Apple Logic Express 8 - Manual (Page 477)

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Quantizing MIDI Events
Quantization is the rhythmic correction of notes to a specific
time grid. Any inaccurately played notes are moved to the
nearest position on this grid.
As an example, if the shortest notes in a passage are 1/16th notes, you would use 1/
16th quantization to move all notes to their ideal rhythmic position on the grid. This
will only work, however, if no note was played more than 1/32nd from an ideal
position. Any very loosely played notes will be moved 1/16th later or earlier than the
desired position.
You have the choice of quantizing complete MIDI regions or individual events:
 Region-based quantization affects all note events in a MIDI region. It is used on MIDI
regions in the Arrange area.
 Event-based quantization can be applied to any individual MIDI event (not only note
events) within a MIDI region. Individual event quantization is performed in the MIDI
editors.
1 3 2 4 1 2 3 4
1 3 2 4 1 2 3 4
Unquantized note events
Quantized note events, aligned to the nearest beat position