Now that you are familiar with beats and divisions, we will learn about how they work within simple meters.

3.1   Introduction

In the last chapter, we learned several things about beats:

• Any note can equal one beat, and that beat can be evenly divided into two (forming a division) and evenly divided into four (forming a subdivision).
• Not all parts of the beat carry the same weight: notes that fall on the beat (“1”) are stronger than other parts of the beat.
• To process music more efficiently, notes with flags within beats are grouped together with beams.

Just as notes are organized into beats, beats are also grouped together so musicians can process music more effectively. Grouped beats are separated by bar lines. The distance from one bar line to the next is called a measure or bar. Most commonly, there are two, three, or four beats within a measure.

Recall that not all parts of the beat have equal weight. Similarly, not all beats within a measure are equally emphasized. The first beat, known as the downbeat, is typically stronger than the others. While the downbeat’s accent is not as obvious or bold as notes with explicit accent marks, there is a subtle emphasis on it (Example 3.1.1).

Example 3.1.1. Weighted beats

In Example 3.1.1, the downbeats are marked by the blue Ss.

• Example 3.1.1A:
  • The half note gets one beat and there are two beats per measure.
  • When there are two beats per measure, the downbeat is strong (S) and the second beat is weak (w).
• Example 3.1.1B:
  • The quarter note gets one beat and there are three beats per measure.
  • When there are three beats per measure, the downbeat is strong, the second beat is less strong (LS), and the third beat is weak.
• Example 3.1.1C:
  • The eighth note gets one beat and there are four beats per measure.
  • Notice that the eighth notes are not beamed together. This is because each eighth note equals one beat. We only beam them when they combine to form one beat.
  • When there are four beats per measure, the downbeat is strong, the third beat is less strong, and the second and fourth beats are weak.

Strong beats are accented while weak beats are unaccented. Tap your foot while listening to the next three examples.

Example 3.1.2. Two beats per measure: Sousa^[1], “The Stars and Stripes Forever”

At first glance, you might think the quarter note gets one beat and there are four beats per measure in Example 3.1.2. However, when listening to the excerpt, do you tap your foot four times or only twice per measure? Chances are you only tap your foot twice per measure, which means there are two beats per measure and the half note gets one beat.

Example 3.1.3. Three beats per measure: Strauss^[2], “The Blue Danube Waltz”

There are three beats per measure in Example 3.1.3, with the quarter note receiving one beat. Strauss emphasizes the downbeat more than the other two beats in this example. In fact, the downbeat is so strong that the third beats of measures 2 and 3 actually sound more like an introduction to the next downbeat (indicated by the arrows), rather than the final beat of the measure.

Example 3.1.4. Four beats per measure: Foster^[3], “Jeanie With the Light Brown Hair”

There are four beats per measure in Example 3.1.4. Since beats 1 and 3 are stronger than beats 2 and 4 in a measure with four beats, it can be hard to tell the difference between two beats per measure and four beats per measure. However, because Example 3.1.4 is so slow, it is more likely to tap your foot four times per measure.

You might have noticed two things about Example 3.1.4.

• The example begins with a single note called an anacrusis or upbeat. We will learn about the upbeat in detail in Section 3.7.
• The eighth notes are not beamed according to beats because the music is a vocal score. Music for voices often disregards beaming to align notes with syllables and words.

In the three examples above, the number of beats and accented downbeats repeat in every measure. For instance, Example 3.1.3 has three beats per measure, and this pattern applies to all measures. When the same beats are accented within repeated groups of measures, it creates a meter. In this chapter, we will learn about the simple meters, which are a way of grouping measures where the beat evenly divides into two.

3.2   Time Signatures

We learned that beats can equal any note, but the half note, quarter note, and eighth note are most common. We also learned that beats are organized into groups separated by bar lines, and that groups of two, three, and four are most common. We can communicate all this information with a time signature. A time signature consists of two numbers (one above the other) at the beginning of a piece of music. In two cases, the time signature is a symbol instead of two numbers.

The time signature is only written once at the beginning, unlike clefs, which are written for every system (Example 3.2.1).

Example 3.2.1. Time signature versus clef

• Each system must begin with a clef.
• The time signature only appears at the start of the composition or when the time signature changes. Do not rewrite the time signature at the start of each system.
• Every system must end with a bar line if the measure is complete.
  • Sometimes students will not add a bar line at the end of a system, assuming it is unnecessary. However, think of the bar line as a period at the end of a sentence. Although it may be obvious that it is the end of your sentence, it would look very odd if your sentence did not end with a period

In this section, we will cover how to interpret, identify, and properly write music in simple time signatures.

Interpreting Simple Time Signatures

This chapter focuses on simple meters, which means the beat is a note (not a dotted note) that is evenly divided into two parts. Time signatures in simple meters are simple to interpret (see Example 3.2.2).

