Now that you are familiar with beats and meters within simple meters, we will explore the role they play in compound meters.

5.1   Introduction

In Chapter 1, we learned that a dot after a note adds half the note’s value (Example 5.1.1).

Example 5.1.1. Dotted notes

In Chapter 2, we learned that any note can equal one beat. If the note is not dotted, it divides evenly into two parts; if the note is dotted, it divides equally into three parts (Example 5.1.2).

Example 5.1.2. Divisions

In Chapter 3, we learned about simple meters: where the beat is a note without a dot, and the beat divides evenly into two. In this chapter, we learn about compound meters, where the beat is a dotted note that divides equally into three.

Just like with simple meters, not all beats are equal, and beats that fall on the first beat are stronger than the others (Example 5.1.3).

Example 5.1.3. Weighted beats

In Example 5.1.3, the downbeats are marked by the blue S’s.

• Example 5.1.3A:
  • The dotted half note receives one beat, with two beats per measure.
  • When there are two beats in a measure, the downbeat is strong (S) and the second beat is weak (w).
• Example 5.1.3B:
  • The dotted quarter note receives one beat, and there are three beats in each measure.
  • When a measure has three beats, the downbeat is strong, the second beat is less strong (LS), and the third beat is weak.
• Example 5.1.3C:
  • The dotted eighth note receives one beat, and there are four beats per measure.
  • Note that the dotted eighth notes are not beamed together because each dotted eighth note equals one beat. We only beam them when they combine to form a single 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 as you listen to the following three examples (Examples 5.1.4-5.1.6).

Example 5.1.4. Two beats per measure: Suppé^[1], Light Calvary, Overture

• Example 5.1.4 is in A major and begins with an anacrusis.
  • Remember that an anacrusis is not a complete measure, but only a note or notes leading into the downbeat of the first measure. This is clarified by the rest in the bass clef. Usually, a whole rest would fill an entire measure, but here, an eighth rest accompanies the two sixteenth notes in the treble clef.
• After the anacrusis, there are two beats per measure since you would tap your foot twice per measure. As usual, the downbeat is stronger than the second beat.

Example 5.1.5. Three beats per measure: “Morning Has Broken”

• Example 5.1.5 is in C major and also starts with an anacrusis.
• The pattern with the anacrusis repeats for each measure, not each beat as in Example 5.1.4, and there are three beats per measure.

Example 5.1.6. Four beats per measure: Chopin^[2], Nocturne, Op. 9, No. 2

• Example 5.1.6 begins in E♭E flat major. After the initial anacrusis, there are four beats in each measure.
• Because of the slow tempo of Chopin’s Nocturne, the divisions are clearly audible, and someone might mistakenly tap their foot twelve times per measure.

5.2   Time Signatures

Any dotted note can equal one beat, but the dotted half note, dotted quarter note, and dotted eighth note are most common. Beats are grouped with bar lines, and groups of two, three, and four are most typical.

Like simple meters, time signatures for compound meters are also two numbers stacked vertically, but the meanings of the numbers are entirely different. Unlike simple meters, which have common time and cut time, there are no specific symbols for time signatures in compound meter.

Remember that for simple meters, the top number indicates how many beats are in each measure. The bottom number shows which type of note gets the beat. Usually, the top number is 2, 3, or 4, and the bottom number is 2, 4, or 8. This is not how you interpret the time signatures for compound meters.

Interpreting Compound Time Signatures

Let’s take the compound time signature of 6/8.

• Right away, we see that the top number is not 2, 3, or 4. This immediately tells us that 6/8 is not a simple meter—it is a compound meter.
  • However, there are not six beats per measure. Instead, there are two beats per measure.
• The bottom number is 8, which refers to an eighth note.
  • However, the eighth note does not get one beat. Instead, the dotted quarter note gets one beat.

How does 6/8 mean there are two beats per measure (not six), with the dotted quarter note getting one beat (not the eighth note)? A visualization might help clarify this.

The time signature 6/8 means there are literally six eighth notes per measure.

However, because 6/8 is a compound meter, the eighth note does not serve as the beat itself but as a division. A division of three forms one beat.

Now we can see that there are two beats per measure (not six), and that each beat equals a dotted quarter note (not an eighth note)

Let’s visualize a few more compound time signatures. The time signature 9/16 means there are literally nine sixteenth notes per measure.

However, because 9/16 is a compound meter, the sixteenth note does not serve as the beat itself but as a division. A division of three forms one beat.

Now we can see that there are three beats per measure (not nine), and that each beat equals a dotted eighth note (not a sixteenth note).

Let’s break down one more time signature. The time signature 12/4 means there are literally twelve quarter notes per measure.

