Beats in music : Off-beat and On-beat

To understand beats, one must have a clear idea of time signatures(discussed earlier).

In music, a "beat" is refers to a single impulse in a "meter / measure". A meter or "measure" - rhythm unit of the piece of music, is succession of an equal number beats, often even number. A typical song consists of repeating sequences of meters of equal length. This ensures that the song will have a regular rhythm. Indeed, the contrary is rare and often harsh to the ear.

A meter commonly consists of three, four, six, eight, twelve beats. It is a function of the time signature of the song and hence, also depends on how fast the song is played (referred to as the tempo). The faster the tempo, the quicker the beats come in succession. One thing must be clarified here. Irrespective of how the notes fall -

beats are always counted at regular intervals

Its a matter of equally spaced and regular counts - like 1,2,3,4-1,2,3,4 or 1,2,3-1,2,3-1,2,3 or 1,2,3,4,5,6,-1,2,3,4,5,6. Thus the beat structure of the song is akin to a regular framework upon which notes are strewn as the composer desires.

Now, form the above discussion, we come to the conclusion that beats and notes may or may not occur together at all times in a piece. This difference in the time between when the beat is counted and the note sounded forms the basis of off-beats and on-beat. Moreover the song may start on or around any beat of the meter and leave the rest of the beats either unsounded to be filled by percussion. In general, it tends to be expressed as a "stress" on a beat. Commonly, in a 4/4 time, the 1st beat is sounded the loudest and then the 3rd beat. If any of these is the strongest beat, the tune is said to be "On-beat." In case it is not and the 2nd or the 4th note is sounded the loudest and the 1st or 3rd is not, then the tune is said to be "Off-beat". If the meter has either three or six beats (such as in a 3/4 or 6/4 rhythm), the expected emphasis is on the 1st and the 4th beat.

Examples:
       #             #
     | 1    2    3 | 1    2   3|

stress on 1st beat for 3/4 = on-beat

       #         #        #        #
     | 1    2    3    4 | 1    2   3    4 |

stress on 1st and / or 3rd beat for 4/4 = on-beat

       #              #             #             #
     | 1    2    3    4    5    6 | 1    2   3    4   5   6|

stress on 1st and / or 4th beat for 6/4 = on-beat

stress anywhere else = off-beat

Point to be noted: if the note is played anywhere other than the designated beats, that too constitutes off beats.

Off-beats form the backbone of jazz and blues music and tends to be harder to master. On-beat songs are far more common, ranging from classical pieces to pop, rap, rock, grunge and metal. RnB and Indie tend go either way.

Now, especially for guitarists, the positions of on-beats tend to be the positions where a chord change commonly takes place. That may not be so in off-beat songs. The 1st of an on-beat song is commonly a down-stroke as well.
http://basicmusictheory.blogspot.com/2011/06/beats-in-music-off-beat-and-on-beat.html

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