Example 3.2.2. Time signature in simple meter

• The top number of a time signature in simple meter refers to the number of beats per measure.
  • We learned that there are most commonly two, three, or four beats per measure, so the top number will be 2, 3, or 4.
• The bottom number of a time signature in simple meter refers to the type of note that receives one beat.
  • We learned that the half note, quarter note, and eighth note are most commonly equal to one beat, so the bottom number is usually 2, 4, or 8. The quarter-note beat (4) is most common, but you may also come across the half-note beat (2) and eighth-note beat (8).
  • Although other note values, such as the sixteenth-note beat (16) and thirty-second-note beat (32) are possible, they are not very common.

In one symbol, Example 3.2.2 shows us that there are three beats per measure and that the quarter note equals one beat. A common mistake is that students write a number on the bottom that does not exist, such as 3. Remember that the bottom number represents a note value, and since there is no such thing as a third note, 3 cannot be on the bottom.

There are two time signatures that do not have numbers; instead, they have unique symbols.

If we take the same examples from Example 3.1.1 and add time signatures, we get Example 3.2.3.

Example 3.2.3. Added time signatures

• Example 3.2.3A: The time signature tells us there are two beats per measure, and the half note gets one beat.
  • This example could have also been written in cut time.
• Example 3.2.3B: The time signature tells us there are three beats per measure, and the quarter note gets one beat.
• Example 3.2.3C: The time signature tells us there are four beats per measure, and the eighth note gets one beat.

Now let’s interpret some time signatures in real music (Examples 3.2.4-3.2.5).

Example 3.2.4. Interpreting the time signature: Bonis,^[4] Berceuse

The time signature 3/4 means there are three beats per measure, with a quarter note receiving one beat. The boxes in the bass clef of the first measure clearly illustrate the three beats and how each box equals one beat. Example 3.2.5 is also clear because of the bass clef.

Example 3.2.5. Interpreting the time signature: Bonis, Bourrée

Cut time is equivalent to 2/2. There are two beats per measure, and each beat equals a half note. Notice that there are not two eighth notes, but four eighth notes in each box. This is because each box shows the subdivision, not the division. The division of a half note is two quarter notes, while the subdivision is four eighth notes.

Now that we know how to interpret simple time signatures, let’s learn how to identify them.

Identifying Simple Time Signatures

Let us revisit Examples 3.1.2, 3.1.3, and 3.1.4 to see which time signatures are used. For Example 3.1.2, we only tapped our foot twice in “The Stars and Stripes Forever.” Tapping our foot twice per measure means two boxes per measure (Example 3.2.6).

Example 3.2.6. Identifying the time signature: Sousa, “Stars and Stripes Forever”

• There are two beats per measure, so the top number is 2.
• The half note receives one beat, so the bottom number is 2.
• The time signature is 2/2 or cut time. Sousa chose cut time (Example 3.2.7).

Example 3.2.7. Cut time: Sousa, “Stars and Stripes Forever”

For Example 3.1.3, we tapped our first three times per measure for “The Blue Danube Waltz.” This results in three boxes (Example 3.2.8).

Example 3.2.8. Identify the time signature: Strauss, “The Blue Danube Waltz”

• There are three beats per measure, so the top number is 3.
• The quarter note receives one beat, so the bottom number is 4.
• The time signature is 3/4. A waltz is a dance that has three beats per measure, so this time signature is no surprise (Example 3.2.9).

Example 3.2.9. Time signature 3/4: Strauss, “The Blue Danube Waltz”

We tapped our foot four times per measure in Example 3.1.4, which gives us four boxes (Example 3.2.10).

Example 3.2.10.  Identify the time signature: Foster, “Jeanie with the Light Brown Hair” 

• There are four beats per measure, so the top number is 4.
• The quarter note receives one beat, so the bottom number is 4.
• The time signature is 4/4 or common time. Foster chose to use common time (Example 3.2.11).

Example 3.2.11. Common time: Foster, “Jeanie With the Light Brown Hair”

Identifying the time signature for “Jeanie with the Light Brown Hair” may have been more difficult because the beats were not clearly written. As previously mentioned, vocal scores 3.2.8 do not show beaming. However, in Example 3.1.4, we established that because of the slow tempo, we tapped our foot four times per measure. (As mentioned earlier, this example begins with an anacrusis, which we will learn about later.) Tapping our foot four times per measure leads to a quarter-note beat. Therefore, the time signature is common time (or 4/4).

Now, let’s identify the time signature in two duets by Beethoven. What is the time signature for Example 3.2.12?

Beethoven 3.2.12. Identify the time signature: Beethoven,^[5] Duet for Two Violins, WoO 34

• How many beats do you see in each measure? Write this number as the top number of the time signature.
• What type of note gets one beat? Write this number as the bottom number of the time signature.

If you guessed common time (or 4/4), you are correct. There are four beats per measure, and the quarter note gets one beat. What is the time signature for Example 3.2.13?

