A beam is a thick horizontal line which links the tails of two or more notes.
Figure 1: Two quavers beamed together.
Notes are beamed together according to the musical context (meter). For example, in 4/4 time you could group a bar of quavers as followed:
Figure 2: Three bars of quavers, each beamed differently.
Beams are written above or below the group of notes depending on the greater number of pitches written above or below the centre-line:
Figure 3: A group of notes with it's beam written above.
Figure 4: A group of notes with it's beam written below.
Beams may also be angled according to the contour of the grouped notes:
Figure 5: An angled beam.
In some music (i.e. percussion notation) it is customary for beams to always be drawn horizontal and never on an angle.
Beams are split up into two different layers: primary and secondary.
Primary and Secondary Beams
The primary beam is the one furthest from the noteheads whereas secondary beams are any beam in-between:
Figure 6: The primary and secondary beams outlined in a bar of notes.
This method of beaming allows the rhythm to be read clearly.
Beam Between Notes
In older scores (particularly in violin notation), if a group of notes are very low then very high (or vice versa), you will sometimes see the beam running between the notes:
Figure 7: A beam between notes.
Beam Across Barlines
Beams may carry on from one bar to the next as shown in this bass clarinet part of Stravinsky's Petrouchka:
Figure 8: A beam running across a barline (even a system).
In keyboard and harp notation, notes from both staves may be beamed together to indicate a flowing between the hands:
Figure 9: Beaming between the great staff.
In contemporary music, extra beams sometimes "play out" from a single beam to indicate an accelerando or ritenuto:
Figure 10: Two feathered beams.
Also see Notes | Dotted Note.