I. Fundamentals

# Compound Meter and Time Signatures

Chelsey Hamm and Mark Gotham

Key Takeaways

• are meters in which the beat divides into three, and then further subdivides into six.
• have groupings of two beats, have groupings of three beats, and have groupings of four beats. You can determine these groupings aurally by listening carefully and tapping along to the beat.
• There are different conducting patterns for Duple, Triple, and Quadruple meters; these are the same in both compound and simple meters.
• in compound meters express two things: how many divisions are contained in each measure (the top number), and the —which note gets the division (the bottom number).
• Rhythms in compound meters get different counts based upon their division unit. Beats that are not articulated (because they contain more than one beat or because of ties, rests, or dots) receive parentheses around their counts.

In the previous chapter, Simple Meter and Time Signatures, we explored rhythm and time signatures in —meters in which the beat divides into two, and further subdivides into four. In this chapter we will learn about —meters in which the beat divides into three, and further subdivides into six.

# Listen to and Conducting Compound Meters

Compound meters can be , , or , just like simple meters. In other words, the beats of compound meters group into sets of either two, three, or four. However, you will want to listen carefully to the beat division in each of the following three examples, noticing that their beats divide into three divisions instead of two:

• Listen to “End of the Road” (1992) by Boyz II Men. Tap along to the beat and notice how it divides into three parts instead of two. If you further divide the beat (by tapping twice as fast) you will feel that the beat subdivides into six parts. “End of the Road” is in a . In other words, the beats group into a two-pattern.
• The second movement (Minuet) of Franz Joseph Haydn’s Sonata No. 42 in G Major (1784) is in a compound . Listen for the groupings of three beats, each of which divides into three.
• Finally, a compound contains four beats, each of which divides into three. Listen to “Exogenesis Symphony Part III” (2010) by the alternative rock band Muse. This is in a compound quadruple meter; in other words, the beats are grouped into a four-pattern.

In general, it is less common for music to be written in compound meters. Nonetheless, you must learn how to read music and perform in these meters in order to master Western musical notation.

Review the conducting patterns for simple meters as they are the same for compound meters.

# Time Signatures

in compound meters are equivalent to one beat grouping (duple, triple, or quadruple), just as they are in simple meters. In compound meters, still express two things, but not the same information as in simple meters. The top number of a time signature in compound meter expresses the number of divisions in a measure, while the bottom number expresses the —which note is the division. A common compound meter time signature is seen in Example 1:

Again, these numbers still do not form a fraction, and there is no line in between the two numbers. Time signatures still come after a clef. In Example 1, the top number (“6”) means that each measure will contain six divisions; the bottom number (“8”) means that the eighth note is the division. This means that each measure in this time signature will contain six eighth notes; you can see that this is true by examining Example 1.

In compound meters, the top number is always “6,” “9,” or “12.” These numbers correspond to either duple, triple, or quadruple meters. Divide the top number by three to come up with a corresponding number in simple meter, in order to determine if the meter is duple, triple, or quadruple. Six divided by three is two, and therefore a time signature with “6” on top is duple; nine divided by three is three, and therefore a time signature with “9” on top is triple; and twelve divided by three is four, and therefore a time signatures with “12” on top is quadruple. In compound meters, the bottom number is usually one of the following:

• “8,” which means the eighth note receives the division.
• “4,” which means the quarter note receives the division.
• “16,” which means the sixteenth note receives the division.

The following table summarizes the six categories of meters that we have covered so far:

Simple or Compound? Duple, Triple, Quadruple? Beat Grouping Beat Division Example time signatures
Simple Duple 2 2 $\begin{smallmatrix}2\\4\end{smallmatrix}, \begin{smallmatrix}2\\8\end{smallmatrix}, \begin{smallmatrix}2\\2\end{smallmatrix}, \begin{smallmatrix}2\\16\end{smallmatrix}$
Simple Triple 3 2 $\begin{smallmatrix}3\\4\end{smallmatrix}, \begin{smallmatrix}3\\8\end{smallmatrix}, \begin{smallmatrix}3\\2\end{smallmatrix}, \begin{smallmatrix}3\\16\end{smallmatrix}$
Simple Quadruple 4 2 $\begin{smallmatrix}4\\4\end{smallmatrix}, \begin{smallmatrix}4\\8\end{smallmatrix}, \begin{smallmatrix}4\\2\end{smallmatrix}, \begin{smallmatrix}4\\16\end{smallmatrix}$
Compound Duple 2 3 $\begin{smallmatrix}6\\8\end{smallmatrix}, \begin{smallmatrix}6\\4\end{smallmatrix}, \begin{smallmatrix}6\\16\end{smallmatrix}$
Compound Triple 3 3 $\begin{smallmatrix}9\\8\end{smallmatrix}, \begin{smallmatrix}9\\4\end{smallmatrix}, \begin{smallmatrix}9\\16\end{smallmatrix}$
Compound Quadruple 4 3 $\begin{smallmatrix}12\\8\end{smallmatrix}, \begin{smallmatrix}12\\4\end{smallmatrix}, \begin{smallmatrix}12\\16\end{smallmatrix}$

Example 2. Categories of meters.

