Dancing at the Emerson School in West Hopkinton. Photo from Vivian Mitchell who organized the dance, 1990s.
People have been dancing in New England since colonial days. In the early days, not surprisingly, our music and dance were very much tied to what was happening with English and French music and dance. I remember at one of the early Ralph Page Dance Legacy Weekends there was a presentation, possibly by Chip Hendrickson, in which that topic came up. It turns out that the earliest round trip from here to England and back for the purpose of learning and bringing back the latest dances was in the very early 1800s. That was far from a trivial trip in those days, which says a lot about the importance of the dance at that time.
The following is an overview of the music and dance. For more details there is an article in Wikipedia, and there are many other presentations on the web.
The square dance bands also played waltzes and foxtrots. They often included saxophones, drums, electric guitar, etc. (Photo, Vivian Mitchell, 1990s)
The two dominant forms of New England country dancing have been contra and square dancing for a long time. Both have changed a lot over the years, and their relative popularity has fluctuated rather drastically over the years. The contradances can be traced to English country dance, and the squares to the French quadrilles.
Contras are done in line formation: two parallel lines with partners generally across from each other. Some contras are in proper formation meaning that all the men are in one line and all the women in the other. Others are in improper formation, meaning that every other couple switches places with their partners. A more modern formation has everyone next to their partners, facing another couple in the opposite line. This is known as Beckett formation, named after the Beckett Reel which was the first dance in that formation. Each time through the dance you dance with one couple; at some point you progress, or move on to the next.
Squares are danced in square formation (of course), with one couple on each side of the square. Many New England squares are visiting couples dances, in which the active couple goes out to each of the others and does a set of figures. There are also dances in which the head couples (facing toward or away from the band) are active together, alternating with the side couples. Some squares are breakdowns, meaning that everyone is active all at once.
Contradance bands are more likely to include fiddles and piano (these days more likely a keyboard, sometimes a guitar instead). There may also be a flute, mandolin, and occasionally hammered dulcimer. This is the Lamprey River Band playing for the Dover contradance in July, 2006.
Contras and New England squares (as opposed to club-style Western square dancing) are nearly always danced to live music. As most contradances are of a specific length, contradance tunes are of that length too.
A contradance tune generally has two parts (called the A and B parts), each of which is 8 measures (16 beats) long. Generally each part is played twice in the pattern AABB for a total of 32 measures, the length of a dance.
Each part of the tune is divided into shorter phrases, generally in multiples of two. So there are generally four-measure phrases and sometimes even two-measure phrases. These match the phrasing of the dance which is divided into several figures, usually four or eight measures long and sometimes two measures long.
Music for square New England squares tends to be similar, except there are a number of squares where the calling is sung to specific tunes from the repertoire of popular songs of the last century or so.
Sometimes the band is quite small (e.g. fiddle and piano); other times it's prety large, and sometimes there are as many sit-in musicians as band members
A basic band would be fiddle and piano. Beyond that you could add in guitar, bass, flute, another fiddle, accordion, or other instruments (e.g. hammered dulcimer, mandolin, etc.). At one time instrumentation was different, including horns, saxophones, drums, etc. These days guitars are replacing pianos at some dances. Sometimes sit-in musicians are encouraged, sometimes they aren't permitted. Sometimes there are even more sit-in musicians than band members.
Tunes have clear phrasing so the dancers can hear when to start a new figure. Musicians play the melody clearly and rhythmically. Accompaniment is also done strongly and rhythmically. Some harmony is also fine, as is variation, as long as you don’t lose the phrasing and rhythm. It’s important to play in a strong rhythmic fashion for dancing, and to give lift to the music so people feel like moving and dancing. When the excellent dance piano player Bob McQuillen was asked what advice he'd give to someone who was learning to play, he said, "Keep the beat!"