Because sound is by its nature a temporal phenomenon, any musical characteristic can change in time. The way in which music is organized in time is called rhythm, or, at a higher level, form or structure. Because all music must exist in time, it therefore makes no sense to say that a piece of music "has no rhythm," although it may not have a beat, as we shall see.
Very often, loudness changes over a short time interval as a string, for example, is plucked. Before the pluck there is silence, then a sudden change to maximum loudness, and a gradual decay of the sound. Because much music consists of sounds with characteristic beginning and ends such as this, they each are known as notes, and the characteristic change in loudness over the life of the note is called the envelope. Notes help the brain organize sounds into discrete events that can then be associated with times.
The brain is very good at fitting events into patterns. When it is able to find a common denominator to the timing of notes, we may find ourselves tapping our foot along with it. That regular pulse is called the beat. Certainly not all notes are a beat long, but as long as they begin on the general grid of beats, the brain has no trouble in identifying the beat.
The relative speed of the beat is called tempo, and the tempo of most music is usually between 50 and 180 beats per minute. Not all music has a beat, and such music is sometimes called non-metric or non-pulsatile.
Depending on the music, it may also seem natural to clap along every two or three beats or to clap twice per beat. Such groupings of beats seem natural because time is usually organized into multiple divisions of time in addition to the beat. The organization of time into beats, groups of beats, and beat divisions is called meter. The most common numbers of beats in a group or divisions of a beat are either two or three, although five or other numbers are possible. A meter in which the beat divides into two is called a simple meter; divisions into three define a compound meter.
A meter in which beats are grouped into twos is called a duple meter and threes a triple meter. Therefore a simple duple meter is one in which the beats are divided into twos and grouped into twos, as in a march (and many other types of pieces). The next most common meter is probably divisions into two and groups of three, which is therefore a simple triple meter, like a waltz. Groups of twos and divisions into threes is a compound duple meter, such as a jig. Groups of threes and divisions into threes is a compound triple meter, which is not very common.
Simple duple: 
Simple triple: 
Compound duple: 
Compound triple: 
Once a meter is established, we expect that notes will align to these beats, groups of beats, or divisions of beats. Sometimes, however, composers will deliberately evade such an expectation by emphasizing a division that would otherwise be unstressed. Such a stressed note occurring on a relatively unstressed beat in the meter is called a syncopation. Certain types of music are characterized by a relatively high amount of syncopation, such as ragtime, jazz, and many forms of Latin American music.
