Introduction

Using Western music notation to communicate rhythm and metre is primarily a matter of clarity and consistency. Readers and performers of music need to be able to grasp the timing of musical events accurately and efficiently. The more complex the notated music becomes, the more important it is to maintain good practice. Being able to write music clearly in this way also aids our understanding of the rhythmic and metric organisation of music.

This chapter covers basic principles of organising the duration of notes and rests in simple rhythmic configurations in the context of musical time and metre. More complex topics are covered elsewhere. For fundamental concepts around metre, you can read the chapter on metre; you can also review the chapter on time signatures, which covers the standard time signatures and traditional concepts of simple and compound time.

The Value of the Bar

In most music with a regular metre, bars form a fundamental span of measured time (hence the alternative term, “measure” favoured in North American music theory texts).  The length of a bar is defined by the active time signature. The total duration of the rhythmic content (notes and rests) of each and every bar must be equal to exactly the number and value of the primary beat level. For instance, in time there are three crotchets in each bar, so the total value of rhythmic content in a bar of must neither exceed nor fall short of exactly three crotchets. Likewise, to give one more example, a bar of must contain a total rhythmic content equal to two dotted crotchets (or six quavers).

This might seem self-evident, but it is often cause for confusion in the early stages of writing music and, if not understood, may cause problems later. The following example shows cases where the total value of the rhythmic content of a bar does not match the time signature. Where there are too many values (a), the extra values must go into a new bar; where there are too few (b), rests should be added to make up the shortfall.

It is also important when you are working with multiple bars not to allow the rhythmic content in one bar to “spill over” into the next bar and “compensate” by reducing the rhythmic content in that bar. In such cases, a note at the end of the bar must be tied to a note at that start of the next so that the total value of each bar reflects the time signature.

In Example 00, three minims are placed across two bars of time. Mathematically, this would seem to fit because three minims are worth six crotchets (3 × 2 = 6), and there are six  crotchet beats in two bars of time (2 × 3 = 6).  But it contradicts the principle of filling the value of every bar exactly—there are two many values (four crotchets) in the first bar and two few (two crotchets) in the second. The solution is to rewrite the second minim by turning it into two crotchets joined by a tie across the bar line.

Finally, in case it is not fully clear, when we talk about the “total rhythmic value of a bar,” we are referring to single and simultaneous events alike.  As far as time and metre are concerned, a single crotchet, a pair of crotchets played as a harmonic interval, a crotchet played as a thick chord on the piano, and so on, all the way to a full orchestral “hit” of one crotchet, are all worth exactly one crotchet of time.

Proportional Spacing

We have noted elsewhere that rhythmic notation is not strictly proportional.  That is, the horizontal space taken up by a minim is not twice that taken up by a crotchet, nor four times the space taken up by a quaver, and so on.

Instead, rhythmic notation follows a principle of relative proportion—longer note or rest values should take up somewhat more space that the next shortest value, but in nothing like an exact 1:1 ratio of value.

In the following example, an identical two bars of a rhythmic idea comprising a mix of values is shown in strict proportional positioning (a) and positioning that follows the principle of relative proportions (b).  The strict spacing lacks the economy and readability of the relative spacing. Also, note that the multiples of “x” in (b) are a guide—you don’t have to measure these values with a ruler, but you should develop an eye for these proportions when writing by hand.

Musicians have become very accustomed to reading rhythms in the relative proportions shown in (b) and anything that violates this, such as (a), seems instantly wrong. To take this to a further extreme, consider (c) and (d) in Example 00. In (c) we have just spaced every note head an equal distance apart. In (d) a completely random spacing is used, with some shorter values actually taking more space than longer ones. Both show poor rhythmic notation and are very difficult to read with any accuracy; the wild spacing of the numbered beats confirms the problems.

Alignment of More than One Part

In music composed of more than a single part, in presenting these parts in a score, it is essential to make sure that all parts are aligned according to the time signature and its subdivisions.  In short, simultaneous events must be absolutely aligned vertically, as shown in the example below.

In the example above, if we take the individual parts separately, then each part in (b) might actually follow the approximate proportion requirement better than in (a) but, for readability of the score, having the rhythmic event onsets aligned vertically takes preference.

The problems of not aligning parts become compounded when the music involves a great deal of rhythmic complexity and difference between parts.  In Example 00, the alignment of parts becomes quite critical owing to the complex and varied rhythmic nature of the two parts, in addition to the fact that while one part has a lot notes, the other has considerably fewer.

