time signature homework

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

I. Fundamentals

10 Compound Meter and Time Signatures

Chelsey Hamm and Mark Gotham

Key Takeaways

Compound meters are meters in which the beat divides into three and then further subdivides into six.
Duple meters have groupings of two beats, triple meters have groupings of three beats, and quadruple meters 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.
Time signatures in compound meters express two things: how many divisions are contained in each measure (the top number), and the division unit — 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.

Chapter Playlist

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

Listening to and Conducting Compound Meters

Compound meters can be duple , triple , or quadruple , just like simple meters. In other words, the beats of compound meters group into sets of either two, three, or four. The difference is that each beat divides into three divisions instead of two, as you can hear by listening carefully to the following examples:

“End of the Road” (1992) by Boyz II Men is in a duple meter —the beats group into a two pattern. 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.

T he second movement (Minuet) of Franz Joseph Haydn’s Sonata no. 42 in G Major (1784) is in a compound triple meter . Listen for the groupings of three beats, each of which divides into three.
Finally, a compound quadruple meter 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 in the previous chapter , as they are the same for compound meters.

Time Signatures

Measures in compound meters are equivalent to one beat grouping (duple, triple, or quadruple), just as they are in simple meters. However, the two numbers in the time signature express different information for compound 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 division unit —which note value is the division. Example 1 shows a common compound-meter time signature.

A percussion clef, compound meter time signature (6/8) and six eighth notes

Just like in simple meter, compound-meter time signatures are not fractions (and there is no line between the two numbers), and they are placed after the clef on the staff. 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, as you can verify by examining Example 1 .

In compound meters, the top number is always a multiple of three. Divide this number by three to find the corresponding number of beats in simple meter: top numbers of 6, 9, and 12 correspond to duple, triple, and quadruple meters respectively. 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:

[table “36” not found /]

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 , which is in [latex]\mathbf{^6_8}[/latex].

https://musescore.com/user/32728834/scores/8394558/embed

Example 3. Counting in a compound duple meter.

In this time signature, each measure has two beats (6÷3=2), indicating duple meter. Each dotted quarter note (the beat) gets a count, which is expressed in Arabic numerals, like in simple meter. For notes that are longer than one beat (such as the dotted half note in the fourth measure of Example 3 ), the beats that are not counted out loud are still written in parentheses. Divisions are counted using the syllables “la” (first division) and “li” (second division). As the final measure of Example 3 shows, further subdivisions at the sixteenth-note level are counted as “ta,” with the “la” and “li” syllables on the eighth-note subdivisions remaining consistent.

The third measure of Example 3 presents two of the most common compound-meter rhythms with divisions, so make sure to review this measure carefully if you are not familiar with compound meter.

Please note that your instructor may employ a different counting system. Open Music Theory privileges American traditional counting, but this is not the only method.

Example 4 gives examples of rhythms in (a) duple, (b) triple, and (c) quadruple meter. Just as with simple meters, compound duple meters have only two beats, compound triple meters have three beats, and compound quadruple meters have four beats.

https://musescore.com/user/32728834/scores/8394447/embed Example 4. (a) Compound duple has two beats, (b) compound triple has three beats, and (c) compound quadruple has four beats.

Like in simple meters, beats that are not articulated because of rests and ties are written in parentheses and not counted out loud, as shown in Example 5 . However, because dotted notes receive the beat in compound meters, dotted rhythms do not cause beats to be written in parentheses the way they do in simple meters.

https://musescore.com/user/32728834/scores/6296091/embed

Example 5. Beats that are not counted out loud are put in parentheses.

Counting with Division Units of 4 and 16

So far, we have focused on meters with a dotted-quarter beat. In compound meters with other beat units (shown in the bottom number of the time signature), the same counting patterns are used for the beats and subdivisions, but they correspond to different note values ( Example 6 ).

https://musescore.com/user/32728834/scores/8394456/embed

Example 6. The same rhythm written with three different beat units: (a) dotted quarter, (b) dotted half, and (c) dotted eighth.

Each of these rhythms sounds the same and is 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), which then determines the beat unit.

Beaming, Stems, and Flags

In compound meters, beams still connect notes together by beat; beaming therefore changes in different time signatures. In the first measure of Example 7 , sixteenth notes are grouped into sets of six, because six sixteenth notes in a [latex]\mathbf{^6_8}[/latex] time signature are equivalent to one beat. In the second measure of Example 7 , sixteenth notes are grouped into sets of three, because three sixteenth notes in a [latex]\mathbf{^{\:6}_{16}}[/latex] time signature are equivalent to one beat.

https://musescore.com/user/32728834/scores/8394474/embed Example 7. Beaming in two different meters.

When the music involves note values smaller than a quarter note, you should always clarify the meter with beams, regardless of whether the time signature is simple or compound. Example 8 shows twelve sixteenth notes beamed properly in two different meters. The first measure is in simple meter, so the notes are grouped by beat into sets of four; in the second measure, the compound meter requires the notes to be 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 downward on the left side of the note, and for notes below the middle line, stems and flags point upward on the right side of the note. Stems and flags on notes on the middle line can point in either direction, depending on the surrounding notes.

