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1.
Hardcore dancing is a form of mosh (or slam dancing), an activity performed in a mosh pit at hardcore music shows. Generally the dancing is done to certain visceral parts of hardcore songs specially written to make the audience move around. Common names for these parts are "breakdowns", "beatdowns", "throwdowns" and "two-steps." Some common derogative terms for said dance are "Ninja Dancing" (named because the dancers look like they are fighting invisible Ninja), "Karate Dancing", and "Straight-edge Ballet".

The practice grew mostly out of the East Coast hardcore scene, especially in New York City. Besides the usual mosh pit routine of pogoing and crashing into each other, participants enjoyed floorpunching to the beat when a slower, more groovy riff was being played. During shows by bands like Gorilla Biscuits, Edgewise, Agnostic Front, Sheer Terror, Killing Time, and The Horror Novel. this style of dancing was common. In the following years as bands incorporated slower syncopated, metallic rhythms into their songs, the modern "breakdown" and the dancing that went with it was introduced. Sometimes called "kickbox moshing" by its detractors, hardcore dancing now included violent windmills with the arms, karate style spinkicks, and "crowd-beating", the act of simply tackling a group of non dancing onlookers, sometimes into the wall. Early Earth Crisis and Biohazard shows were extremely common areas for such activity.

The two-step is also common in hardcore dancing. It is used exclusively during mid-tempo punk rock styled riffs and beats. Much like the two step in breakdancing or country line dancing, it involves placing one foot in front of the other and hopping forward onto it, then repeated with the other foot, etc. Combined with forward thrusts by the arm opposite to the forward-stepping foot, the dance creates a sort of "running in place" illusion. The move is commonly practiced and refined to look slick or interesting. The "two step" was taken from another form of dancing known to ska music, "skanking."
Some hxc bands (including popular ones) have included examples of hxc dancing in their videos. New York hxc punk band Sick Of It All (though not critical of dancing, as their early shows surely brought just as much hxc dancing as any band) featured a tongue-in-cheek "how to" parody of dancing in their music video for "Step Down." One can easily find videos taken by fans at various hardcore punk shows by typing "dancing" or "mosh" into the Kazaa or Soulseek search programs. Of the many videos found on there, among the most popular are 3 preview videos for DVDs put out by the Guerilla Warfare Video Fanzine. All three feature a large array of dancing clips, including people literally bouncing off the wall, circle pitting, and even various injuries, filmed all over the world.
by xBleedingXedgex July 02, 2006
 
2.
a thoroughly idiotic-looking version of moshing. involves flailing of arms. also involves getting slaughtered if done at a metal gig.
hxc dancing:
Look at that fucking kid!!
*much blood and guts ensues*
by funnylittleman July 15, 2008
 
3.
Just kick, punch and generally flail your limbs to the tune of hxc music.
hxc dancing kid: *flails around like a beached Great White*

Me: THAR SHE BLOOOWS!! *readies harpoon*
by Poemeiser January 12, 2007
 
4.
First of all, "hxc" is a lazy way of saying Hardcore, which usually means the genre of music that has a mix of singing and screaming (the better hardcore bands are closer to metal, the bands that are hxc danced to are "scene")

Hardcore dancing is basically a scenekid's equivalent to a mosh pit. It is when someone with a thousand different colors in their hair flail their arms and legs around like a moron, but won't go into the pit and shove people around.
A girl with straightened hair, dyed all the colors of the goddamn rainbow, ran into the open center of the crowd and began hxc dancing - and was promptly knocked unconcious by a metalhead who ran into her from the most pit
by WCMetalhead September 12, 2010