A.P. Music Theory Lessons
Rhythm and Meter
In music notation, the shape of a note or rest indicates the duration of the pitch. Their duration is relative to the tempo of the music. Tempo is reliant upon beat. The note names are based upon fractions. In the chart below, we will treat a whole note as 1, as the remainder of the notes and rests are fractions of the whole. In the chart, find that the note and is corresponding rest are in line with one another. Notice also how all of the values listed below are divisible by 2.
For those of you who prefer a more visual representation of how the divisions of the rhythmic values work, see the "rhythm tree" below.
There are also rhythmic values that are divisible by three. We call these notes dotted notes. A dot after the note increases the note by 1/2. For instance, a dotted half note = 1 half note + 1 quarter note = 3 quarter notes. Note: the answer is divisible by 3.
An eighth note that is dotted = 1 eighth note + 1 sixteenth note = 3 sixteenth notes
If we were to make a rhythm tree similar to the one show above but with dotted values, each note would have 3 branches off of it instead of two.
When notes are tied, it indicates that the two tied note values should be added together for one total duration period. For instance, a half note tied to a quarter note would be held for a total of 3 quarter notes. A whole note tied to a quarter note would be held for 5 quarter notes.
The example below is a traditional tune that has been notated using ties.
Listeners can find that most music tht has a steady beat, will divide itself into strong and weak beats.
When speaking or humming the lyrics of "Jingle Bells," you will find that if you tap your foot, you will feel that every other beat is stronger.
The highlighted syllables are where the strong beats are.
"Dashing through the snow
On a one horse open sleigh
O'r the fields we go
Laughing all the way"
Because the strong beats occur every other beat (strong-weak-strong-weak), the song has a feeling of being in "two." The following example has the beats grouped in three. Once again, the strong beats are highlighted.
"My country tis of thee
Sweet land of liberty
Of thee I sing"
There are also songs with four beat groupings. In quadruple beat groupings, there is a strong 1, and a slightly less strong beat 3.
1 2 3 4 1 2 3 4 1 2 3 4
Because there is a strong beat one AND beat three, many songs in 4 (quadruple), get confused with songs in 2 (duple).
To figure out if a song has simple or compound divisions, we have to examine the beat itself. Each beat is divisible by either two or three. As with the main chorus of "Jingle Bells," we find that the beat is divided by two. That means that between the strong and weak beat, there is an even weaker subdivision of the beat. We'll call the strong beat "1," the weak beat "2," and the subdivision of the beats "+."
Jingle Bells, Jingle Bells
1 + 2 + 1 + 2 +
Jingle all the way..........
1 + 2 + 1...........
If the song has a beat that is divisible by 2, it is then referred to as having a simple beat. If a beat is divisible by 3, it is considered to have a compound beat. Cosider the song "When Johnny Comes Marching Home Again." If you were to sing this, or hear it played, you would probably tap your foot to the highlighted beats.
(When) Johnny comes marching home again
The highlighted syllables are where there is a natural emphasis placed, just like when certain words are emphasized when reading poetry. Underlying these accented syllables there is a natural subdivision of the beat. In this case, the subdivision of the beat is in three. We'll call the strong beat "1," and the other two weaker beats "2 & 3."
(When) Johnny comes marching home again Hur-rah, Hur-rah
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
Since the above tune has a beat that is divsible by three, that beat will be called compound.
There are are different combinations of beat groupings and beat divisions that can be made. As noted above, there can be beat groupings that are duple, triple and quadruple. All of these groupings can be paired with simple or compound divisions.
Therefore, you can have the following combinations:
Simple Duple Simple Triple Simple Quadruple
Compound Duple Compound Triple Compound Quadruple
Meter how we measure the rhythmic patterns produced by grouping together strong and weak beats. We do this by using a time signature. A time signature shows up in the music at the beginning of the piece in the left hand side of the staff. A time signature tells us three things.
1.) The number of beats in each grouping
2.) The division of the beat
3.) The type of notation to be used.
Below is an example of a time signature.
Pay attention to where the time signature is placed in a music score. First, we find the clef sign - in this case, a treble clef. Then, we find the key signature - in this case, there are 2 sharps, so we are in the key of D major (or b minor). Finally, we find the time signature. In this case, we are in 3/4 time signature (Please note: we will be using the number/number configuration in this lesson; however, in true musical notation, the numbers appear vertical, with no slash or division symbol). Because a time signature shares its appearance with a mathematical fraction, we will briefly use the terms numerator and denominator. The numerator indicates the number of beats in each grouping (duple, triple, etc.), while the denominator indicates the note value that receives the divisions. In the 3/4 example above, the numerator 3 tells us that we are using a triple grouping, while the denominator indicates that a quarter note (1/4 of a whole note), is what receives the beat. Therefore, there are 3 beats per measure, with a quarter note getting the beat. Even more simply put - there are 3 quarter notes per measure.
In simple meter, the numerator is either 2, 3, 4, and the division of the beat is simple. Examples of simple meter are:
Simple Duple Meter: 2/1, 2/2, 2/4, 2/8, 2/16, 2/32
Simple Triple Meter: 3/1, 3/2, 3/4, 3/8, 3/16, 3/32
Simple Quadruple Meter: 4/1, 4/2, 4/4, 4/8, 4/16, 4/32
In compound meter, the numerators are usually 3, 6, 9, or 12. Compound meters also use compound beats. Like simple meter, the numerator tells you how many beats are in the measure, and the denominator tells you what note receives the division of the beat. Unlike simple meter, the note getting the division of the beat is NOT how the beat is felt. For instance, in 6/8 meter, there are six eighth notes in the measure. However, if you divide the numerator by 3 (the basis of compound meter is that it is divisible by three), you get the number 2. In 6/8 meter, you actually FEEL two beats. The 2 beats you feel are dotted quarter notes. Compound meter can also be duple, triple, or quadruple. Examples of compound meter are given below.
Compound Duple Meter: 6/2, 6/4, 6/8, 6/16, 6/32
Compound Triple Meter: 9/2, 9/4, 9/8, 9/16, 3/32
Compound Quadruple Meter: 12/2, 12/4, 12/8, 12/16, 12/32
Numerators of 5 and 7 sometimes appear in music. In the example of 5 as a numerator, the meter is simple, with two uneven groupings of the beat, one of two and one of three. The emphasis could be 2 +3, or 3+2 (123 12 OR 12 123). The same can be true of 7. Let's use 7/8 as an example. There are 7 eighth notes per measure. The uneven beat groupings could be: 123 12 12, 12 123, 12 or 12 12 123
Examples of this "other" type of meter caption are:
5/2, 5/4, 5/8, 5/16
7/2, 7/4, 7/8, 7/16
There are many other types of time signatures that exist in 20th century music. These time signature involve knowledge of the composer, composition and time period.