However, because 12/4 is a compound meter, the quarter note does not serve as the beat itself but as a division. A division of three forms one beat

Now we can see that there are four beats per measure (not twelve), and that each beat equals a dotted half note (not a quarter note).

What do you notice when we compare these three compound time signatures side by side (Example 5.2.1)?

Example 5.2.1. Compound time signatures

• Top number: Tells you how many beats per measure.
  • Divide the number by three.
• Bottom number: Tells you what type of note equals one beat.
  • Convert the number to a note value.
  • Move to the next higher note value.
  • Add a dot to the note.

Let’s interpret the compound time signatures we just visualized, beginning with 6/8.

• Top number: Divide the number by three to determine the number of beats per measure.
  • 6 divided by 3 = 2
  • Therefore, there are two beats per measure.
• Bottom number: Convert the number to a note value, move to the next higher note value, and add a dot to determine which note type receives one beat.
  • 8 = eighth note
  • Next higher note value = quarter note
  • Add a dot = dotted quarter note
  • Therefore, the dotted quarter note receives one beat.
• The time signature 6/8 means there are two beats per measure, and the dotted quarter note receives one beat.

Now let’s break down 9/16.

• Top number: Divide the number by three to determine the number of beats per measure.
  • 9 divided by 3 = 3
  • Therefore, there are three beats per measure.
• Bottom number: Convert the number to a note value, move to the next higher note value, and add a dot to determine which note type receives one beat.
  • 16 = sixteenth note
  • Next higher note value = eighth note
  • Add a dot = dotted eighth note
  • Therefore, the dotted eighth note receives one beat.
• The time signature 9/16 means there are three beats per measure, and the dotted eighth note receives one beat.

Now let’s decode the time signature of 12/4.

• Top number: Divide the number by three to determine the number of beats per measure.
  • 12 divided 3 = 4
  • Therefore, there are four beats per measure.
• Bottom number: Convert the number to a note value, move to the next higher note value, and add a dot to determine which note type receives one beat.
  • 4 = quarter note
  • Next higher note value = half note
  • Add a dot = dotted half note
  • Therefore, the dotted half note receives one beat.
• The time signature 12/4 means there are four beats per measure, and the dotted half note receives one beat.

We will now explore how compound meters work in real music (Examples 5.2.2 and 5.2.3). Example 5.2.2 is in 12/8.

Example 5.2.2. Interpreting 12/8: Carreño,^[3] Un rêve en mer

Using our steps, we find that 12/8 has four beats per measure, with a dotted quarter note serving as the beat (divided into three eighth notes). We can group notes into beats to clearly see how this works (Example 5.2.3).

Example 5.2.3. Four dotted quarter note beats: Carreño, Un rêve en mer

The time signature 12/8 means there are twelve eighth notes per measure, as seen in measure 1 of the treble clef. Since 12/8 is a compound meter, the eighth notes are the division, and three eighth notes equal one beat. These three eighth notes are beamed together to clearly show four beats, each worth a dotted quarter note.

Example 5.2.4 is in 6/4. Although the excerpt does not come from the beginning of the movement, the time signature has recently changed, so it has been rewritten.

Example 5.2.4. Interpreting 6/4: Princess Elisabeth,^[4] Romanze for Clarinet and Piano

We know that 6/4 has two beats per measure, with a dotted half note as the beat (divided into three quarter notes). We can group notes into beats to clearly see how this works (Example 5.2.5).

Example 5.2.5. Interpreting 6/4: Princess Elisabeth, Romanze for Clarinet and Piano

The time signature 6/4 means there are six quarter notes per measure, as seen in measure 2 of the treble clef. However, since 6/4 is a compound meter, the quarter notes are divisions, and three quarter notes make up a beat. It is harder to distinguish the groupings because the quarter notes cannot be beamed. Still, in this example, the dotted half notes in the bass clef clearly show the two beats per measure.

Identifying Compound Time Signatures

When we identify a compound time signature, we will work backwards.

• Multiply the number of beats per measure by three to determine the top number of a compound time signature.
• “Divide” the note value that represents one beat by three to determine the bottom number.
  • Alternatively, look for the note value that is beamed in threes—this is the division (bottom number of the time signature).

Let’s apply these steps to an earlier example, Example 5.1.3 (Example 5.2.6).

