A hemiola is a section of music that technically spans two bars, but acts like it spans three, or vice-versa. The technique was popular in the Baroque era, and was used in many Viennese waltzes. Essentially, musicians play two triplets in 3/4 time as if they were three duplets in 2/4 time. This can be difficult to distinguish in a piece of music, but the accents usually employed at the beginning of each bar allow listeners to distinguish the change. Generally, square brackets will surround the groups of notes in a hemiola to show how they should be played.
Basic understanding of musical time signatures is required to understand what exactly a hemiola is. Music is split into bars, which are basically set periods of time containing a predetermined number of beats. The period of time is indicated by the bottom number in the time signature, and the number of beats is indicated by the top number. In 4/4 time, or common time, there are four beats in a bar, equally spaced at quarter-bar intervals. A hemiola can only occur in 3/4 time, where there are three beats spaced out over a bar at one third of a bar intervals.
In a standard bar of 3/4 music, there will be three quarter notes split up over the length of a bar. Thinking of a clock face can help laymen understand this idea. In a standard 4/4 bar, the beats will occur at the 12 o' clock, three o' clock, six o' clock, and nine o' clock positions. In a 3/4 bar, the beats occur at 12 o' clock, four o' clock and eight o' clock.
The length of a bar is not a fixed term, so technically speaking, two bars of 3/4 time and three bars of 2/4 time both have six beats spaced out evenly. This means that they cannot easily be distinguished from one another. The only technique used to indicate the beginning of a bar is accenting, whereby the first beat of a bar is played with emphasis. In a hemiola, instead of accenting every third beat as per 3/4 time, every second beat is accented as if it were in 2/4 time.
Musical notation generally uses square brackets to indicate when musicians should perform a hemiola. If the group of three notes has a square bracket over them, the first note of the three should be accented, as if the three notes were together. In a hemiola, the notes in two 3/4 bars will be split into groups of two by square brackets. This shifts the emphasized note and creates the effect often employed by Baroque-era musicians.