Hearing Rhythm and Meter

Analyzing Metrical Consonance and Dissonance in Common-Practice Period Music

Matthew Santa

• Editorial: Routledge
• Año: 2019
• ISBN:
  9781351204293
• Edición: 1
• Categoría: Media & Performing Arts
• Categoría: Music

Hearing Rhythm and Meter: Analyzing Metrical Consonance and Dissonance in Common-Practice Period Music is the first book to present a comprehensive course text on advanced analysis of rhythm and meter. This book brings together the insights of recent scholarship on rhythm and meter in a clear and engaging presentation, enabling students to understand topics including hypermeter and metrical dissonance. From the Baroque to the Romantic era, Hearing Rhythm and Meter emphasizes listening, enabling students to recognize meters and metrical dissonances by type both with and without the score. The textbook includes exercises for each chapter and is supported by a full-score anthology.

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chapter 1
Notated Meter and Sounding Meter

Like key signatures, time signatures serve to facilitate reading music. Together with bar lines, beaming, and ties, time signatures help us to group music into familiar rhythmic cells that are easy to recognize and thus read quickly at sight. While time signatures work best when they represent the sounding meter, it is important to recognize that the time signature does not always represent the meter, just as a key signature does not always represent the key of a particular musical passage. Accidentals are routinely added to certain passages to produce keys that are not reflected by the key signature, and, in the same way, grouping and accentuation patterns within a passage can create a sounding meter that is not reflected by the time signature. Listen to mm. 16–20 from the second movement of Schumann’s String Quartet Op. 41/2 and conduct along while following Example 1.1 in order to feel how well the music fits the notation.

Example 1.1 Passage in 12/8.

The notation of the music in Example 1.2 seems to reflect the music fairly well, but Schumann’s score in fact looks quite different, and it is given as Example 1.2.

Example 1.2 Schumann, String Quartet, Op. 41/2, II, mm. 17–20.

No one can be certain as to why Schumann chose his notation over the alternative provided as Example 1.1 (though we will do much speculating about such choices later in the book), but the difference between these two examples draws attention to the fact that time signatures and bar lines do not always reflect the sounding meter.

Sometimes the sound of a passage doesn’t clearly establish any meter at all, but is nevertheless written in traditional notation. Listen to the beginning of Beethoven’s String Quartet, Op. 127 and conduct along while following Example 1.3 in order to determine how well the music fits the notation.

Example 1.3 Passage in 2/4.

Again, the notation of the music in Example 1.3 seems to reflect the music fairly well. The three fermatas, however, prevent any strong sense of regular pulse from emerging, and thus any strong sense of meter from being established. Beethoven’s notation for this passage is given as Example 1.4.

Example 1.4 Beethoven, String Quartet Op. 127, I, mm. 1–5.

Notice how easily one can accept either notation for the same performance. In Example 1.3, the notated measures are coordinated with the changes of harmony and with the sforzando markings, while in Example 1.4, the notated measures are marked by a steady quarter note pulse, albeit one that the performers must keep internally, since the only quarter notes in the passage actually cut against the quarter note pulse that defines the notated meter. Now listen to the beginning of the second movement from Beethoven’s Piano Sonata, Op. 7, and conduct along while following Example 1.5 in order to feel how well the music fits the notation.

Example 1.5 Passage in 3/4.

The notation of the music once again seems to reflect the music fairly well, and this time the attacks are more regularly spaced, and so a sense of meter is established. Beethoven’s notation of this passage is given as Example 1.6.

Example 1.6 Beethoven, Piano Sonata, Op. 7, II, mm. 1–4.

Again, notice how easily one can accept either notation for the same performance. In Example 1.5, the notation places the changes of harmony on the downbeats, while in Example 1.6, the harmonic changes are on beat 2. If either notation seems to fit the performance, then which one of these is actually the sounding meter? In many such situations, there might not be a single correct answer, but in order to arrive at any answer with certainty, we should first address the question of what meter is and how it becomes established as a sounding phenomenon.

Establishing Meter

A rhythm is a pattern of note durations and rests. While a rhythm may be regular or irregular (i.e. the notes may or may not be evenly spaced), meter depends upon regularity for its definition. Meter is a musical pattern of accentuation created by two coordinated layers of evenly spaced pulses. For meter to be established as a perceptual reality (not just a notational convenience in a score), we first must hear these two layers. The process of establishing a meter need not take long. We need only hear two pulses in a single layer to predict when the next pulse will occur, and if the third pulse in that layer arrives as predicted, it confirms that layer in our minds as part of a meter. Example 1.7 illustrates two models for establishing meter.

Example 1.7 Two Models for Establishing Meter.

