Originally Posted by: dlwalke

If you have 4 quarter notes in a measure, in 4/4 time, the quarter notes occur on the beats (i.e., 1, 2, 3, 4) and I would think that the first beat occurs at the onset of the measure.[/quote][p]Yes, unless there is a pickup measure (technically called an anacrusis).

[quote=dlwalke]However, when you see sheet music, there is space between the vertical line that indicates the beginning of the measure and the first note.

Where did you see this?

Typically there can be a line on the extreme left edge of the staff. Then that is followed by the clef sign, key sig & time sig. Then the notes start.

The exception I can think of is if there is a repeat sign indicating to return to the notes of the first measure.