Beethoven 3.2.13. Identify the time signature: Beethoven, Allegro and Minuet for Two Flutes, WoO 26

• How many beats do you see in each measure? Write this number as the top number of the time signature.
• What type of note gets one beat? Write this number as the bottom number of the time signature.

Did you get common time or cut time? Beethoven used cut time, but both time signatures would be correct guesses for the flute duet (Example 3.2.14).

Beethoven 3.2.14. Cut time or common time?: Beethoven, Allegro and Minuet for Two Flutes, WoO 26

• If you interpreted the flute duet in common time, you would hear four beats per measure, with a quarter note equal to one beat (shown in red ovals).
• If you interpreted it in cut time, you would hear two beats per measure, with a half note equal to one beat (shown in blue boxes).

One reason why cut time might be a slightly better choice is the tempo marking, which we will learn about at the end of the chapter. Allegro con brio means “quickly with energy,” so the music moves fast. Listen to the example again and tap your foot. How many times did you tap? Twice per measure, or four times per measure?

Because beat three is considered a strong beat in a measure of four beats (though less strong than the first beat), identifying the top number of a simple time signature as 4 or 2 is often interchangeable. Many students in music theory do not like to hear this—they believe there should only be one correct answer. However, as you advance in music theory, you’ll find that there are many instances where multiple correct answers exist (and, of course, multiple incorrect ones as well).

You may have chosen cut time or common time based on how the beats were beamed. Indeed, it is important to know how to correctly write simple meters.

Beaming Simple Time Signatures

Previously, when we used rhythm syllables to count rhythms, we only used the number “1” because we were only applying it to one beat. However, now that we are learning about two, three, and four beats per measure, we will use different numbers for notes that fall on beats other than the downbeat. Refer to Example 3.2.2A.

• Because there are two beats per measure, the downbeat is beat one, and the second half note is beat two (not beat three).
• We say “1” for the first half note and “2” for the second half note.

We can apply what we learned about divisions and subdivisions and fill these measures with different rhythms (Example 3.2.15).

Example 3.2.15. Rhythms

Notice that all the examples above end on a strong beat. This is important to remember—do not end on a weak beat.

• Example 3.2.15A:
  • Because the half note equals one beat, the division is two quarter notes, and the subdivision is four eighth notes.
  • The half-note beat can be difficult for students because they tend to see the quarter note as the beat. However, you need to shift perspective and view a quarter note as half of a beat.
  • In measure 2, because four eighth notes are beamed together, we immediately recognize this as a subdivision rather than a division.
  • In measure 3, we cannot beam “1 e – a” because the quarter note does not have a flag.
  • In measure 4, the final note ends on the strong downbeat. A long dash appears after the rhythm syllable “1” because it is held out beyond beat 2.
• Example 3.2.15B:
  • Because the quarter note equals one beat, the division is two eighth notes, and the subdivision is four sixteenth notes.
  • Notice how the beaming helps to distinguish beats.
  • Since there are only three quarter-note beats per measure, we cannot end with a whole note because that would equal four quarter notes. Instead, a dotted half note falls on the downbeat and fills the final measure.
• Example 3.2.15C:
  • Since the eighth note equals one beat, it divides into two sixteenth notes, and the subdivision consists of four thirty-second notes.
  • The first eighth note is not beamed to the next two sixteenth notes because an eighth note equals one beat.
    • Compare the two boxed areas in Example 3.2.3. The rhythms are the same (eighth note + two sixteenth notes), but since the note values of the beats differ, we write and count them differently.
  • This example does not end on the downbeat, but on beat 3. This is acceptable because beat 3 is still a strong beat, even though it is less strong than the downbeat.

Remember that rests are equivalent to notes, but represent silence. Any of the notes in Example 3.2.15 could be replaced with its corresponding rest.

When writing rhythms accurately within a time signature, some students find it helpful to draw a box around each beat and then write the beaming correctly within each beat (Example 3.2.16).

Example 3.2.16. Beat-boxes

When we break rhythm into individual beat-boxes, reading music becomes much easier.

• Each box represents a beat, and begins with a number.
• In measure 2, there are three thirty-second notes between beats 1 and 2. However, the three thirty-second notes are not beamed together because they belong to different beats.

There is one anomaly in Example 3.2.16. Notice the last quarter note—it crosses into two boxes. In the rhythm syllables, this is shown by the long dash. Crossing boxes is acceptable when longer note values cross into other beats only if they begin on a strong beat. In Example 3.2.16, beat 3 is a strong beat in the time signature 4/8. If you look back to Example 3.2.15, each example concludes with a longer note value that crosses into other beats. In each case, this is acceptable because they all start on a strong beat.

