Pitch is only half of music. The other half is time: when notes start, how long they last, and how they group. A melody stripped of its rhythm is usually unrecognisable, while a rhythm alone can still be a piece of music.
The beat
Underneath most music runs a steady pulse, the beat. It is what you tap your foot to, and it is felt rather than necessarily played: the beat can be perfectly clear at moments when no instrument marks it.
How fast that pulse runs is the tempo, given in beats per minute. Around is a slow walk, is brisk and is where a great deal of dance music sits.
Metre
Beats are not all equal. They group into repeating patterns of strong and weak, and that grouping is the metre, written as a time signature.
In four-four, beats come in fours with the first strongest, which is the metre of most rock, pop, and folk. In three-four, they come in threes, giving the lilt of a waltz. Six-eight groups six quick pulses into two sets of three and produces a rolling feel, common in jigs and ballads.
Metre matters because it creates expectation. Once a listener has locked onto a grouping, they know where the strong beat is coming, and every rhythmic effect in music is built on either satisfying or frustrating that.
Note values
Durations are written as fractions of each other, which makes the system easy to read. A whole note lasts twice a half note, which lasts twice a quarter note, which lasts twice an eighth, and so on down.
In four-four, a quarter note gets one beat and four of them fill a bar. A dot after a note adds half its length again, so a dotted quarter lasts a beat and a half, and rests work the same way for silence. Because everything is defined by ratio rather than absolute duration, changing the tempo speeds up or slows down the whole structure without altering a single written value.
Syncopation
The most powerful rhythmic device is to put emphasis where the metre says it should not be. Syncopation accents the weak beats, or the gaps between beats, pulling against the pulse the listener is already feeling.
Nearly every style that makes people want to move runs on it: jazz, funk, reggae, Latin music, hip hop. The effect depends entirely on the metre being established first, since you cannot subvert an expectation the listener has not yet formed.
That is the general shape of how music works. A framework is set up, whether a key, a scale, or a metre, and the art lies in playing against it: departing far enough to create tension, and returning in a way that feels earned.