Yes, but you have always a duality problem between tempo and beat, i.e. are they two eight notes at that tempo, or two quarter notes at twice quicker tempo...

Yes, but you have always a duality problem between tempo and beat, i.e. are they two eight notes at that tempo, or two quarter notes at twice quicker tempo... You can assume that the most prevalent duration is a quarter note, but it is not always what would be on the score. But it's more a problem related to transcription than to DJing (where the representation of the beat as a whole note, a quarter note, or anything else is eventually not important, I think).