Example 5.2.6.  Weighted beats

• Example 5.2.6A:
  • Top number:
    • There are two beats per measure.
    • 2 x 3 = 6
    • Therefore, the top number is 6.
  • Bottom number:
    • The dotted half note gets one beat.
    • A dotted half note is divided into three quarter notes.
    • The quarter note is represented by the number 4.
    • Therefore, the bottom number is 4.
  • The time signature is 6/4.
• Example 5.2.6B:
  • Top number:
    • There are three beats per measure.
    • 3 x 3 = 9
    • Therefore, the top number is 9.
  • Bottom number:
    • The dotted quarter note gets one beat.
    • A dotted quarter note is divided into three eighth notes.
    • The eighth note is represented by the number 8.
    • Therefore, the bottom number is 8.
  • The time signature is 9/8.
• Example 5.2.6C:
  • Top number:
    • There are four beats per measure.
    • 4 x 3 = 12
    • Therefore, the top number is 12.
  • Bottom number:
    • The dotted eighth note gets one beat.
    • A dotted eighth note is divided into three sixteenth notes.
    • The sixteenth note is represented by the number 16.
    • Therefore, the bottom number is 16.
  • The time signature is 12/16.

Example 5.2.7 shows Example 5.2.6 with the time signatures added in.

Example 5.2.7.  Added time signatures

Now, let’s determine the time signatures for the real music examples we saw in the first section of this chapter, Examples 5.1.4, 5.1.5, and 5.1.6. In Example 5.1.4, we tapped our foot twice per measure (Example 5.2.8).

Example 5.2.8. Identify the time signature: Suppé, Light Calvary, Overture

• Top number:
  • There are two beats per measure.
  • 2 x 3 = 6
  • Therefore, the top number is 6.
• Bottom number:
  • The dotted quarter note gets one beat.
  • A dotted quarter note is divided into three eighth notes.
  • The eighth note is represented by the number 8.
  • Therefore, the bottom number is 8.
• The time signature is 6/8 (Example 5.2.9).

Example 5.2.9. Time signature 6/8: Suppé, Light Calvary, Overture

Now let’s turn to Example 5.1.5, “Morning Has Broken” (Example 5.2.10).

Example 5.2.10. Identify the time signature: “Morning Has Broken”

• Top number:
  • There are three beats per measure.
  • 3 x 3 = 9
  • Therefore, the top number is 9.
• Bottom number:
  • The dotted half note gets one beat.
  • A dotted half note is divided into three quarter notes.
  • The quarter note is represented by the number 4.
  • Therefore, the bottom number is 4.
• The time signature is 9/4 (Example 5.2.11).

Example 5.2.11. Time signature 9/4: “Morning Has Broken”

Finally, we will determine the time signature for Example 5.1.6 (Example 5.2.12).

Example 5.2.12. Identifying the Time Signature: Chopin, Nocturne, Op. 9, No. 2

• Top number:
  • There are four beats per measure.
  • 4 x 3 = 12
  • Therefore, the top number is 12.
• Bottom number:
  • The division is three eighth notes.
  • The eighth note is represented by the number 8.
  • Therefore, the bottom number is 8.
• The time signature is 12/8 (Example 5.2.13).

Example 5.2.13. Time Signature 12/8: Chopin, Nocturne, Op. 9, No. 2

Now that we have learned the steps to interpret and identify compound time signatures, we will focus on how to write correctly in compound meters.

Beaming Compound Time Signatures

Recall that the rhythm syllables to count divisions of three (i.e., compound meters) are different than those to count simple meters (Example 5.2.14).

Example 5.2.14. Dotted beat rhythm number system

We can take what we learned about divisions and subdivisions and fill these measures with different rhythms.

Example 5.2.15. Different rhythms

• Example 5.2.15A:
  • Since the division is three quarter notes, the dotted half note equals one beat, and the subdivision is six eighth notes.
  • In measure 2, there are six eighth notes beamed together. Because six notes are beamed together, we immediately know that this is a subdivision and not a division.
  • In measure 3, we cannot beam “1 la – ta” because the quarter note lacks a flag.
  • In measure 4, the final note finishes on the strong downbeat. There is a long dash after the rhythm syllable “1” because it is sustained past beat 2.
• Example 5.2.15B:
  • Since the division consists of three eighth notes, the dotted quarter note equals one beat, and the subdivision is six sixteenth notes.
  • Notice how helpful the beaming is for distinguishing beats.
  • Since there are only three dotted-quarter-note beats per measure, we cannot end with a dotted whole note (because that would equal four dotted quarter notes). Instead, a dotted half note falls on the downbeat and ties to a dotted quarter note to fill the final measure.
  • Since there are only three dotted-quarter-note beats per measure, we cannot end with a dotted whole note because that would equal four dotted quarter notes. Instead, a dotted half note occurs on the downbeat and ties to a dotted quarter note to complete the final measure.
• Example 5.2.15C:
  • Since the division is three sixteenth notes, the dotted eighth note equals one beat, and the subdivision is six thirty-second notes.
  • The first eighth note is not beamed to the next three sixteenth notes because a dotted eighth note equals one beat.
    • Compare the two boxed areas in Example 5.2.15. The note values are identical (dotted eighth note + three sixteenth notes), but since the note values of the beat differ, they are written and counted differently.
  • This example does not end on the downbeat but on beat 3. This is okay because beat 3 remains a strong beat, although it is less strong than the downbeat.