When you tried to guess the time signature for the Beethoven flute duet (Example 3.2.14), did you guess common time but the beaming threw you off? Another anomaly you may come across is four eighth notes beamed together in ôæ. When the quarter note equals one beat, we expect two eighth notes to be beamed together; four notes beamed together imply a subdivision. However, four eighth notes are often beamed together in common time. Recall that when there are four beats per measure, the downbeat is the strongest, followed by beat 3. Because beats 1 and 3 are stronger, four eighth notes are beamed together (Example 3.2.17).

Example 3.2.17. Beaming in 4/4

• Example 3.2.17A: The time signature 4/4 literally means there are four quarter-note beats per measure. Typically, the quarter-note beat divides into two eighth notes, which are beamed together. Although this appears correct, there is another way that occurs more often (see Example 3.2.14B).
• Example 3.2.17B: In 4/4, it is more common to beam together four eighth notes. This is allowable because both beats 1 and 3 are strong. Be careful not to assume the four eighth notes are a subdivision.
• Example 3.2.17C: This type of beaming is incorrect because the group of four eighth notes begins on beat 2, which is a weak beat.

For simple time signatures, always remember that the top number refers to the number of beats per measure, while the bottom number shows what type of note gets one beat.

Directions:

• Complete the table.

Directions:

• Listen to the following melodies and write the most likely time signature onto the staff.

1.  Tchaikovsky^[6], 1812 Overture

2.  Tchaikovsky, “Waltz of the Flowers” from The Nutcracker

3.  Tchaikovsky, “Dance of the Sugar Plum Fairy,” from The Nutcracker

3.3   Meter and Beat Classifications

Time signatures can be classified by meter and beat.

• We learned that a simple meter is a type of meter classification where the beat divides evenly into two. When the top number of a time signature is 2, 3, or 4, it tells us it is simple and that there are two, three, or four beats per measure.
• Having two, three, or four beats per measure refers to a beat classification. Beat classifications can be duple (2), triple (3), or quadruple (4). We combine beat and meter classifications to describe time signatures.

Example 3.3. Meter and beat classification

Notice that the bottom number of the time signature does not matter when we refer to meter and beat classifications.

• Top number 2 = simple duple
• Top number 3 = simple triple
• Top number 4 = simple quadruple

Refer back to Examples 3.2.6-3.2.8:

• Example 3.2.6: Sousa’s “The Stars and Stripes Forever” is in simple duple because the time signature is cut time.
• Example 3.2.7: Strauss’s “The Blue Danube Waltz” is in simple triple because of the 3/4 time signature.
• Example 3.2.8: Foster’s “Jeanie With the Light Brown Hair” is in simple quadruple because the time signature is common time.

Directions:

• Fill in the table.

3.4   Whole Rests

As we learned, notes and their corresponding rests are equivalent. For example, a quarter note and a quarter rest are equivalent. However, the whole note and the whole rest are not always equivalent.

The whole note is worth four beats if a quarter note is worth one beat; it is worth two beats if a half note is worth one beat. This means that in the time signatures 4/4 (common time) or 2/2 (cut time), a whole note will fill an entire measure. However, in other time signatures, you cannot use a whole note because it is too large or too small.

Example 3.4.1. Whole note

• Example 3.4.1A: A whole note fills an entire measure because there are four quarter notes in one measure.
• Example 3.4.1B: A whole note fills an entire measure because there are two half notes in one measure.
• Example 3.4.1C: You could not use a whole note in 2/4 (m. 3), because 2/4 has only two quarter notes per measure. You must use a half note to fill the measure (m. 4).
• Example 3.4.1D: You could not use a whole note in 3/8 (m. 5), because 3/8 has only three eighth notes per measure. You must use a dotted quarter note to fill the measure (m. 6).
• Example 3.4.1E: In 3/2, there are three half notes in one measure. In this case, a whole note does not fill an entire measure. Instead, a whole note is only worth two beats. To complete the measure, it requires another half note.

While all other notes and their corresponding rests are equivalent (e.g. for example, a half note and a half rest always have the same value), whole notes and whole rests are often different: in most cases, a whole rest specifically signifies a full measure of rest.

• As we saw in Example 3.4.1, the whole note varies in value depending on the time signature.
• The whole rest always signifies an entire measure of rest, unless it is in a time signature in which a whole note would not fill the entire measure and there is another note in the measure.

Example 3.4.2. Whole rest

• Example 3.4.2A: A whole rest fills an entire measure.
• Example 3.4.2B: A whole rest fills an entire measure.
• Example 3.4.2C: In 2/4, a half note would fill an entire measure.
  • However, writing a half rest is incorrect (measure 3).
  • Instead, a whole rest fills an entire measure (measure 4).
• Example 3.4.2D: In 3/8, a dotted quarter note would fill an entire measure.
  • However, writing a dotted quarter rest would be incorrect (measure 5).
  • Instead, a whole rest fills an entire measure (measure 6).
• Example 3.4.2E: In 3/2, the half note is equal to one beat and there are three beats in one measure.
  • In this case, the half note is worth one beat, and the whole rest is worth two beats: the whole rest does not mean an entire measure of rest. To avoid confusion, composers often use two half rests instead of a single whole rest.
  • A whole rest by itself in 3/2 means an entire measure of rest.

