I'm on a railroad train, I hear the whistle blow the note: F# You hear the whistle blow a clear low C. The whistle actually blows F#.
Coming toward you, you hear a high E, but the whistle is actually blowing F#.
This is not true of time dilation. You would hear the low C going both ways. This indicates a true paradox.
The whistle changes pitch because of its relative speed to you.
It dilates going away, and it contracts coming back, all the while blowing a clear F#.
Time-dilation occurs because of my relative speed to the railroad tracks. You hear what the railroad tracks hear in time-dilation. This way, the whistle always blows an F#, but you always hear a low C.
Deep in the well of gravity, there's more railroad track around your clock.