Twentieth-Century Rhythmic Techniques
CHAPTER SUPPLEMENT
SUPPLEMENTARY MATERIAL
Minimalism Partially inspired by the techniques of Indian music, composers in the latter half of the twentieth century developed a style of music that involves a limited palette of melodic and rhythmic source materials. This style of Western art music is called minimalism. Minimalism makes use of both the melodic and rhythmic aspects of musical organization inherent in Indian music. It is also another musical technique that has a counterpart in the visual arts. A list of well-known minimalist composers includes John Adams, Philip Glass, Terry Riley, and Steve Reich. Minimalist music usually takes a brief melodic motive, often only three or four notes in length as its starting point. That motive is repeated over and over and, as time passes, it gradually evolves and often modulates. The rhythmic style of minimalism is often simple, and many compositions use combinations of only quarter and eighth notes. The style is considered by many to be hypnotic due to its constant repetition of short figures, and the actual composition may be quite lengthy despite the brevity of the source material. Over the course of a composition, the dynamic levels, harmony, articulation, and timbre tend to remain fairly constant. Examples of minimalism include Clapping Music by Steve Reich as shown in Example 1. There are several YouTube videos of this work available online. The work is purely rhythmic in nature with the performers only using their hands to clap. There is no meter, only thirteen measures, and two parts labeled “clap 1” and clap 2.” Each measure is repeated twelve times before proceeding to the next measure. The rhythm in the “clap 1” part does not vary from measure to measure. The interest comes from the “clap 2” part, where there are subtle changes in rhythm from measure to measure. Example 1. Steve Reich, Clapping Music, mm. 1–3
1 clap 1 clap 2
Ú 160-184 Repeat each bar 12 times 3 2 j j .. œ œ œ ‰ œ œ ‰ œ ‰ œ œ ‰ .. .. œ œ œ ‰ œ œ ‰ œ ‰ œ œ ‰ .. .. œ œ œ ‰ œ œ ‰ œj ‰ œ œ ‰ .. .. œ œ œ ‰ œ œ ‰ œ ‰ œ œ ‰ .. .. œ œ ‰ œ œ ‰ œ ‰ œ œ ‰ œ .. .. œ ‰ œ œ ‰ œ ‰œ œ ‰ œ œ .. J J J J J
1
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Ametric Music In the early part of the twentieth century, American composer Charles Ives wrote the Concord Sonata for piano, in which large sections of the work have no barlines and no metrical indication. The first eleven pages of the first movement, “Emerson,” are written with no meter and only sparsely scattered bar lines. A meter is finally introduced and then changes frequently, but later in the same movement, it disappears again. Likewise, no meter is used in the third movement, “The Alcotts,” shown in Example 2. Example 2. Charles Ives, Concord Sonata, “The Alcotts,” beginning
j œ & b œœ œœœ œœœ œœœ b b œœœ œœœ œœœ œœ œ œ b œ ? j œ b œ œ œ œœ bœ œ œ
œ œ œœ
j ‰ Œ ‰ œj œ œ œ œ ˙ œ œ‰˙ b ˙˙ œœ œœ ‰ ˙˙ J
jœ œ œ Œ Œ ‰ œ # œœ œœ œœ n œœ œ œ b œ b b œ & œ œ œœ ? b b b œœ œœ œœ ‰ œœ œœ œœ ‰ œœ œœ œœ b œ œ œ œ œ œ œ œ œ J J J
œ œœ œ œœ œ b œœ œ œj b ˙ . bb œ œœ œ œœ œœ œœ ‰ b b œ bœ œ œ b b J
j œœ œ œœ œ . œœ œ œ œ nœ œ . J œ œ œ œ œ ‰ œœ œœ œœ ‰ œœ œœ J
j œ b œ œœ ˙˙ .. bœ ˙ . œ œ œ œœ ‰ œœ œœ J
œ œœ ‰ J
The bar lines that do appear in the preceding excerpt are there only to call attention to the changes of key signature and do not serve any metrical or rhythmic function. The term used to describe this type of rhythmic device is ametric.
Irregular Meters Composers of the twentieth century frequently made use of meters that were seldom used in previous century. Irregular meters such as 5/8 and 7/8 are found in the works of many twentieth-century composers such as Copland and Prokofiev. Any time signature with a top number that is not divisible by 2 or 3 can be considered an irregular meter. Example 3 shows the use of an irregular meter in a composition by Prokofiev.