When writing rhythms accurately within a time signature, many students find it helpful to box each beat and then write the beaming correctly within each beat (Example 5.2.16).

Example 5.2.16. Beat-boxes

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

• Each box stands for a beat, and each one starts with a number.
• Notice that there are no beams across beat-boxes.

Remember that rests are equivalent to notes, but they represent silence. Any note can be replaced with its corresponding rest.

Directions:

• Complete the table.

Directions:

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

1.  Ignore the anacrusis. Wagner^[5], Die Walküre, “Ride of the Valkyries,” Act III, Scene i

2.  Ignore the anacrusis. Gounod^[6], Funeral March of a Marionette

3.  Mozart^[7], Requiem, Lacrimosa

5.3   Meter and Beat Classifications

We learned that a simple meter is a 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 the meter 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 of duple, triple, or quadruple. We use both meter and beat classifications to describe time signatures.

We do the same with compound meters. The meter classification of a dotted-note beat that divides equally into three is compound. When the top number of a compound time signature is 6, 9, or 12, the beat classification indicates it is compound and that there are two, three, or four beats per measure: duple, triple, or quadruple (Example 5.3.1).

Example 5.3. Meter and beat classification

Note that the bottom number of the time signature does not matter when we discuss meter and beat classifications.

• Top number 6 = compound duple
• Top number 9 = compound triple
• Top number 12 = compound quadruple

Let’s label the meter and beat classifications for two works for violin and piano. What is the meter and beat classification for Example 5.3.2?

Example 5.3.2. Meter and Beat Classification: Coleridge-Taylor,^[8] Two Romantic Pieces for Violin and Piano, Lament, Op. 9

Since the top number of the time signature is 6, this functions as a compound meter with two beats per measure. Therefore, the meter and beat classification is compound duple.

Now, let’s determine the meter and beat classification for Example 5.3.3.

Example 5.3.3. Meter and Beat Classification: Coleridge-Taylor, Suite of Pieces for Violin and Piano, Pastorale, Op. 3

The top number of the time signature in Example 5.3.3. is also 6, signifying a compound duple meter and beat classification. Remember that you only use the top number of the time signature to determine the meter and beat classifications.

Directions:

• Fill in the table.

5.4   Comparing Simple and Compound Meters

Now that we have learned about simple meters (Chapter 3) and compound meters, let us review by placing them side by side.

1. What makes the meter simple or compound?

• • Simple: The beat is a note without a dot that is evenly divided into two parts.
  • Compound: The beat is a dotted note divided into three equal parts.

2. What does the top number of the time signature mean?

• • Simple: The top number is 2, 3, or 4, and refers to the number of beats per measure.
  • Compound: The top number is 6, 9, or 12 and represents the number of divisions per measure. To determine the number of beats, divide the top number by three.

3. What does the bottom number of the time signature mean?

• • Simple: The bottom number is a note value (usually 2, 4, or 8) and shows which type of note gets one beat.
  • Compound: The bottom number is a note value (usually 4, 8, or 16) and specifies which type of note receives the division.
    • To find the note that gets the beat, move to the next higher note value and add a dot.

4. How can you tell if a time signature is simple or compound?

• • Look at the top number:
    • If the top number is 2, 3, or 4, it is simple.
    • If the top number is 6, 9, or 12, it is compound.

5. How can you tell if the music you’re listening to is simple or compound?

• • One technique you can try is to tap your foot to the beat while tapping your finger along with the division.
    • If you can tap your finger evenly twice for each beat, the meter is simple.
    • If you can tap your finger evenly three times for each beat, the meter is compound. Additionally, compound meters often produce a swinging feel.

Let’s figure out the time signature for “Twinkle, Twinkle, Little Star”  (Example 5.4.1).

Example 5.4.1. Finding the time signature: “Twinkle, Twinkle, Little Star”

• We immediately know “Twinkle, Twinkle” is in a simple meter because there are no dotted notes and no divisions of three.
  • Be cautious, however, because dotted notes can appear in simple meters. When you see a dotted note in simple meters, it either has a longer duration (like a dotted half note) or is paired with a note that is half the note’s value (such as a dotted eighth note with a sixteenth note).
• Once we determine it’s simple, we then need to figure out how many beats are in each measure.
• There are clearly four quarter notes per measure, so the time signature could be 4/4 or common time.
  • However, from the pattern of notes (two repeated Cs, two repeated Gs, etc.), we see that the first note of each pair is louder than the second. This suggests that the quarter note is not the beat itself, but rather the division. If so, the time signature would be cut time or 2/2. Either time signature would work since in 4/4, beats 1 and 3 are the stronger beats.

