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I have been playing this chord progression that I came up with (which is almost the same shape constantly), but I want to understand why it sounds good.

The progression is: DminAdd9 C Bb6 A7

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It probably sounds good for reasons other than music theory: you recognize it from all kinds of songs, including "Hit the Road Jack." Your progression is the same, you just added a 9th in the first chord and a 6th in the third chord.

This particular progression is an example of what we call the lament bass. Also called a "step-descent bass," it's exactly what it sounds like: a bassline that moves down by step. Your progression is an embellished i–♭VII–♭VI–V, which is a very common lament bass progression. So common, in fact, it has its own name: the Andalusian cadence.

As for your added notes, note that they are chord tones of the next chord: The add9 above D (E) is in the subsequent C chord, and the 6 above B♭ (G) is the 7th of the A7 chord.

See also What chords should accompany descending bass notes in a scale? for some other harmonizations of this idea.

  • A variation on the Spanish sequence? – Tim May 16 '18 at 7:49
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    'Music theory' is fine with this progression, it both recognises and labels it - you've quoted a couple of the labels. Theory does not demand that a progression should be all in one scale, or describable as a string of dominants and resolutions - two things that seem to legitimise a progression for many people. "Theory describes, it does not command." – Laurence Payne May 26 '18 at 17:23
  • Pretty much the same as what Knopfler plays in "Sultans of Swing" throughout the song as well. – JakeD May 27 '18 at 1:40
  • @LaurencePayne I agree. Just out of curiosity, did anything in my answer suggest I believed otherwise? – Richard May 27 '18 at 1:42
  • 'It probably sounds good for reasons other than music theory' suggests that theory can't cope with it. – Laurence Payne May 27 '18 at 17:16

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