The difference between part and a part has to do with the context and intent of the sentence, not the noun that the part is referencing.
According to ODO, the two most common definitions of part are:
- An amount or section which, when combined with others, makes up the whole of something:
'divide the circle into three equal parts'
- Some but not all of something:
'the painting tells only part of the story'
Source: Oxford Dictionaries Online, "part"
Definition 1 comes off as more segmented and distinct than definition 2. Imagine definition 1 as talking about slices of a pie, and definition 2 as talking about ingredients mixed into a cake. Both are parts, but one is separable, the other is not.
When you say something is a part something, you are using definition 1. So to make something a part of our music means that we want to incorporate that specific element (dubstep wobble, or cowbell, for instance) into our music.
When you say something is part of something, you're using definition 2. So to make something part of our music means that we want to make it integral to our music, an inseparable defining element.
Hope this helps!