The following three excerpts illustrate examples using whole rests (Examples 3.4.3 to 3.4.5). Example 3.4.3 compares how a different note and rest fill an entire measure in the time signature 2/4.

Example 3.4.3. Whole rests in 2/4: Chaminade^[7], Après de ma mie (Beside my Darling)

Example 3.4.3 begins at measure 60. Time signatures are usually written only at the start of the composition, but one has been added here for clarity.

In 2/4, there are two beats per measure and a quarter note receives the beat.

• When a note fills an entire measure, the note is a half note.
  • The half notes in the last measure of the piano part have been highlighted, but there are several other half notes in the piano’s part as well.
• However, when a rest fills an entire measure, the rest is a whole rest.
  • The whole rest in the last measure of the vocalist’s part has been labeled, but there are also other whole rests in the vocalist’s part.
• Compare the vocalist’s part to the piano’s part in the last bar. They both use a half note and a whole rest to fill the entire measure.

In Example 3.4.4, the difference between note and rest is demonstrated in the time signature 3/4.

Example 3.4.4. Whole rests in 3/4: Bertin, Piano Trio, Op. 10, Largo

In 3/4, there are three beats per measure and a quarter note receives the beat.

• When a note fills an entire measure, the note is a dotted half note.
  • In measure 3, the violin begins with a dotted half note that spans the entire measure.
• However, when a rest fills an entire measure, the rest is a whole rest.
  • In the first two bars, the violin remains silent, and those measures are filled with whole rests.
• Compare measures 2 and 3 in the violinist’s part, where a whole rest is placed next to a dotted half note.

Example 3.4.5 illustrates when a time signature requires more than one whole note to fill a measure.

Example 3.4.5. Whole rest in 3/2: Bach^[8], “Crucifixus” from Mass in B Minor, BWV 232

Example 3.4.5 begins at measure 21, but a time signature has been added here for clarity.

In 3/2, there are three beats per measure where a half note receives the beat.

• When a note fills an entire measure, the note is a dotted whole note.
  • In measure 21, a dotted whole note fills the entire measure.
• However, when a rest fills an entire measure, the rest is a whole rest.
  • In measure 24, a whole rest fills the entire measure.
• Measure 23 calls for two beats of rest. Instead of a single whole rest, there are two half rests to prevent confusion with the following whole rest. As mentioned earlier, using two half rests in this situation is common.

Although most note and rest values are equal, the whole rest is an exception.

Directions:

• Add rests to complete each measure when necessary.

3.5   Ties

Listen to the first four measures of Elgar’s “Pomp and Circumstances.” It might be familiar to you if you have attended a graduation ceremony (Example 3.5.1).

Example 3.5.1. Slurs: Elgar^[9], Pomp and Circumstances Military March, Op. 39, No. 1

Recall that the curved lines connecting two or more notes are called slurs. Notes between the ends of slurs are to be performed smoothly.

Now listen to the next four measures of Elgar’s “Pomp and Circumstances.”

Example 3.5.2. Tie: Elgar, Pomp and Circumstances Military March, Op. 39, No. 1

Did you notice that the final A was not replayed? Instead, the A in measure 7 was held out for two bars. This is because the curved line connecting the two As is not a slur, but a tie. A tie is a curved line that connects two of the same pitches and holds out the note. That is, the note is sustained and not resounded.

The symbol for a tie is the same as the symbol for a slur (i.e., a curved line connecting noteheads). There are several ways to distinguish a tie from a slur.

• Ties connect the same note without any notes in between.
• Slurs connect different notes or the same note with notes in between.

Example 3.5.3 illustrates the difference between ties and slurs. Be sure to listen to the examples.

Example 3.5.3. Ties versus slurs

• Example 3.5.3A: This is a tie because it connects the same note without any notes in between (G to G).
• Example 3.5.3B: These are ties because they connect the same note without any notes in between (G to G to G).
• Example 3.5.3C: This is a slur because it connects different notes (A to G).
• Example 3.5.3D: This is a slur because, although it connects the same note (A to A), there is a note (G) in between.

You might have wondered why a dotted quarter note was not used in Example 3.5.3B. The answer becomes clear when we add beat-boxes.

Ex. 3.5.4. Ties versus dotted notes

• Example 3.5.4A: This is incorrect use of a dotted note because the dotted note starts on a weak part of the beat and continues into the next beat-box.
  • Remember that notes can only cross over beats when they begin on a strong beat.
• Example 3.5.4B: This is the correct way to write Example 3.5.4A (and Example 3.5.3B). When holding a note starting on a weak beat or weak part of the beat, use a tie.

