We have seen how onset timing can be specified when the music has no pulse, by measuring time by the clock (see Pulseless onset timing). When the music does have a pulse, it establishes its own time scale, and this provides a more meaningful measure of onset timing than minutes and seconds. Our horizontal time scale will then be calibrated, not in seconds, but in pulses or beats.

These equal units of musical time are incorporated into the “manuscript paper” for our score in the form of equally spaced vertical lines called “beat lines.”

Beat lines are drawn the same thickness as layer lines, which is thinner than the lines in the “rotated T” symbol for sounds specified duration. In a layer of unspecified pitch, if symbols are to be placed only above the layer line, the beat lines extend from the layer line up. The beat lines are drawn longer than the height of the symbols so that they will still be visible even if they coincide with the left-hand edge of a symbol.

Beat lines above the layer line

If symbols are to be placed both above and below the layer line (see Specifying other information where duration is unspecified), the beat lines extend in both directions. Again, they extend beyond the height (or depth) of the symbols.

Beat lines above and below the layer line

Tempo is indicated with a “hurdle” (see Pulseless onset timing) extending from the first to the second beat line and, above the hurdle, a figure preceded by the “at” sign @ which indicates the number of beats per minute. For example, “@84” is shorthand for “at a tempo of 84 beats per minute.”

Tempo hurdle

When the score contains more than one system, the beat line at the end of a system represents the same moment in time as the one at the beginning of the next system.

Score with two systems

Symbols for sounds of either specified or unspecified duration can then be placed along the layer line(s) to specify onset timing in relation to the beats. When an onset falls “on” a beat, the left-hand edge of the symbol will coincide with the relevant beat line.

For the simplest possible example, if we wanted to notate the ticking of a metronome, our score would show an onset on every beat.

Metronome beat score

As a metronome can go on ticking indefinitely, we here introduce a way of representing repetition without having to write out the same passage repeatedly. This will be useful for many of our examples from now on. The sign for repetition, placed at the top of a system, is a right-angle bracket within which is written the mathematical symbol for “times” (x) followed by the number of times the passage is performed. If we don’t want to specify a definite number of repetitions, but just to indicate that the passage is repeated indefinitely, this number is given as “infinity” (∞).

If the repeated passage starts from the beginning of the score, a bracket is placed at the end of the passage only, with its horizontal arm pointing back to the repeated passage. If it starts from a different point, an additional, reversed bracket is placed at the beginning of the repeated passage. The vertical arm of a bracket specifies the moment where the repeated passage begins or ends. For example, a passage performed twice, starting at a point other than the beginning of the score, would be marked as below.

To return to onset timing: we now know how to indicate onsets that fall on a beat. In most music, however, onsets will occur on some beats and not others, and some onsets will occur between the beats. Moreover, the beats themselves are not uniform and undifferentiated like the ticking of a metronome. Instead, they are grouped into regularly recurring units of a certain number of beats, with some beats having more (or different) emphasis than others. We therefore need a way of representing both the grouping and the division of beats.