In (a) every simultaneous event is perfectly aligned.  To create (b), relative proportional spacing was applied to each part separately and then they were combined.  Individually, each part is coherent, but in combination, the rhythmic notation becomes extremely problematic.  The dotted arrows that were perfectly vertical in (a) now diverge at seemingly random angles in (b), emphasising the misalignment of parts. In particular note how this results in anomalies at the points marked x, y and z. At x, it appears as thought the crotchet rest in the lower part coincides with the G initiating the scale of demisemiquavers. At y, the lower part’s quaver rest at beat 4 lines up with the semiquaver D which precedes this beat. At z, it appears as though the group of four demisemiquavers (C–B–C–D)—whose total value is one quaver—takes the same amount of time as the dotted quaver–semiquaver F♯–D—whose total value is one crotchet. This leads to a very confusing rhythmic layout for the reader.

Beaming and grouping of quavers and smaller values

It is important to organise smaller rhythmic values into groups that clarify the metre and thus make reading easier. Quavers and smaller values can be “flagged” individually or “beamed” together in various groups.  When we group these values we organise groups to emphasise the metrical basis of the music.  For instance, if we take a set of six quavers (either flagged or beamed), these might fit into either a bar of or .  Accordingly, we would group these six quavers using beams into three groups of two or two groups of three.  See Example 00.

The “ski-hill” graphs on either side show the different paths to grouping (beaming) these quavers.  In both cases the longest metrical value is the bar (equal here a dotted minim), below this the tactus (either crotchet or dotted crotchet) and first subdivision (quavers).

All “standard” time signatures have fairly conventional ways of grouping subdivision of values at the quaver and below. It is not possible to be exhaustive, but the next two examples show the usual options for simple and compound metres.

In simple duple time (a) the subdivision of the primary beat is straight forward.  For the next subdivision (in this example dividing quavers into semiquavers) standard practice is to retain the beaming that reflects the primary beat. However, as shown in the third bar, further subdivision (semiquaver to demisemiquaver) usually means dividing the beam groups into four, which is more visually manageable (reflecting a quaver subdivision) or, to retain the primary beam (the outer beam) at the primary beat level (crotchet) which “spitting” the secondary beams (inner beams)—either is an acceptable and common practice.

In simple triple time (b), the beaming will either reflect the primary beat or sometimes, as shown in the second bar, will reflect the value of the bar—this is common in faster tempos in certain styles.  However, at the next level of subdivision (quavers to semiquavers, as shown in bar three) it is clearest to group according to the primary beat.

In simple quadruple or common time (c), the first subdivision often joins beats 1 and 2, and 3 and 4 of the primary beat level (first bar), although it is also common to beam quavers in pairs (second bar).  At the next level of subdivision, beaming of semiquavers reflects the primary beat—beaming more than six values is best avoided.

In the “all breve” or cut common time (d)—which is effectively a simple duple metre—we would normally beam quavers in fours to reflect the two-in-bar feeling; however, at the next subdivision into semiquavers, it is standard to beam in groups of four (second bar).  To retain a semblance of the primary beat through grouping, a split secondary beam can be used, but it is best to avoid a full group of eight semiquavers (bar three).

In compound time where the primary beat division is a dotted crotchet, see (a) and (c), the first subdivision is beamed in groups of three quavers, and the next subdivision will usually retain this grouping, giving six semiquavers under a single pair of beams—see the second bar of each example. At a further level of subdivision, it is common practice to split beams at the previous level of subdivision while retaining the primary beam to reflect the primary subdivision.

In a compound time where the primary division is a dotted minim b), it is not possible to show an obvious grouping at the first level of subdivision (crotchets); however, at the next subdivision, quavers will be beamed in groups of six.

In compound time where the primary beat division is a dotted quaver (d), beaming is similar to (a) and (c) above, but with one extra beam to reflect the smaller scale of values.

Indicating the Primary Beat in Complex Rhythms

Most music uses a mixture of values to create rhythmic material. Good practice requires that rhythmic notation reflects, as far as possible, the primary subdivision and, in some cases, lower subdivisions.

This involves splitting beams where a beam crosses a subdivision (a), breaking a longer value that crosses a subdivision into two shorter values joined by a tie, with the second value on the subdivision (b) or both (c).

Tempo and rhythmic value

Avoid assuming that fast music always used short values and slow music always uses long values.  Composers chose time, time signatures, tempi and rhythmic value for a vast range of  reasons, including the historical era, style and character of the music, the intended performer, and personal proclivities.  Consider the two excepts from Bach’s famous Goldberg Variations below.