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I came up with a chord progression the other day:
Fm7 Ebmaj7 Abmaj7 G7
It's clearly in C minor. But instead of resolving to Cm, I was looping through it. What catched my attention was that it sounded in C minor, despite not containing any C chords, and it didn't sound modal to me. And I couldn't remember any songs (at least popular ones) that sound in a key but don't contain the tonic. All examples I could think of were actually modal.
So, is there a name for this? Is it common?
I assume you're looping this chord progression?
If so, note that Fm7 always follows your G7. In other words, your progression always moves V7–iv7.
This is actually a pretty common occurrence in popular music, especially rock. The music theorist David Temperley published an article called "The Cadential IV in Rock" wherein, among other things, he discusses the deceptive IV. (Note: some people on here will hate that I just gave a term for this, but you did ask...)
Basically, the "deceptive IV" is the appearance of a IV chord at a cadence where one would typically expect to hear tonic. In your progression, every time you play a V7 (which we expect to go to tonic), you resolve it deceptively to iv7.
One of the reasons this progression works is because the tonic pitch is included in the IV. And in your cause, two members of the tonic chord—C and E♭—are included in the Fm7.
Usually the progression will eventually find its way to tonic at some point, but yours doesn't yet, and that's fine. As you say, it still clearly creates a sense of C minor. Whether the progression ever actually reaches C minor is up to what you're trying to do with the piece you're writing.
One way to establish a key is to state its tonic chord (for long enough that it doesn't seem to be just a passing chord). But, as you've shown, that isn't necessary. So how does your loop of four chords manage to suggest C minor?
So you establish C minor not by a particular chord but by unambiguously indicating the C minor scale.
Here's a piece which shows the same phenomenon on a larger scale. It's the Prelude op 11 no 9 by Scriabin/Skryabin. It's in E, but we don't really get a chord of E until the very end. Note that there is a hint of a chord of E in the 3rd beat, but it's only in first inversion on a weak beat, and anyway, the C# that comes next suggests that the chord was c# min7 anyway, not E. For me, what clinches that the piece is in E are the ii7-V7 (f#min7-B7) imperfect cadences in b.4 and b.8. Given what pitches have been played so far, what else could the key be but E major? and we have dominant sevenths, even though they don't resolve onto the tonic.
