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The song is in the key of C: At about 30 seconds, he plays the chord D major(not in the key of C), with the notes C G and E (all non chord tones). Soon after there's what appears to be an arpeggio of the chord Ab diminished(not in the key of C), all of these moves sound palatable to the ear. Why does this work? Thanks!

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Immediately before the D major, he/she plays an E major followed by an A with no 3rd, which you can count as A minor. (It sounds like the 3rd is omitted by mistake.) So the song modulates to A minor, where a D major chord fits in quite well. The F# in it doesn't belong to the natural minor scale but does belong to the Dorian scale, which is used quite often as an alternative. Playing a C over a D major is not unusual, it turns the chord into a D7 if you want to consider it part of the chord. The E is a 9, which is used quite frequently as well. Most people would say the G doesn't really fit unless it replaces the F#, making the chord a Dsus4. But it is short and not emphasized.

The Ab (or G#) diminished is a bit strange. It could be an E7 without the root; in which case the C at the top would be a b13. In that case, I would expect an A minor as the next chord, but instead the song progresses to C major, which doesn't even work as a surprise because it's the tonic. There may be other ways to interpret it, but I wouldn't bet on it because it doesn't actually sound good to my ears.

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