Observe how “Twinkle, Twinkle” appears in a compound meter (Example 5.4.2).

Example 5.4.2. “Twinkle, Twinkle, Little Star” in compound meter

• We immediately recognize Example 5.4.2 as being in a compound meter because it features dotted note beats and divisions of three.
• Since the dotted quarter note gets the beat, this means the division is made of three eighth notes. Therefore, the bottom number of this compound time signature would be 8.
• Based on the dotted quarter note beat, we also find that there are two beats per measure.
  • In compound meters, when there are two beats per measure, the top number is 6. Therefore, the time signature would be 6/8.

Without listening to the examples, let’s attempt to identify the time signature from two excerpts of Ricardo Castro’s Aires Nacionales Mexicanos (Example 5.4.3).

Example 5.4.3. Time signature: Castro,^[9] Aires Nacionales Mexicanos, Capricho brillante, Op. 10

Answer these questions to determine the time signature.

1. Is the example in a simple or compound meter?
   • It is in a compound meter because three eighth notes are beamed together, and each bar ends with a dotted quarter note.
2. How many beats are in each measure?
   • There are two beats per measure, so the top number of the time signature is 6.
3. What type of note gets one beat?
   • The dotted quarter note gets the beat. Since it’s a compound meter, we divide it into three eighth notes. The bottom number is 8.
4. What is the time signature?
   • The time signature is 6/8 (Example 5.4.4).

Example 5.4.3. Time signature of 6/8: Castro, Aires Nacionales Mexicanos, Capricho brillante, Op. 10

Once you have established that the time signature is 6/8, listen to the example. Do you hear how the music swings? Because compound meters have divisions of three, the music often has a swinging feel. Now let’s determine another excerpt’s time signature (Example 5.4.5).

Example 5.4.5. Time signature: Castro, Aires Nacionales Mexicanos, Capricho brillante, Op. 10

Answer these questions to determine the time signature.

1. Is the example in a simple or compound meter?
   • It is in a simple meter because two eighth notes are beamed together.
   • You may have seen dotted half notes in every bar and mistaken this for a compound meter. Remember that dotted notes can appear in simple meters as well, but they will never be the beat itself.
2. How many beats are in each measure?
   • There are three beats in each measure, so the top number of the time signature is 3.
3. What type of note gets one beat?
   • The quarter note gets the beat, so the bottom number is 4.
4. What is the time signature?
   • The time signature is 3/4 (Example 5.4.6).

Example 5.4.6. Time signature of 3/4: Castro, Aires Nacionales Mexicanos, Capricho brillante, Op. 10

Listen to Example 5.4.6. Do you notice how even it sounds compared to the swinging feel of Example 5.4.5? What’s interesting about these two time signatures (6/8 and 3/4) is that they both literally have six eighth notes in each measure (Example 5.4.7).

Example 5.4.7. Six eighth notes in each measure (without beams)

• Example 5.4.7A: Although there are only two beats per measure, 6/8 means six eighth notes per measure.
• Example 5.4.7B: There are three quarter notes in 3/4. When dividing each quarter note, they become eighth notes, resulting in six eighth notes per measure.

Despite both having six eighth notes in each measure, the two time signatures sound very different because one is a compound meter and the other is a simple meter (Example 5.4.8).

Example 5.4.8. Six eighth notes in each measure (with beams)

• Example 5.4.8A: As a compound meter, 6/8 divides into groups of three eighth notes with two beats per measure.
• Example 5.4.8B: As a simple meter, 3/4 divides into groups of two eighth notes with three beats per measure.

There are many factors that make the two examples from Castro’s Aires Nacionales Mexicanos sound so different. The tempos and the extreme dynamics highlight the differences. While example in 6/8 was Andantino and piano, the example in 3/4 has a faster tempo and grows from fortissimo to fortississimo. The meter alson plays a vital role in music. Although both 6/8 and 3/4 consist of six eighth notes, the fact that one is a compound meter and the other is a simple meter creates a significant difference in how you perceive and perform the music.

Directions:

• Look for clues in the following examples and write what you think the time signature would be.
• Under the musical example, write the key.

Directions:

• Complete the table.

Directions:

• Complete the table.

5.5   The Ambiguous “3”

We learned that the top number of simple meters tells us how many beats are in each measure (e.g., 2, 3, or 4). Listen to Example 5.5.1, which is in simple triple.