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Example 3. Sergei Prokofiev, Piano Sonata no. 7, op. 83, mm. 1–4
? b b 78 œœœ Precipitato
œ ‰ œœ œœœ œœœ œœœ œœœ
P ? b b 78 ‰ j # œ j Œ œ œ œ # >œ œ
œœœ œœœ n œœœ œœœ J
‰ œj ‰ # œj ‰ Œ œ #œ
œ œ œ œ œœ ‰ œœ œœ n œœ œœ b œ J J
‰ œj # œ œj Œ œ # >œ œ
œœœ # œœ œœœ J n Jœ J
j ‰ œj ‰ œ ‰ Œ œ œ
Changing Meters In combination with the use of irregular meters, composers frequently use changing meters. A favorite technique of some modern composers is to change the meter every measure or every few measures of a composition. In Example 4 from the music of Bartók, notice not only that the meter changes every measure but also the manner in which Bartók notated the score to call attention to that fact. Example 4. Béla Bartók, Music for Strings, Percussion, and Celeste, 1st movement, mm. 1-4 3.4.Vln.
1.2.Vla.
&
Andante tranquillo
8 8j
12 j 8
B œ b œj# œ n œ n œj ‰ œ
j b œ # œ œ b œJ n œ n œ b œ ‰# œ
8 8 nœ
# œ n œ œ # œ n œ ‰n œ
7 8 bœ
Ó
‰ ‰ œj
œ# œ œ n œ b œ J
Polymeter and Polyrhythm Two terms that are commonly used to describe rhythmic techniques in twentieth-century music are polymeter and polyrhythm. Although they sound similar, they represent entirely different practices. The term “polymeter” can be broken down into its two components, “poly-” meaning many (or more than one) and “-meter.” Therefore, polymetrical music contain more than one meter appearing simultaneously. This is a different practice than the technique seen previously where one meter follows another, which is known as changing meters. One of the simplest forms of polymeter occurs when a compound and a simple meter that contain the same number of beats per measure are used simultaneously. The performance of a rhythm like this would be similar to performing any two-against-three rhythmic combination. A more difficult example of polymeters would be a combination of meters that do not have the same number of counts per measure. Stravinsky adopted this approach to polymeters in the ballet, Petrushka, shown in Example 5.
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Example 5. Igor Stravinsky, Petrushka, 2nd tableau, “Danse de la foire,”, mm. 31–34
• œ 5 b & 8 œ
œ œ
œ œ
31
œ œ
œ œ 88 œœ œœ œ œœ œ œœ œ œ œ
œ œ
78
& b 24
œ œ œ œ œ œ œ 34 œ œ œ œ œ œ œ œ œ œ œ œ 34 œ œ œ œ œ œ œ œ œ œ œ • œœœœ œ œ œ œ œ œ œ œ œœ 7 5 œ œ œ &b 8 ‰ œ œ œ œ 8 œ 3
33
3 &b 4
œ œœ œ œœ œ œ œ 24 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ 3
3
3
3
3
3
The term “polyrhythm” refers to music in which two distinct rhythms occurs simultaneously, usually implying distinct meters. Although there is a single simultaneous meter used for a polyrhythm, the music sounds as if it were written in two different meters. In Example 6, notice the manner in which the notes are beamed. Example 6. Stravinsky, Le Chant du Rossignol, “Marche Chinoise,”, mm. 33–36
# # # # 4 œœ œœ œœ œœœ # 8 œ œ & 33
? # # # # 48 œœ œ œ # œ œœ
œœ œ
œœ œ œ œ œ œ œ œœ œœ œœœ œœ 5 œœ œœ œœœ œœœ œœ 3 œœ œ œœ œœ œœ œ 8 œ œ 8
œ œœ
œœ
œ
58 œœ 38 œ œ œ œ œœ œ œœ œ
œœ
In the bass staff of the preceding example, all eighth notes are beamed in groups of three giving the visual effect of a triple meter. Also, each group of three notes has a distinctive intervallic pattern which, in addition to the visual effect, will give the aural effect of a triple meter. Notice that even though the meter changes from measure to measure, the lower voices maintain their three-note groupings. The suggestion of triple meter in the lower part is set against an upper part that aligns the beats with the meter. The beaming of the upper part does not cross any bar lines and the patterns change as the time signature changes. What kind of scale forms the basis for the notes of the treble staff in this example?
