that it doesn’t take the vocals much out of the original range, and the new key is harmonically unrelated, which makes the key change feel significant. It also feels like you are building tension when the song needs a little build. If it works once, why not do it again?
Now I challenge anyone to name a tune where the modulation is a half-step each verse, but in the DOWNward direction. Very rare. It feels melancholy, and I once saw it used very effectively for a song intended to be sung by a baaad witch in a musical.
I’m willing to bet quite a few songs meant to be “looped” (I know a song that gets on everybody’s nerves maybe? Can’t recall the tune right now so can’t say) may end on a half cadence.
If it modulates into D minor by the end then it would be on the tonic, at least I was always taught the tonic is whatever the I (or i) chord is at the current key, rather than what the song begins with, at least for cadential purposes (if you modulate to minor and end going vii(dim)->i, you probably would mark it as an Authentic Cadence, not a Deceptive Cadence). If you go into C locrean, no matter how bad that i(diminished) chord sounds, it’s still the tonic.
Man, I hear these every so often, but the only one that comes to mind immediately is The Beatles’ “A Day In The Life,” whose tonic is G, but final chord is E.
Laura Nyro’s “Save the Country,” but only the version that appears on the album New York Tendaberry. It also ended Side A of that LP, which must have bugged the hell out of people in 1969. (The CD goes directly on to “Gibsom Street,” the first tune on Side B.)
Not to open a can of worms – I’ve heard of friendships being irrevocably broken debating “What chord begins ‘A Hard Day’s Night’” – but the song opens and closes on Fadd9 (I believe that’s the proper name for “F with a G on top”) while the verses are in G.
That doesn’t take into account the D in the bass. I expect disagreement, but I say that the famous opening is a G chord–specifically, a G9sus4 in second inversion.
I know that this chord is an endless controversy, but when I was played this song in a band years ago, playing an F plus 9 on a Rickenbacker 12 while the bass player played a D sounded close enough that everyone knew what the song was.
Back on topic: Rain King by Counting Crows ends on the IV chord.
Speaking of the Beatles, what about the last note of “A Day in the Life”? It bothered me because it seems different from what chord “should” be played, but I’m not a trained musician and even if I were can’t tell what chord is actually played.