Example 5.5.1. Farrenc^[10], Trio for Flute, Cello, and Piano, ii – Andante

Although there are dotted notes, the dotted eighth notes are paired with a sixteenth note and beamed together to form one beat. The quarter note equals one beat, and there are three beats per measure (as shown clearly in measure 3), resulting in a simple triple meter. The Andante tempo emphasizes the triple meter, as you would tap your foot three times per measure. The time signature of 3/4 confirms the simple triple meter.

Now listen to Example 5.5.2, which also appears to be in simple triple.

Example 5.5.2. Farrenc, Trio for Flute, Cello, and Piano, iii – Scherzo. Vivace

How many times per measure did you tap your foot while listening to Example 5.5.2? Most likely, you only tapped your foot once per measure since the tempo (Vivace) is so fast. In instances like this, 3/8 is not a simple meter, but a compound meter.

The top number of compound meters shows how many divisions are in each measure. Since compound meters divide beats into groups of three, the top number is always divisible by three (e.g., 6, 9, or 12). However, the number 3 is also divisible by three.

If we divide the top number 3 by three, it implies the time signature is compound and that there is only one beat per measure, making the meter and beat classification compound single.

Deciding when a time signature with the top number 3 is simple or compound can be challenging. If Example 5.5.2 were played slightly slower, one may tap their foot three times per measure, making the example simple triple.

In Chapter 3, we looked at Strauss’s “Blue Danube Waltz,” and discovered that it was in 3/4. We learned that it was a waltz, and waltzes are known to be simple triple meters (i.e. that is, having three beats per measure). Example 5.5.3 shows another waltz, this time by Chopin. What is the meter and beat classification?

Example 5.5.3. Waltz: Chopin, Waltz, Op. 64, No. 1

There are a few reasons why you might believe the meter and beat classification is simple triple.

• It is a waltz.
• The recording clearly emphasizes three beats per measure.

However, there are stronger reasons to think of this waltz as compound single.

• The tempo is marked Molto vivace (very lively and fast).
• The music is marked leggiero, which means light.
• The slur begins on the first note and continues through to the last, lasting ten full bars. Imagine that this melody should be sung in one breath.

Between the tempo marking, expression marking, and slur, this waltz should be played very quickly. Listen to the recording below while tapping your foot to the beat.

How many times did you tap your foot per measure? Mostly likely once per measure, making this waltz an example of a compound single meter. This waltz is known as Chopin’s “Minute Waltz” and has an interesting story. It is said that Chopin was intrigued by his partner’s small dog chasing its tail in circles and wanted to convey this in music. The title “minute” does not refer to the measurement of time, but rather a variation of the word “miniature.” It should take less than two minutes to perform. Listen to the entire waltz when you have two minutes to spare.

The Chopin excerpt is a great example to show how much you have learned so far.

• The pitches and rhythm in both the treble and bass clef
• The proper use of a whole rest
• The tempo marking: Molto vivace
• The articulation mark: the accent on the first note
• The use of the accidental in G♮G natural because it is ascending to A♭A flat
• The courtesy accidental in measure 8
• The slur that connects the first note to the last
• The key of D♭D flat major
• The meter and beat classification of compound single

All of these factors contribute to what makes music musical. As you progress, you will discover even more important characteristics, such as the zigzag symbol in the last measure. We will learn about this later in this chapter.

Directions:

• Would you perform the following examples as simple triple or compound single? Write your answer in the blank.
• Below the musical example, write the key.

1.  Wieck Schumann^[11], Three Preludes and Fugues, Op. 16, Fugue No. 2: ______________________________

2.  Wieck Schumann, Caprice, Op. 2, No. 8: ______________________________

3.  Wieck Schumann, Caprice, Op. 2, No. 2: ______________________________

5.6   Transposition: Rhythm

Some students feel most comfortable writing and reading compound meters where the dotted quarter note is the beat. However, they sometimes struggle when the beat is a dotted half note or dotted eighth note. One strategy these students can use is rhythmic transposition to temporarily think of the time signature where a dotted quarter note equals a beat. Remember that transposition means changing all notes by the same proportion. Compare the examples below (Example 5.6).

Example 5.6.  Rhythmic transposition

We know all the notes in Examples 5.6A, B, and C are proportionally equal because the rhythm syllables are the same.

There is a simple shortcut for doubling or halving dotted notes:

• To double a dotted note, write a dotted note of the next higher value (for example, doubling a dotted quarter note results in a dotted half note).
• To halve a dotted note, write a dotted note of the next smaller value (for example, halving a dotted quarter note results in a dotted eighth note).

Directions:

• Transpose the rhythms into the given time signature and key signature.
  • Fill in the blanks with the correct major key.
• Keep all pitches, articulations, and dynamics.

