# Beat division

We’ve seen how to indicate regular beats and their grouping into bars (see Beats; Bars). That is, we now know how to deal with the moderate and slow rates of pulsation in music; but we still need to know how to handle the fastest rate of pulsation, the rate of what we are calling the “pulses.”

For this fast rate of pulsation to be discernible at all, some of the onsets must be falling on a pulse that is not a beat—that is, a pulse that comes between the beats. In our score, therefore, the left-hand edge of some symbols must be placed somewhere between the beat lines. To decide exactly where to place the symbols within that space, we need to know how the beat is divided, in other words how many pulses make one beat.

The most common beat division is by two, where the pulses come twice as fast as the beats. In this situation, when an onset falls on a pulse that comes between beats, the left-hand edge of the symbol appears exactly half-way between two beat lines. The fact that the beats are divided by two is indicated at the beginning of the score by writing “/2” after the figure that indicates the number of beats per bar. Optionally, the tempo can then be specified in the usual way, with the @ sign following the “/2” and preceding the figure for beats per minute.

For example, the sports cheer “Two, four, six, eight, who do we appreciate?” is based on a meter of four beats to a bar, with onsets at first coinciding with the beats but then coming twice as fast and implying an underlying pulse that divides the beats by two.

The figures above the bracket here mean “4 beats per bar, each divided into 2 pulses, at a tempo of 140 beats per minute.” To save time, they could be read as “four over two at one-forty,” giving a concise indication of the meter and tempo.

The well-known “Shave and a haircut, two bits” rhythm is based on the same meter and beat division, even though only one beat (the second) is actually divided by an onset.

On the other hand, the American folk song “Risselty, Rosselty” has two beats to a bar with beat division by three. The triple beat division is indicated by “/3.” (The rhythm of the refrain is shown here with specified durations but unspecified pitch.)

A triple beat division is also often implied by the way jazz drummers play the common “ride” cymbal pattern, with a stroke two-thirds of the way between beats (even though there may be no strokes at the “one-third” position). In this case, as usual in jazz, there are four beats to a bar. As the tempo can vary widely, no tempo figure is given here. (The right-angle bracket with “x∞” indicates that the pattern is repeated indefinitely; see Beats.)

A meter of four beats to the bar with beat division by four has been standard in many styles of popular music since the 1970s, including funk, hip hop, and disco. Here it is illustrated by the Bee Gees’ 1977 hit “Stayin’ Alive.” (This excerpt shows the rhythm of the vocal part for the first one-and-a-half bars of the chorus.)

(Note that “4/4” here does not mean the same as “four-four time” in staff notation. “Four-four time” tells you that there are four beats per bar but doesn’t tell you how the beats are divided, whereas in global notation “4/4” tells you that there are four beats per bar, each divided into four pulses.)

A fast rate of pulsation can be implied even when no two onsets fall on consecutive pulses. This is the case with the famous clave pattern of Latin American music. The clave is based on four beats to the bar, but because its second stroke falls three-quarters of the way between beats, a pulsation four times as fast as the beats is implied (and is often made explicit by other instruments in the ensemble). That is the slowest rate of pulsation that can account for all of the onsets (i.e., the slowest at which every onset falls on a pulse).

We now know how to specify onset timing when the onsets fall on pulses that divide the beat in various ways. In actual performance, onsets may even fall between the pulses, for instance when performers use rapid ornaments or slight variations of timing for expressive effect, and for some purposes that level of precision may be wanted in the score. A piece of music may also use more than one beat division, either sequentially or simultaneously. Global notation can represent such situations, but they are a little “advanced” for our present stage.

If you are interested in notating music that is based, not on dividing time into equal units, but on adding together unequal units of time (as in the 5- and 7-beat meters of some Eastern European, Middle Eastern, and South Asian music), see Additive meter.

Otherwise, a more immediate need is the ability to represent more than one rhythm played simultaneously, as happens more often than not in most kinds of music. This will require the principles we’ve discussed to be extended to examples with more than one layer.