iTunes

I have recently transferred all my old data to a new iMac. When in iTunes, I can play some songs but not others. The error message that is prompted is that the song is NOT authorised to play on the iMac because it is not authorised. I proceed to authorise the song using my one and only Apple ID whereby the error still occurs with the same message. I have authorised the new iMac - only 2 of 5 of my devices are authorised so it I have not exceeded the limit.

I don't understand why this is happening.