1.  Grieg^[12], Peer Gynt, “Morning Mood”

2.  “Home on the Range”

5.7   Ornaments

In this chapter, you might have noticed some unfamiliar symbols, such as the zigzag symbol in Chopin’s Minute Waltz. These symbols are called musical ornaments. A musical ornament, or embellishment, is an added note or notes that decorate the main note. It can be shown by a small note or a symbol.

There are more ornaments than those in Example 5.7.1, and ornaments have changed meaning over the centuries. In this chapter, we will only cover these five ornaments and the most common ways to perform them.

Example 5.7.1.  Ornaments

The first line in Example 5.7.1 shows how the ornaments look, and the second line shows how to perform the ornaments.

• Example 5.7.1A:
  • The grace note, also called the acciaccatura, originates from the Italian word “acciaccare,” which means “to crush.”
  • The grace note is a small note with a slash that appears before a note on a beat. The grace note should be played quickly and immediately before the main note falls on the beat.
  • There can be more than one grace note before the main note, but usually, there is no slash on the small notes in those cases.
• Example 5.7.1B:
  • The appoggiatura resembles a grace note, but it has no slash.
  • The appoggiatura is performed very differently from the grace note. The small note occurs on the beat and lasts half the duration of the following main note.
  • There can be multiple appoggiaturas before the main note.
• Example 5.7.1C:
  • The mordent resembles a double zigzag or two mountain peaks and has several variations.
  • The mordent can occur before the beat or on the beat.
  • If there is a vertical line through the middle of the mordent, it becomes a lower mordent, where the notes in Example 5.7.1C would be D-C-D instead of D-E-D.
• Example 5.7.1D:
  • The turn is curved and resembles a sideways “S.” It decorates the note from both above and below.
  • Like the mordent, it can fall before the beat or on the beat.
  • Also, like the mordent, if there is a line through the middle of the turn, the turn first descends, then ascends. Example 5.7.1D would be C-D-E-D instead of E-D-C-D.
• Example 5.7.1E:
  • The trill has the letters “tr” and can vary in length.
  • Trills involve repeating alternating notes.
  • Trills can extend across several measures, commonly indicated by a squiggly line.

We will now look at some ornaments in context (Examples 5.7.2 and 5.7.3)

Example 5.7.2.  Ornaments: Martinez^[13], Piano Sonata in E Major, i – Allegro

• The anacrusis of Martinez’s E Major Piano Sonata starts with a mordent, which is played as B-C♯C sharp-B.
• In measure 1, the appoggiatura signals that the G♯G sharp falls on the downbeat, and the G♯G sharp and E are played as two sixteenth notes.
• The grace note in measure 3 shows that the B sounds before the downbeat.
• Also in measure 3, there is a trill on the A that lasts the entire measure. This is illustrated with a long squiggly line.
• The number “3” in measure 2 is not an ornament, but represents a triplet, which we will explore in chapter 7.

Let’s look at another sonata by Martinez (Example 5.7.3).

Example 5.7.3.  Ornaments: Martinez, Piano Sonata in A Major, i – Allegro

• Martinez’s A Major Piano Sonata begins with a lower mordent, which would be played as A-G♯G sharp-A.
• The lower mordent features a vertical line in the center, unlike the mordent in Example 5.7.2.
• In measure 2, the appoggiatura on E instructs the performer to play it as an eighth note on the downbeat.
• As a result, the trill lasts only for half a beat.
• Because the trill is much shorter than the one in Example 5.7.2, the squiggly line was not needed.

We have observed two types of mordents in Examples 5.7.2 and 5.7.3. Turns offer even more possibilities. In general, the turn symbol encompasses many meanings within a single symbol.

1. Perform the note above the written note on time. Do not enter early.
2. Perform the written note.
3. Perform the note below the written note.
4. Return to the written note.

The beat should be divided into four equal parts of the written note. Although the steps above describe a basic turn, there are many more variations. Example 5.7.4 shows just one of the many possible turns.

Example 5.7.4.  Turn: Chopin, Nocturne, Op. 9, No. 2

The turn in measure 2 has a flat sign above it and a natural sign below. These accidentals apply to notes in the turn: the pitches are D♭D flat-C-B♮B natural-C. The table in Example 5.7.5 outlines the possible variations the turn could have had in the Chopin example.

Example 5.7.5. Variations of possible turns

• In each example, the turn evenly divides the C into four thirty-second notes, and does not start early.
• Examples 5.7.5A-D demonstrate turns where the first note starts above the written note, while Examples 5.7.5E-H show turns that begin with a note lower than the written note.
• When a flat is written above the turn, the D is to be performed as D♭D flat, while a natural sign under the turn means that B♭B flat is performed as B♮B natural.

Most ornaments come in several variations. There may be more than one grace note before a main note. One well-known piece of music features multiple grace notes (Example 5.7.6).

