It has often been asserted that Metal is to one extent or another a continuation of Romantic Classical, if this is the case, then I have to suggest that Hardcore Punk music may be a continuation of folk music.
I see many parallels: Hardcore is structurally simple music by definition. It is usually made casually by a group of close friends, often with some of the members not particularly musically inclined aside from playing their instruments. They often view it more as a way to socialize and have fun than an artistic desire to create something of beauty, although that may and often does factor in as well.
The songs are usually short, rarely longer than 5 minutes. I've been told that back in the heyday of Hardcore, punks were often preferred bands from their general area over foreign bands, even when music from far away was available. Such regionalism is a rather folkish sentiment in my view.
In addition, the way Metal and Hardcore Punk have interacted over the years mirrors the relationship between classical and folk. Metal sometimes uses hardcore punk technique to imbue the music with a sense of fun, excitement and youthfulness, such as Speed Metal. Casualness, for lack of a better word. Many Hardcore bands that slowly turn more Metallic album after album often do so in an attempt to show off their musical ability, as if to prove they can write complex music as well. When they do this, the music often becomes more heavily structured and sometimes more serious. The first three Suicidal Tendencies albums show this pattern in particular.
There are many more parallels between the genres that I can't quite put into words right now, so I leave it to you fine Hessians to discuss.