Like in simple meters, partial beams can be used for mixed rhythmic groupings. If you aren’t yet familiar with these conventions, pay special attention to how the notes in Example 9 are beamed.

https://musescore.com/user/32728834/scores/6296096/embed Example 9. The most common partially beamed variations with a division unit of the eighth note.

Compound Meter Tutorial (musictheory.net) (compound meter starts about halfway through)
Video Tutorial on Compound Meters and Beats (YouTube) (start at 1:49 for compound meter)
Compound Meter Counting and Time Signatures (John Ellinger)
Compound Meter Counting (YouTube)
Compound Meter Rhythmic Practice (YouTube)
Compound Meter Beaming (Michael Sult)
Meter Identification (Simple and Compound) ( .pdf ,), and with Bar Lines ( .pdf )
Meter Beaming (Simple and Compound) ( .pdf ), and pp. 4 and 5 ( .pdf )
Time Signatures (Simple and Compound) ( .pdf )
Counting in 6/8 ( .pdf , .pdf , .pdf )
Time Signatures ( .pdf , .pdf , .pdf )
Bar Lines ( .pdf ), and p. 2 ( .pdf )
Notes, Rests, Bar Lines ( .pdf , .docx )
Re-beaming ( .pdf , .musx )

A meter that divides the beat into three parts.

A meter with two beats per measure.

A meter with three beats per measure.

A meter with four beats per measure.

An indication of meter in Western music notation, often made up of two numbers stacked vertically.

The note value that divides the beat into two or three parts (in simple or compound meters, respectively); for example, the eighth note in 4/4 or 6/8.

A meter that divides the beat into two parts.

Created by bar lines, a measure (or bar) is equivalent to one beat grouping.

The horizontal lines that connect certain groups of notes together.

Music Theory Academy

Time signatures, what is a time signature.

A time signature appears at the beginning of a piece of music to show the time or meter of the music. It consists of two numbers on top of each other (a bit like a fraction in math, but without the line) . The top number shows the number of beats in every measure (bar) . The bottom number shows what type of beats they are . e.g. crotchets (quarter notes) , quavers (eighth notes) , semiquavers (sixteenth notes) , etc..

Why do we need a Time Signature?

Theoretically, music does not need a time signature. When counting the beat of a piece of music we could start at the number “1” and keep going to whatever number we got to by the end of the piece. However, there would be 2 main problems with this approach….

We would soon lose count! Similar to the way we don’t like to go beyond “G” in the alphabet, we musicians don’t really like to count beyond “4”. Sometimes we’ll go to 6 and, if we’re really pushed, we may even count as high as 12!! But, we tend to like 3 or 4!!
We would not establish a “groove” . The groove (or the “feel”) of a piece of music stems largely from how the beats are grouped together. The feel of a Viennese Waltz and a march differ for a wide variety of reasons, but a key foundation is the different groupings of the pulse.

Let me explain…

If I was teaching you how to march then I would probably stand in front of you and shout “1-2-3-4” at a suitable speed for you to walk in time to. My natural instinct would be to then start at “1” again rather than going on to “5-6-7-8…”. This is because it “feels” like the right and natural thing to do. Something in me makes me want to arrange my counting into groups of 4.

In music, these “groupings” are called measures or bars . As a result, a march-like piece will have 4 beats in every measure and these beats will most likely be quarter notes (crotchets) . So, the time signature would have a number “4” at the top (4 beats in every measure) and a number “4” at the bottom (these beats would be quarter notes (crotchets)) .

However, if I was teaching you how to waltz (an unlikely scenario given my lack of ability on the dance floor(!!)) then I would want to count “1-2-3” and then return to “1” because this is the grouping that fits with the dance steps:

As a result, the top number of the time signature for a waltz would be a “3” (3 beats in every measure) and the bottom number would probably be a 4 again (quarter notes) .

The first beat of every measure/bar is accented (played slightly louder) and this helps to give the characteristic feel of a particular grouping.

What do Time Signatures show?

As we have discussed, a time signature is made up of 2 numbers (one on top of the other) found at the beginning of the stave. It shows 2 things:

How many beats are in a bar ( top number )
What type of beats they are ( bottom number )

The top number is easy to understand. If it is a “2” then you should count the pulse in groups of 2 and each bar should add up to 2. If it is a “3” then the pulse will be counted in groups of 3 and each bar will add up to 3. If it is a “4”, etc…… You get the idea.

Bottom Number

Common time and alla breve.

Quite often you will see what looks like a large “C” at the start of a piece of music instead of the usual time signature numbers. This is either common time or alla breve depending on whether the C has a line through it or not.

Time Signature Examples

Here are some other common time signatures that you will come across in music:

Beware the changing Time Signature

The thing you must do when looking at a piece of music for the first time is check to see whether the time signature changes at all. Sometimes a composer will put a new time signature in during a piece of music. It’s really important that you have a look through before playing a piece because a change of time signature which catches you unaware can totally wreck your performance. If you’re playing as part of a group or a band then it can spell real trouble!!

Share this post: on Twitter on Facebook on Google+

About The Author

Ben Dunnett LRSM is the founder of Music Theory Academy. He is a music teacher, examiner, composer and pianist with over twenty years experience in music education. Read More