Example 5.7.6.  Grace notes: Mendelssohn^[14], Spring Song

Example 5.7.5 includes numerous grace notes. However, because there is more than one grace note preceding each main note, the grace notes do not have slashes. They are still meant to be played like grace notes (and not appoggiaturas), so that all the little notes are performed before the main note, which falls on the beat.

Ornaments have changed meaning throughout the centuries; a mordent in 1750 may not be performed the same as a mordent in 1880.  Moreover, individual performers may interpret ornaments differently. For the scope of this theory book, we will not go into detail about the many variations on how these symbols can be performed, but simply that they are decorations and do not alter the analysis. This section gives you the basics of five common musical ornaments.

Directions:

• Identify and label all musical ornaments.
• Briefly explain how each ornament should be performed.

1.  Montgeroult^[15], Piece for Piano, Op. 3, i – Adagio non troppo

2.  Lang^[16], Mazurka, Op. 49, No. 2

3.  Röntgen-Maier^[17], Violin Sonata in B Minor, i – Allegro

5.8   Endings

We have learned about three types of bar lines.

• Single bar line: Also known as simply “bar line,” the single bar line separates measures.
• Double bar line: Featuring two closely spaced thin lines, the double bar line is commonly used in examples and exercises to separate measures or sections.
• Final double bar line: The final double bar line also consists of two closely spaced bars, with the first being thin and the second thick. It is used to mark the end of a piece or example.

Along with the double bar line, repeat signs  can bee added to tell musicians to perform certain sections or the whole piece again (Example 5.8.1).

Example 5.8.1.  Repeat signs

The repeat sign features two dots placed in the second and third spaces of the staff. These dots are located within the inside of the final double bar lines. Note that at measure 5, the double bar lines are reversed, with the thicker line appearing first.

Example 5.8.1 should be read like this:

• Read measures 1 through 4, then repeat measures 1 through 4.
• Read measure 5 to the end, then repeat it.

Repeat signs can include first and second endings (see Example 5.8.2).

Example 5.8.2.  First and second endings

Example 5.8.2 should be read like this:

• Read measures 1 through 4, which is the first ending. Then return to the beginning.
• Read measures 1 through 3, then skip the first ending and go directly to the second ending.
• There will be eight measures in total.

Another common sign you might encounter is D. C. al Fine (da capo al fine). The words “da capo” mean “from the beginning,” and “al fine” mean “to the end.” You would go back to the start and stop at the final double bar line (Example 5.8.3).

Example 5.8.3.  D. C. al Fine

Example 5.8.3 should be read like this:

• Read measures 1 through 8, then go back to the beginning (da capo).
• Read measures 1 through 4 (al fine).

There is no final double bar line at measure 8 because measure 8 is not the end; measure 4 is the end. The double bar line appears only at measure 8, and the actual final double bar line is at measure 4.

In addition to D. C. al Fine, you may also see D. S. al Fine (dal segno al fine). The words “dal segno” mean “from the sign.” Instead of returning to the beginning, you go back to the sign (Example 5.8.4).

Example 5.8.4.  D. S. al Fine

Example 5.8.4 should be read like this:

• Read measures 1 through 8, then go back to the sign.
• Read measures 3 through 4 (al fine).

Another variation includes D. C. al Coda (da capo al coda). At D. C. al Coda, go back to the beginning (da capo) until the coda sign (al coda). Then jump to the other coda sign until the end (Example 5.8.5).

Example 5.8.5.  D. C. al Coda

Example 5.8.5 should be read like this:

• Read measures 1 through 8, then go back to the start (D.C.).
• Read measures 1 to 2, then jump to the coda sign.
• Read measures 9 to 10.

Both the segno and coda signs may be used in D. S. al Coda (dal segno al coda) (Example 5.8.6).

Example 5.8.6.  D. S. al Coda

Example 5.8.6 should be read like this:

• Read measures 1 through 8, then go back to the sign.
• Read measures 3 through 6, then jump to the coda sign.
• Read measures 9 to 10.

The different endings can seem confusing at first, but sometimes several pages of music are repeated. Adding one of the labels from this section makes reading music much simpler.

Directions:

• List how you would read the following example (see sample below).
  • Remember that the anacrusis does not count as a measure.

“Jarabe Tapatio,” Mexican Hat Dance

Terms

• appoggiaturacompound meters
  • compound duple
  • compound triple
  • compound quadruple
  • compound single
• D. C. al Coda (da capo al coda)
• D. C. al Fine (da capo al fine)
• D. S. al Coda (dal segno al coda)
• D. S. al Coda (dal segno al fine)
• grace note (acciaccatura)
• mordent
• ornament
• repeat sign
  • first ending/second ending
• trill
• turn