Tremolos are a musical shorthand which indicate the rapid repetition of notes and chords.
There are two types of tremolos:
1. The repetition of the same note or chord, notated with strokes through the stem (or where the stem would've taken place for stemless notes)
2. The alternating repetition of two different notes or chords, notated with strokes between the two figures.
Figure 1: An array of different tremolos.
Tremolos are not to be mixed up with vibrato (the wavering/oscillation of pitch)!
2 tremolos have one slash through their stem and are subdivided into two separate units.
Figure 2: 2 tremolos.
4 tremolos have two slashes through their stem and are subdivided into four separate units.
Figure 3: 4 tremolos.
8 tremolos have three slashes through their stem and are subdivided into eight separate units.
Figure 4: 8 tremolos.
16 tremolos have four slashes through their stem and are subdivided into 16 separate units.
Figure 5: 16 tremolos.
32 tremolos have five slashes through their stem and are subdivided into 32 separate units.
Figure 6: 32 tremolos.
A buzz roll is a special kind of tremolo used in percussion notation which indicates to repeatedly strike the note or chord as fast as possible.
Buzz rolls are notated with a Z through the stem.
Figure 7: Three different buzz rolls.
Tremolo with Next Note
Putting the tremolo slashes in-between two notes or chords indicate they are both to be alternately repeated. The same "number of slashes" rule applies here for the frequency of repetition.
Figure 8: A tremolo with the next note.
When notating a tremolo with the next note, each of the two note are written as if they lasted for the whole length of the tremolo:
Figure 9: The correct notation for a tremolo with next note.
Also see Ornaments.