Example 3.5.3B also illustrated a note being held out by two ties in a row. Indeed, a series of ties can be used to sustain a sound for multiple measures, as shown in Example 3.5.5.

Example 3.5.5. Multiple ties: Mayer^[10], Violin Sonata, Op. 19, ii – Scherzo

Every curved line in Example 3.5.5 is a tie, except for the one labeled as a slur. The first two ties connect E for three full bars, while the last three ties hold out E for four full bars.

Ties and slurs can occur simultaneously, as seen in Example 3.5.6.

Example 3.5.6. Ties and slurs: Mayer, Violin Sonata, Op. 19, iii – Adagio

Besides occurring across bar lines, ties can replace dots when a note starts on a strong beat. There is a tie at the beginning of measure 2. We recognize it as a tie (not a slur) because it connects F to F without any notes in between.

• Why wasn’t a dotted note used instead? A dot after an eighth note would add a sixteenth note. However, this eighth note is tied to a thirty-second note.
• In this case, a dot would be mathematically incorrect, so a tie had to be used.

The two rests that conclude Example 3.5.6 are not tied because rests are never tied—only notes are tied. Since rewritten rests imply continued silence, ties are unnecessary with rests.

With the exception of the tempo marking (which we will cover at the end of this chapter), we have already learned about many parts of Example 3.5.6.

• There are three slurs that instruct the musician to connect those notes smoothly.
• The time signature is 3/4, which is simple triple.It means there are three beats per measure, and the quarter note equals one beat.
• Notice how the music is clearly divided into beats.
  • In measure 2, the last thirty-second note is not beamed to the last eighth note because the eighth note starts a new beat.
• The example begins piano, meaning that it begins softly.
• There is a D♯D sharp in measure 1. It is written as D♯D sharp and not its enharmonic equivalent, E♭E flat, because its goal is to ascend to E. Sharps imply upward movement.
• There is a courtesy accidental in measure 2 (D♮D natural). Parentheses are not required for courtesy accidentals.
  • Although the bar line cancels the D♯D sharp from the previous measure, the natural sign reminds us that the pitch is D♮D natural.

Directions:

• Identify and label all slurs and ties in the following examples.

1.  Viardot^[11], Sonatine for Violin and Piano, i – Allegro

2.  Viardot, Sonatine for Violin and Piano, i – Allegro

3.6   More Dots

We learned that you can increase the duration of a note or rest by half by adding a dot (Example 3.6.1).

Example 3.6.1. Dotted notes and rests

If we add another dot, it becomes a double-dotted note or double-dotted rest and increases the duration of a note or rest by half of the dot’s value.

Example 3.6.2. Double-dotted notes and rests

In Example 3.6.2, a quarter note is worth one beat.

• Example 3.6.2A:
  • A quarter rest equals one beat.
  • The first dot adds half the value of the note: +½.
  • The second dot adds half the value of the first dot: +¼.
  • A double-dotted quarter note is equal to 1¾
• Example 3.6.2B:
  • A half note equals two beats.
  • The first dot adds half the value of the note: +1.
  • The second dot adds half the value of the first dot: +½.
  • A double-dotted half note is equal to 3½
• Example 3.6.2C:
  • A whole note equals four beats.
  • The first dot adds half the value of the note: +2.
  • The second dot adds half the value of the first dot: +1
  • A double-dotted whole note is equal to 7 beats.

The most common mistake students make is adding half the value of the note for the second dot instead of half the value of the first dot (Example 3.6.3).

Example 3.6.3. Incorrect addition of double-dotted note

The second dot is equal to half of the first dot, not half of the beat. In Example 3.6.3, another ½ is incorrectly added.

Example 3.6.4 shows a double-dotted note in context.

Example 3.6.4. Double-dotted notes: Park^[12], Violin Sonata, Op. 13, No. 1, i – Andante Maestoso

• In 3/4, the quarter note is worth one beat. The eighth note is worth ½ beat, the first dot is worth ¼ beat, and the second dot is worth one-eighth of a beat.
• ½ + ¼ + one-eighth =  seven-eighth of a beat. A note value of  one-eighth of one beat is required to fill one beat.
• If a quarter note is worth one beat, then an eighth note is worth ½ beat, a sixteenth note is worth ¼ beat, and a thirty-second note is worth one-eighth beat. Therefore, a thirty-second note is beamed to the double-dotted eighth note to complete each beat in measure 1.

Example 3.6.4 also includes several things we have already learned.

• The music begins forte and on the “and” of measure 2, the dynamics suddenly drop to piano.
• The last two notes are slurred.
• There is no bar line at the end because the example stops in the middle of a measure.

Dotted notes are very common, double-dotted notes are less common, and triple-dotted notes/rests are even less common.

