A type of dance where you hold your partner, and one partner leads while the other follows. Usually the (designated) male leads, it's kind of old-fashioned that way. Typically the dance has a series of basic and advanced steps, as well as a specific beat, that mark it.
For North American consumption, ballroom dance comes in several flavors. The most commonly played style is the foxtrot (also called the two-step) which makes up about 80% of what you'll hear at a dance hall. This is because it's easy both musically and dancewise. In fact, the basic foxtrot step can be done without any risk of toes being stepped on!
Most well known is the waltz, which is an elegant and formal dance that is most often encountered at weddings. It takes a bit more coordination and knowledge than the foxtrot. However, because it can be done as a box step it is more suitable for small dance floors.
Also played on occasion is the rhumba (a.k.a. rumba). This is also a box step but includes Cuban motion which makes it more sensual (when done properly, anyway).
The rumba leads to the more dramatic Tango which follows Line of Dance somewhat aggressively, and is marked by close contact between partners and dramatic looking turns and breaks.
Also similar in use of Cuban motion is the Cha-cha-cha or Cha-cha, which is another box step style of dance. It's characterized by distinctive music and flourishes that consist of breaks and spins instead of turns.
Also common is swing dancing which works to most early rock and roll like Rock Around the Clock and Mack the Knife and most Elvis songs. There are two variants (slow and quick) and many kinds of turns effected largely by exchanging hands and a specialized dance hold.
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Everybody Dance Now!