# Counting in Compound Meter

While counting compound meter rhythms, it is recommended that you conduct in order to keep a steady tempo. Because beats in compound meter divide into three, they are always dotted. Beats in compound meter are as follows:

• If “8” is the bottom number, the beat is a dotted quarter note (equivalent to three eighth notes).
• If “4” is the bottom number, the beat is a dotted half note (equivalent to three quarter notes).
• If “16” is the bottom number, the beat is a dotted eighth note (equivalent to three sixteenth notes).

In simple meters the beat divides into two parts, the first accented and the second non-accented. In compound meters the beat divides into three parts, the first accented and the second and third non-accented. The counts for compound meter are different from simple meter, as demonstrated in Example 3:

Example 3. A rhythm with counts in a compound duple meter.

Each measure in this time signature should have two beats (take the “6”—the top number—and divide it by three; the result, two, indicates a duple meter). Each dotted quarter note (the beat) gets a count, which is still expressed in . Notes that are longer in duration than the beat (such as the dotted half note) are held over multiple beats, and beats that are not counted out loud are still written in parentheses. Divisions receive the syllables “la” (first division) and “li” (second division). Please review measure 3 of Example 3 carefully if you are not familiar with compound meter, as it presents two of the most common compound meter rhythms with divisions. Please note that your instructor, high school, college, or university may employ a different counting system. Open Music Theory privileges American traditional counting, but this is not the only method.

Example 4 shows how divisions (eighth notes) and subdivisions (sixteenth notes) are counted:

Example 4. The counting of divisions and subdivisions in compound meter.

As you can see in Example 4, further subdivisions at the sixteenth-note level are counted as “ta.” The “la” and “li” syllables remain consistent on the eighth note subdivisions of each beat.

Compound duple meters have only two beats, as shown in Example 5:

Example 5. Compound duple meters have two beats per measure.

While compound triple meters have three beats, as shown in Example 6:

Example 6. Compound triple meters have three beats per measure.

Compound quadruple meters have four beats, as shown in Example 7:

Example 7. Compound quadruple meters have four beats per measure.

Beats that are not articulated because of rests and ties are also not counted out loud. These beats are usually written in parentheses, as shown in Example 8.

Example 8. Beats that are not counted out loud are put in parentheses.

Dotted rhythms do not lead to parentheses in compound meters the way they do in simple meters, because in compound meters dotted notes receive the beat.

# Counting with Division Units of 4 and 16

Compound meters with other division units (the bottom number of a time signature) are counted differently because a different note value gets the beat (and division). Example 9 shows a rhythm with a $\begin{smallmatrix}9\\8\end{smallmatrix}$ time signature:

Example 9. A counted rhythm with the beat unit of a dotted quarter note.

Example 10 shows the same rhythm with the dotted half note as the beat unit:

Example 10. A counted rhythm with the beat unit of a dotted half note.

Example 11 shows the same rhythm with the dotted eighth note as the beat unit:

Example 11. A counted rhythm with the beat unit of a dotted eighth note.

Each of these rhythms sound the same, and are counted the same. They are also all considered compound triple meters. The difference in each example is the bottom number—which note gets the division unit (eighth, quarter, or sixteenth), as well as their beat unit.

# Beaming, Stems, and Flags

In compound meters, stilll connect notes together by beat; beaming therefore changes in different time signatures. This is demonstrated in Example 12:

Example 12. Beaming in two different meters.

In the first measure of Example 12, sixteenth notes are grouped into sets of six, because six sixteenth notes in a $\begin{smallmatrix}6\\8\end{smallmatrix}$ time signature are equivalent to one beat. In the second measure of Example 12, sixteenth notes are grouped into sets of three, because three sixteenth notes in a $\begin{smallmatrix}6\\16\end{smallmatrix}$ time signature are equivalent to one beat.

You should always clarify the meter with beams, regardless of whether the time signature is simple or compound. Example 13 shows twelve sixteenth notes beamed properly in two different meters, one simple and one compound:

As you can see, in the first measure (in simple meter) the notes are grouped by beat into sets of four, while in the second measure (in compound meter) the notes are grouped by beat into sets of six.

The same rules of stemming and flagging that applied in simple meter still apply in compound meter. For notes above the middle line, stems and flags point downwards on the left side of notes, and for notes below the middle line stems and flags point upwards on the right side of the note. Stems and flags on notes on the middle line can point in either direction.

Please also note that partial beams can be used for mixed rhythmic groupings, as seen in Example 14:

Example 14. The most common partially beamed variations with a division unit of the eighth note.

Sometimes these beaming conventions look strange to students who have had less experience with reading beamed music. If this is the case, you will want to pay special attention to how the notes in Example 14 are beamed.

Online Resources
Assignments from the Internet
1. Meter Identification (Simple and Compound) (.pdf,), and with Bar Lines (.pdf)
2. Meter Beaming (Simple and Compound) (.pdf), and pp. 4 and 5 (.pdf)
3. Time Signatures (Simple and Compound) (.pdf)
4. Counting in 6/8 (.pdf.pdf.pdf)
5. Counting in Compound Meter (.pdf)
6. Time Signatures (.pdf.pdf, .pdf)
7. Bar Lines (.pdf), and p. 2 (.pdf)
Assignments
1. Notes, Rests, Bar Lines (.pdf, .docx)
2. Re-beaming (.pdf, .musx)