Could you indicate an example of a song in a certain key that doesn't express the tonic chord (I chord) in its progression? Are harmonic progressions of this type possible in pop music?
There are a few although they may be open to interpretation. Two are very similar, “Dreams” by Fleetwood Mac and “Teenage Dream” by Katy Perry. Both sound like unresolved IV-V vamp progressions (Perry’s has a quick vi between the IV and V). The melodies of each are grounded in the non-existent I chord. Maybe not having a tonic is a “dreamy” sound, that would explain the titles.
Another similar one is “I’ll Be Around” by the Spinners. It is two chords, Emaj7 and D#m/F# with a G# minor pentatonic melody so you can think of it as a VI-v6/4 that never resolves to the i.
To me the Marvin Gaye/Tammi Terrell version of “Ain’t No Mountain High Enough” sounds like the key of D with no tonic chord. Some might say it’s in Bm but it doesn’t sound like that to me. In the Supremes’ version they do a different arrangement in Eb and do resolve to what I consider to be the tonic on the final choruses, Eb. They never go to the D in the Gaye/Terrell version.
The chorus on this one is (analysis is in D):
Gmaj7 Em7 | F#m7 Bm7 | Gmaj7 Em7 | F#m7 Bm7 | Gmaj7 Em7 | F#m7 Bm7 | E7 | G |
This sounds to me like: IV ii iii vi (x3) then II7 IV.
A great example of this is Chopin's Prelude in E Minor, Op. 28 No. 4. The root position
i chord is not heard until the very final chord of the piece.1
Another example is Robert Schumann's "Der Dichter spricht" ("The Poet Speaks"). The piece is in G Major, but again, the root position G major chord is only heard at the very end.
A classic example from Jazz is "Autumn Leaves" (Joseph Kosma/Johnny Mercer). It's in E Minor, but that chord only appears at the end of the A section(s). The song opens with a
ii-7 V7 IMaj7 in G Major.
1 Technically, the piece does start with a
i chord, but it's obscured by appearing in first inversion. The work is considered a classical example of Romantic-era composer's attempts to express the key of a composition without explicitly stating it.