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Metric Modulation A technique developed by American composer Elliot Carter is called metric modulation. This process creates changes of tempo through specific equations involving beats, divisions of the beat, or subdivisions of the beat as the time signature changes throughout a composition. At each change of meter, some aspect of the old time signature is equated to an aspect of the new one. These equations cause the overall tempo of the piece to change over time, either speeding up or slowing down. Figure 1 provides two examples of meter changes. The metronome speed is given at the beginning. Figure 1. Metric modulation q. = 100
q. = q
q. = 100
e=e
& 68 œ œ œ œ œ œ c œ œ œ œ œ œ œ œ mayfield.Figure 46.3b & 68 œ œ œ œ œ c œ œ œ œ œ œ œ œ œ
On the first staff, the speed of the beat does not change when the time signature changes. The beat note of 6/8 time, a dotted quarter, is equated to the beat note of the new meter, so the beat moves at the same speed, 100 beats per minute. On the second staff, there is a different equation at the meter change. The equation involves divisions of the beat, not the beat itself. Since the unit of measurement, the dotted quarter, is moving at 100 beats per minute, the division of the beat moves at 300 beats per minute (three eighth notes per beat, 3 x 100). At the point of the meter change, the division of the beat of the first meter is equated to the division in the new meter. This means that the division of the beat must move at the same speed in the new meter as it did in the old meter, namely 300 divisions per minute. But since in the simple meter, the beat divides into two rather than three equal parts, the overall tempo of the beat note has changed. If the eighth notes move at 300 beats per minute, then the quarter notes will be moving at 150 beats per minute (300 divided by 2). Therefore, the overall tempo of the music has increased from 100 to 150 beats per minute. Figure 2 is another example of metrical modulation. Determine whether the beat speeds up, slows down, or remains the same.
Figure 2. Metric modulation for analysis h = 100 2 &2 ˙ ˙
œ œ ˙
h = h.
34 œ œ œ
œœœ œ
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The unit of measurement, the half note, is moving at 100 beats per minute. At the point of the meter change, the beat of the first meter is equated to a note that represents three beats in the new meter. If the dotted half is moving at 100 beats per minute, then the quarter note will move three times as fast, namely 300 beats per minute. Therefore, the overall tempo of the music has increased from 100 to 300 beats per minute. In one of the most famous compositions to make use of metrical modulation, Carter wrote a work for timpani using only four pitches. The work, humorously titled Canaries, is an extremely complex example of what can be accomplished through the use of metric modulation. The complete composition is 156 measures in length. Four measures are shown in Example 7. Find each point of modulation and assess the impact on the tempo. Does the overall speed of the beat notes become faster or slower? Example 7. Elliot Carter, Canaries, mm. 18–21 e = q.
(q = 180)
? 34 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ 38 œ œ œ 3
3
=180
(e = e ) (q = 270)
3
34 œ œ œ œ œ œ
Music for Analysis
Describe the rhythmic techniques used in the following excerpts.
Example 8. Alexander Scriabin, Piano Sonata no. 10, op. 70, mm. 39–42
œ œb œ œ œn œ b œ œœ b œ œ .bœ œ b œj . œ n œ b œ œ œn œ b œ œœ b œ œj. bœ œ œb œ œj 9 & 16 ≈ œ ≈ œ ≈ œ ≈ b œ ≈ œ ‰ . ≈ n œ ≈ œ ≈ œ ≈ b œ ≈ œ ‰ . . p bœ ≈ ‰ nœ bœ ≈ ? 38 ‰ œ œ b œ b œ R œ bœ bœ R œ œ œ œ b œ b œ bœ bœ
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Example 9 Philip Glass, Metamorphosis Four, mm. 60–63
bb 3 œœœ œ œœœœœ œ œœ œœ œ œœœœœ œ œœ œœœœœ œœœœœ œœœœœ œœœœœ b œ & 4 œ œ œ œ ? b b 34 œœ œ œœ œ œœ œ b œœ œ œœ œ œœ œ œœ œ œœ œ œœ œ œœ œ œœ œ œœ œ b
Example 10. Barbara Kolb, Voyants, portion of m. 166
& &œ
œ bœ œ œ bœ œ œ œ œ œ œœ bœ œœ œ œ
nœ œ
œ œ bœ
œ œ œ #œ œ œ œ #œ
œ œ œ œ œ œ œ œ œœ œ œ
œ œ
œ œ œ
#œ œ œ œ œ œn œ n œ œ n œ #œ œ œ b œ# œ œ œ œ # œ # œ œ # œ œ n œ œ n œ œ & œ œ œ œ #œ œ# œ œ # œ œ œ &
œ bœ nœ
œ œ #œ
œ bœ œ
bœ nœ nœ
œ œ nœ
