A minuet is a stately ballroom dance for two people in triple meter. It is of French origin and was popular in the 17th and 18th centuries. Minuet also describes the musical style that accompanies the dance.
Scène de carnaval, ou Le Menuet, Venice 1755| Giovanni Domenico Tiepolo (1727-1804) | Metropolitan Museum of Art
Here's a short French minuet from the early eighteenth century:
Minuet in D Major (1:13) | Robert de Visée (c.1655-1733)
The early Baroque minuet was a simple binary form (A A B B). Eventually the humble Baroque minuet evolved into a longer and more stylized form called minuet and trio. The minuet and trio was cast in an A B A form was used only for listening, drifting away from its dance origins. A typical minuet and trio form may be diagramed thus:
a a ba' ba'
c c dc' dc'
Notice that the outer sections (minuet) are the same but the final minuet omits the repeated sections. Modulation or mode changes are sometimes used in the trio section for added contrast and tension. The minuet and trio is commonly used as a movement in the classical symphony, chamber music and solo sonatas for piano and guitar.
A Minuet, 1824 | Sir George Hayter (1792–1871) | Yale Center for British Art
Eine kleine Nachmusik
Mozart's Eine kleine Nachmusik, K. 525, is scored for string orchestra and the third movement is a wonderful example of the minuet and trio. Here's the melody from the beginning of the Minuet (A section). Listen carefully and you'll hear it return after the Trio (B section).
Here's the melody at the beginning of the Trio (B section):
Eine kleine Nachmusik, K. 525, III: Minuet & Trio (2:29) | Wolfgang Amadeus Mozart
Here's a simple but charming minuet and trio written by Mozart's friend, Joseph Haydn. The sudden shift from a happy major scale sound to a more serious sounding minor mode at 1:19 is where the Trio or B section starts.