Example 3.6.5. Triple-dotted notes

• Example 3.6.5A: If a quarter note equals one beat, a half note = 2.
  • The first dot adds half of 2 = 1.
  • The second dot adds half of 1 = ½.
  • The third dot adds half of ½ = ¼.
  • Therefore, a triple dotted half note is worth 3¾.
• Example 3.6.5B: If a quarter note equals one beat, a whole note = 4.
  • The first dot adds half of 4 = 2.
  • The second dot adds half of 2 = 1.
  • The third dot adds half of 1 = ½.
  • Therefore, a triple dotted whole note is worth 7½.

Although double-dotted notes are less common than dotted notes, it is important for you to be able to calculate their value. Remember to use the same technique you used for calculating dotted notes.

Directions: Based on the given note that equals one beat, write the value of the other notes. For samples, see Example 3.6.2.

3.7   Anacrusis

We learned that a simple meter’s time signature tells us how many beats there are per measure and what type of note gets one beat. However, sometimes there seems to be a mistake at the start of the piece: not enough beats.

Example 3.7.1. Anacrusis: “It’s Raining, It’s Pouring”

In “It’s Raining, It’s Pouring,” the first measure appears to contain only one quarter note. When a piece of music starts with less than a full measure, it is not considered a complete measure but is an anacrusis, (or pickup or  upbeat).  The anacrusis combines with the final measure of the piece, which is also incomplete, to form a complete measure.

Notice that measure 1 does not start until after the anacrusis because the anacrusis is in an incomplete measure. The second system begins with measure 5, not measure 6.

In Example 3.7.1, the time signature is cut time, which means there are two beats per measure, and the half note gets one beat. The anacrusis is one quarter note, which is worth ½ beat. This means 1½ beats are required to fill the bar. Looking at the last measure, which has a half note and a quarter note, totals 1½ beats in cut time. Therefore, combined with the anacrusis, the last measure completes one full measure.

As mentioned, other names for the anacrusis include the pickup or upbeat. These terms may help you understand how the anacrusis is to be performed. Recall that the strongest beat in any measure is beat one, also known as the downbeat. The upbeat leads into the downbeat. In other words, the anacrusis is not to be performed as the last note of a measure, but rather, the note leading into the following downbeat.

Example 3.7.2. Upbeat: “It’s Raining, It’s Pouring”

When you sing Example 3.7.2, “It’s” connects to “raining”: “It’s raining.” You do not sing “raining, it’s.” Sometimes, students mistakenly see a bar line as a symbol for when music breaks or pauses. However, the bar line is simply a way to organize beats. The downbeat remains the strongest beat, but the preceding pickup connects to the downbeat. We also saw similar upbeats in Strauss’s “The Blue Danube Waltz” in Example 3.1.3.

The anacrusis can consist of more than one note. In Example 3.7.3, the anacrusis has two notes but only counts as one beat. Since one beat does not fill the measure, this example starts with an anacrusis.

Example 3.7.3. Anacrusis: Ponchielli^[13], “Dance of the Hours,” La Giaconda

Even though there are rests in the anacrusis, can you still hear how the upbeat connects to the downbeat?

The anacrusis can also consist of more than one beat. The three notes in the anacrusis in Example 3.7.4 equal 1½ beats.

Example 3.7.4. Anacrusis: Rossini^[14], The Barber of Seville, Overture

Even with three notes spanning over one beat, the anacrusis still leads into the downbeat.

Directions:

• Complete the last measure with the fewest notes possible.

3.8   Transposition: Rhythmic

Some students feel most comfortable reading and writing music where the quarter note is the beat. When the beat is an eighth note or half note, they sometimes find it challenging. One strategy these students can use is transposition, which involves changing the music by the same proportion. Rhythmic transposition is when you rewrite the notes with the same rhythmic syllables but assign a different note to each beat. Compare the three versions below in Example 3.8.

Example 3.8. Rhythmic transposition

We know all the notes in Examples 3.8A, B, and C are proportionally equal because the rhythm syllables are exactly the same.

• Example 3.8A: The first measure may challenge some students because of the double-dotted eighth note followed by a tied thirty-second note.
  • Meanwhile, in Example 3.8B, the quarter note clearly places beat 3 and helps make Example 3.8A easier to understand.
• Example 3.8C: Because of the lack of beaming, the second measure might challenge some students as the beats are more difficult to identify.
  • Meanwhile, in Example 3.8B, the beaming makes the beats clearer.

Rhythmic transposition can be a helpful strategy in aural training if you are asked to write rhythmic dictation for a challenging time signature. There are two steps involved in writing rhythmic transpositions.

1. Write the rhythmic dictation so that a quarter note gets the beat.
2. Convert all notes using the same ratio based on the two note values.
   • For example, if the time signature is 3/8, change all the note values in your rhythmic dictation by half since an eighth-note beat is worth half a quarter-note beat.

Directions:

• Transpose the rhythms into the given time signatures. For a sample, see Example 3.8.
• Keep all pitches, articulations, and dynamics.

