Hi Savio,
I fear that I have failed you for if you do as you describe you will be engaging in some more attachment (!). Try listening to your wife's 80's music and just notice the aural sensations. If you "[try] enjoying it, and [endeavor] to understand why she likes it" then you are still attached to an outcome and listening with preference. Non-attachment demands we interrupt the (for most of us) adamantine link between stimulus and our chosen response. For most people these two separate things are one thing - as you highlight: "gosh, that music is only noise without harmonious melodies" - your normal response.
Instead you just want to notice the sensations without evaluation. Does this make sense? I admit this is difficult work...but it is also most rewarding! For once you can separate stimulus from response then you can hope to choose your interpretation, rather than be subject to preconceptions like preference, prejudice, and mental models. This, in turn, means you can hope to better understand reality as it is, rather than how you prefer it to be.
Hope the weekend is good for you (my preference and hence, attachment!)!,
Jason