I. Fundamentals

# 3.1 Introduction

Chapter 2 outlines the different ways in which the underlying pulse of a piece of music (the beat) can be regularly divided. In this chapter we will continue that discussion by looking at simple meters, those in which the beat is regularly divided into two equal durations. This chapter will also provide a brief description of beaming—a notational device that shows how beat subdivisions group into beats in any particular meter.

# 3.2 Simple meters and time signatures

Consider the following two examples:

Example 3–1. Sophia Maria Westenholz, Theme and 10 Variations (Op. 2), mm. 1–20. Example 3–2. Clara Schumann, Piano Trio in G minor (Op. 17), mm. 1–10. Despite the obvious differences in character, there is an important connection between Example 3–1 and 3–2. Each piece has two beats per measure and each beat tends to divide into two equal durations. Both of these pieces, then, are said to be in a simple duple meter. Any of the beat groupings mentioned in the previous chapter—duple, triple, or quadruple—can represent a simple meter. A simple triple meter, for example, would have three beats per measure, each of which would regularly divide into two equal durations.

You probably noticed that both of these examples—as well most of the examples in the previous chapter—include a pair of large numbers at the beginning of the first line of music. These numbers together are referred to as a time signature (or meter signature). They indicate to the performer the type of meter present in any given piece or passage of music.

Note: The meter is not always consistent all the way through a piece. Sometimes it changes. In such cases, the new meter is typically indicated by a new time signature.

A time signature consists of two numbers, one stacked on top of the other. For simple meters, the top number represents the number of beats and the bottom number the note value of a single beat. In Examples 3–1 and 3–2, we saw the time signature 2/4 and called that meter “simple duple.” The top number, in this case 2, tells us there are two beats per measure (hence, “duple”). The bottom number, in this case 4, tells us that each beat has a duration equivalent to a quarter note.

Consider the following short piece:

Example 3–3. Christian Petzold, Minuet in G major (from the Notebook for Anna Magdalena Bach, BWV Anh. 114), mm. 1–16. We see the time signature 3/4 at the beginning of Example 3–3. Here, the 3 indicates that there are three beats per measure and, once again, the 4 indicates that each beat is the length of a quarter note. As the shorter durations make clear, the meter is simple: each quarter note divides into two eighth notes.

Simple meters are generally very easy to recognize. Any time signature in which the top number is 2, 3, or 4 represents a simple meter.

Note: For simple meters, the general rule of thumb is that the top number of the time signature indicates the number of beats per measure (duple, triple, or quadruple) and the bottom number indicates the beat value. As we will discuss in Chapter 4, however, this rule of thumb does not apply to compound meters.

The following examples show several common simple-meter time signatures:

Example 3–4. Common simple-meter key signatures. b. simple triple c. simple duple d. simple duple Note that Example 3–4c and Example 3–4d (2/4 and 2/2) are both simple duple meters. Both of them have two beats per measure. They differ only in the note value of the beat (a quarter note and a half note, respectively).

Note: The difference between 4/4 and 2/2 is subtle. Both time signatures have measures whose durations are equal to a single whole note (four quarter notes or two half notes). The difference lies in how the music is performed or heard. The former will have four distinct beats per measure, while the latter will have only two.

Frequently, you will encounter other, non-numeric symbols used as time signatures. These are shown in Example 3–5:

Example 3–5. Alternative time signatures.

a. “common time” b. “cut time” (or “alla breve“) These time-signature symbols are often used as a shorthand way to write 4/4 or 2/2.

Note: The symbol used for common time resembles the letter “C”—the first letter of the word “common.” The symbol used for cut time has a vertical line, cutting the “C” in half. These mnemonic devices, though useful, are not grounded by any historical accuracy.

Activity 3-1

Activity 3–1

For each of the following simple-meter time signatures, identify the number of beats per measure and the note value of a single beat.

### Question

How many beats per measure are indicated by the following time signature? Hint

Remember that for simple meters, the top number of the time signature indicates the number of beats per measure.

4

### Follow-up question

What is the note value of the beat, as indicated by this time signature?

Hint

Remember that for simple meters, the bottom number of the time signature indicates the note value of the beat.

half note

### Question

How many beats per measure are indicated by the following time signature? Hint

Remember that for simple meters, the top number of the time signature indicates the number of beats per measure.

2

### Follow-up question

What is the note value of the beat, as indicated by this time signature?

Hint

Remember that for simple meters, the bottom number of the time signature indicates the note value of the beat.

half note

### Question

How many beats per measure are indicated by the following time signature? Hint

Remember that for simple meters, the top number of the time signature indicates the number of beats per measure.

2

### Follow-up question

What is the note value of the beat, as indicated by this time signature?

Hint

Remember that for simple meters, the bottom number of the time signature indicates the note value of the beat.

eighth note

### Question

How many beats per measure are indicated by the following time signature? Hint

Remember that for simple meters, the top number of the time signature indicates the number of beats per measure.

3

### Follow-up question

What is the note value of the beat, as indicated by this time signature?

Hint

Remember that for simple meters, the bottom number of the time signature indicates the note value of the beat.

eighth note

# 3.3 Beaming

Note durations shorter than a quarter note—eighth notes, sixteenth notes, thirty-second notes, etc.—are written by adding flags to the stem. (Refer to Chapter 1 for more on rhythmic notation.) These flags can also be notated as beams: horizontal lines that connect two or more notes. Beams can be a helpful way to make a score appear less cluttered. They can also help emphasize the meter to the performer.

Beams are typically used to reflect the meter by grouping notes that occur within a single beat. Consider the following examples:

Example 3–6. Beaming in a simple meter.

a. incorrect b. correct Both of the rhythms in Example 3–6, if performed, would sound exactly the same. Although the corresponding note durations are identical, the beaming is quite different. Both rhythms are in simple duple meter, with two quarter notes per measure. The dashed lines divide each measure in half, making clear which beats belong to the first beat and which to the second in each measure.

As you can see, in Example 3–6a some of the beams connect notes over the dashed line. This obscures the meter, making it difficult to recognize that there are two beats per measure. (The first measure, for example, looks as though it has three beats.) In Example 3–6b, on the other hand, none of the beams cross a dashed line. The durations of each group of beamed notes add up to that of the beat—a quarter note in this case. It is much easier to recognize the duple meter in Example 3–6b.

Note: If you look closely, you will find that the beaming practice described above is not always followed in some scores. Composers will sometimes break and add beams to indicate phrasings and other expressive gestures. The beams in Example 3–2, for example, are not consistent throughout the excerpt.

Activity 3-2

Activity 3–2

### Question

Which of the measures in the following rhythm have beaming that obscures the meter rather than supports it? m. 2 and m. 4

# 3.4 Summary

The meter of a particular piece is generally indicated by the time signature—a stack of two numbers written on the first line of music, just to the right of the key signature. For simple meters, the top number indicates the number of beats per measure while the bottom indicates the note value of the assigned beat.

Beams—the horizontal lines that connect notes whose durations are shorter than a quarter note—can be used to help express the meter of a particular piece of music. Notes are typically grouped with beams within a single beat instead of across two or more beats. This makes the meter easier to recognize for both the performer and the analyst. 