By the third pulse in the bottom layer of Examples 1.7a and 1.7b, meter has been established. Dots are used in Example 1.7 rather than note values in order to generalize the process. Example 1.8 illustrates how one could substitute quarter notes for the dots in the top layer and half notes for the dots in the bottom layer in Example 1.7a and establish a 2/4 meter, or substitute quarters and dotted halves in Example 1.7b and establish a 3/4 meter. On the other hand, one could substitute eighths and quarters in Example 1.7a and establish 2/8, or substitute eighths and dotted quarters in Example 1.7b and establish 3/8, as shown in Example 1.9.

Example 1.8 One Possible Realization of Example 1.7 Using Note Values.

Example 1.9 Another Possible Realization of Example 1.7 Using Note Values.

One of the two layers establishing any meter is called the beat. The beat is the pulse layer one chooses to count or conduct in a sounding meter, but is often defined as the duration indicated by the lower number of the time signature in a notated meter, or three times that duration if the upper number is 6, 9, or 12, and the tempo is fast enough. While two layers is the minimum number necessary to establish meter, most of the music we hear every day has more than two. We typically categorize meter in terms of three layers. Simple meters divide each beat into two parts, while compound meters divide each beat into three parts, and so these two categories each indicate two different layers. The terms duple, triple, and quadruple meter provide the character of the third layer by indicating whether the beats themselves are grouped into twos, threes, or fours, respectively (larger beat groupings such as quintuple are typically heard as combinations of duple and triple). Example 1.10 illustrates two models for establishing simple duple and compound duple meters, respectively.

Example 1.10 Establishing Simple Duple and Compound Duple Meter.

By the third pulse in the middle layer of Example 1.10a, meter has been established, but it takes an additional two pulses in that layer to establish a meter we can securely identify as simple duple. One could substitute eighth notes for the dots in the top layer, quarter notes for the dots in the middle layer, and half notes for the dotes in the bottom layer in Example 1.10a and establish a 2/4 meter. Similarly, one could substitute eighths, dotted quarters, and dotted halves in Example 1.10b and establish a 6/8 meter.

While it only takes two layers to establish a meter, three layers are required to categorize it in the traditional way. Look at Example 1.7 again. Example 1.7a could represent 6/8 just as easily as 2/4 if we take the top layer to represent beats and the bottom layer to represent downbeats because there would be no layer articulating how the beats are subdivided, and thus we wouldn’t be able to tell whether the meter was simple or compound. It could also represent 2/4, 3/4, or 4/4 if we take the top layer to represent divisions of the beat and the bottom layer to represent beats; because there would be no layer articulating downbeats and grouping the beats into measures, we wouldn’t be able to tell whether the meter was duple, triple, or quadruple. It only takes two layers to establish meter, but it takes three layers to establish a meter that may be unambiguously labeled both by its beat groupings and by how those beats are subdivided.

Conducting and Maintaining Meter

There is one pulse layer that distinguishes itself by being the one we choose to conduct or count; we will call it the tactus. We could call it the beat (the terms “tactus” and “beat” are synonyms when referring to sounding meters), but not without risking confusion later on, since “beat” is often defined differently when referring to notated meters. Musicians typically have strongly ingrained ideas about what gets the beat based on various time signatures, but there are many cases in which what is heard and felt as the tactus does not correspond to what the time signature defines as the beat. The tactus level is also subjective, not universal: there are many cases where different listeners or performers will choose different pulse layers as the tactus for the same passage of music. It is not, however, completely unpredictable. There is a well-documented tendency for listeners and performers to choose the pulse layer moving closest to 100 bpm (beats per minute) as the tactus when the fastest three layers of a meter are all moving between 30 and 240 bpm; this speed is called the natural pace. The range of speeds found in the fastest three layers of a passage are important for the natural pace to hold its predictive power. When the fastest pulse layer in a passage is at or near 100 bpm, listeners more often choose a slower-moving tactus. It is not wrong (or “unnatural”) to choose a layer other than the one closest to 100 bpm as the tactus, even when the fastest three layers are all within the 30–240 bpm range; the natural pace is just useful in predicting what layer most people will hear as the tactus for a given passage (assuming you have a good idea of the tempo in which it will be performed).

Once a meter is established, its tactus must be articulated almost constantly to remain a perceptual reality. The tactus need not be articulated continuously in any one part, and many musical textures will divide up the responsibility of articulating the tactus between multiple parts. However, if too many pulses in a row go unheard in any part—as in the case of a dramatic pause, for instance—the sense of meter will be interrupted and will once again need to be reestablished. This kind of interruption can occur after just two or three missing pulses, depending on the tempo.

In addition to pulses that go missing, new accents that contradict an established meter will also lead to that meter’s replacement unless the layers of the established meter are constantly being rearticulated. Still, established meters are not such fragile things that they can’t withstand some syncopation. It is only when syncopated accents become regular enough to establish new pulse layers that a new meter might be perceived ...