1.  Tchaikovsky, “Russian Dance,” The Nutcracker

2.  Bach, “Crucifixus,” Mass in B Minor, BWV 232

3.9   Tempo Markings

In Chapter 1, we explored articulation marks: symbols that instruct musicians on how to perform specific notes. In Chapter 2, we examined dynamics: symbols that indicate the volume—how soft or loud—to perform particular sections. Since Chapter 3 focuses on meter and rhythm, this final part will concentrate on tempo, which is the speed at which music is performed. Tempo markings specify how fast or slow to perform. There are three ways to indicate the intended speed.

• General tempo marking: Usually an Italian term (for example, allegro) that indicates how fast or slow to perform.
• Specific tempo marking: Beats per minute and/or metronome mark that tells us exactly how fast or slow to perform.
• Relative tempo marking: Usually Italian terms (e.g., ritardando) that say whether to slow down or speed up.

General tempo markings are not always in Italian, but they often are. These markings appear at the beginning of the piece and whenever the music changes tempo. There are too many different tempo markings to list here; however, Example 3.9.1 shows the most common ones.

Example 3.9.1. Tempo markings

The spectrum above shows various tempo markings from the slowest to the fastest.  Just as we thought of piano as soft and forte as loud, we can simply think of adagio as slow and allegro as fast. These are considered general tempo markings because one musician’s interpretation of allegretto may differ quite a bit from another’s. However, the difference between adagio and allegro should be clear.

Since the specifics of articulation, dynamics, and tempi are beyond this book’s scope, it is advisable to note down any new terms you encounter. We have already reviewed two examples of general tempo markings in this chapter (Examples 3.9.2 and 3.9.3).

Example 3.9.2. Tempo marking: Mayer, Violin Sonata, Op. 19, iii – Adagio

In Example 3.9.2, the tempo marking is Adagio, which means slowly. Notice that the example’s name ends with the movement number followed by the tempo marking. This technique is also used when listing movements in program notes.

Dynamics use mezzo– and –issimo to mean “moderate” and “more.” Tempo markings use moderato and molto to mean the same thing. For example, allegro moderato is not quite as quick as allegro, while molto vivace is very fast. Composers can also use words like prestissimo, which is even faster than presto. Other words may be added to supplement tempo markings, such as maestoso (Example 3.9.3).

Example 3.9.3. Tempo marking: Park, Violin Sonata, Op. 13, No. 1, i – Andante Maestoso

In Example 3.9.3, the tempo marking is Andante Maestoso, which means majestically slow.

Specific tempo markings indicate how fast or slow the beat is, either by explicitly stating the beats per minute or by using metronome marks. For example, the music may read [quarter note] = 152, meaning 152 quarter notes per minute.

The specific tempo marking can also state M.M. [quarter note] = 152. M.M. stands for Mälzel’s Metronome, which shows the speed to set on the metronome. The music may even use both a general and a specific tempo marking, such as Allegro [quarter note] = 152 (Example 3.9.4).

Example 3.9.4. Specific tempo marking: Röntgen-Maier^[15], Violin Sonata in B Minor, iii – Allegro molto vivace

• Both a general and specific tempo marking appear in the score, but only the general tempo marking is included in the movement’s title.
  • The general tempo marking uses more detailed words: Allegro molto vivace.
• To highlight that this movement should sound fast, Röntgen-Maier writes the beats per minute as a half note, rather than a quarter note, which is what should get the beat in 2/4.^[16]
• Notice the use of slurs versus ties in measure 7.
• Notice the use of an accent mark instead of crescendo or diminuendo marks in measure 7.

Relative tempo marks are similar to the gradual dynamics we learned: crescendo and diminuendo. For tempos, the most common terms are accelerando (speed up) and ritardando (slow down).

Example 3.9.5. Relative tempo marks: “Twinkle, Twinkle, Little Star”

Directions:

• Arrange the following tempo markings from slowest to fastest by writing their name onto the spectrum arrow below.
  • allegro
  • allegretto
  • largo
  • andante
  • prestissimo
  • presto

Directions:

• Listen to the following examples and write an appropriate tempo marking.

1.   Rimsky-Korsakov^[17], Flight of the Bumblebee

2.  Verdi^[18], “La donna è mobile,” Rigoletto, Act III

3.  Bach, Air on a G String

4.  Brahms^[19], Hungarian Dance No. 5

TERMS

• accelerando
• anacrusis
• beat classification
• common time
• cut time
• double-dotted note/rest
• downbeat
• meter
• meter classification
• pickup
• ritardando
• rhythmic transposition
• simple meter
• tempo
• tempo markings
  • grave
  • largo
  • adagio
  • andante
  • moderato
  • allegretto
  • allegro
  • vivace
  • presto
• tie
• time signature
• transposition
• triple-dotted note/rest
• upbeat