A Variety of Music Speed Types

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It seems simple enough; when music gets faster, we call it an accelerando. Orchestral musicians know they have to watch the conductor, and conductors know they have to give an increasingly faster beat to create the accelerando. As far as it goes, this is all correct. But increasing the beat is not the only way composers and performers create increases in speed. It is the only way they create increases in tempo. But are they the same?

Consider the beginning of the fourth movement of Dvorak’s symphony no. 9, “From the New World.”

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The tempo is constant throughout, but the speed of the music clearly increases. This increase in speed is achieved entirely through rhythmic means. The motif of an ascending semi-tone (half step) is written with a longer duration on the first note of the interval, and is followed initially by two beats of rest, thereby spacing out the second occurrence from the first. After one repetition, the duration of the first note is reduced by half a beat, and the rest between occurrences is also reduced, from two beats to just half of one beat. By the fourth measure, the first note of the interval is down to only half a beat, and the rest in between is down to one-quarter of a beat. In each case, the unit of the beat is the quarter note. By composing the rhythms this way, Dvorak has written an accelerando without increasing the tempo; therefore, accelerando and increase in tempo are not synonymous.

Apart from changes in speed, rhythm is also frequently used to present the same melodic material at the same tempo but at different speeds. Brahms was particularly fond of doing this. For example, in the fourth movement of the A Major Piano Quartet.27, measure 467, the accented material that is heard throughout the movement is played in the violin and viola in its original form, while in the piano, the pianist’s left hand plays it half as fast due to elongation, but at the same tempo.

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From these examples, we can see that relying on tempo to define how fast or slow a piece of music goes is insufficient. Music with an extremely slow tempo may go quite quickly, as with the fast moving string parts playing sixteenth notes that accompany the slow moving  theme written mainly in whole note and half notes in alla breve in the final section of Wagner’s Prelude to Tannhauser. To accurately define the speed of music, we must consider both tempo and rhythm. Music that is perceived as fast has notes that move at a relatively high rate per second, regardless of how they are notated. This can be achieve with a combination of a fast tempo and note duration equal to or divisions of the beat, or with a slow tempo and note durations that are further divisions of the beat. Conversely, music that is perceived as slow can be achieved with a combination of a slow tempo and note durations equal to or elongations of the beat, or with a fast tempo and note durations that are further elongations of the beat.

In either of these cases, a rhythmic hierarchy is likely to be established. Music written primarily with divisions of the beat is likely to be perceived with a beat unit of a longer duration in order to keep the tempo manageably slow, while music that is written primarily with elongations of the beat is likely to be perceived with a beat unit of shorter durations, what musicians call subdivisions, in order to keep the tempo manageably fast, because both excessively fast and excessively slow tempos are difficult to comprehend and cognitively maintain. This is why designating a unit of beat is so important. It makes a tremendous difference if the beat is equal to a half note or a quarter note or an eighth note. The difference from one to the other in each case is halving the tempo.

From the listener’s perspective, the tempo at which music is moving is going to depend to Picture1a large degree on what beat unit he or she perceives, while we could expect the speed of the music, because it is measured in time and not beats, will be more reliable and consistent from on listener to another. An example of this is the first movement of Beethoven’s fifth symphony. A person (or conductor) who perceives the beat in quarter notes is going to find the music has a fast tempo; it has both a fast (quarter note) beat, and mostly durations that are divisions of that already fast tempo beat. A listener (or conductor) who perceives the beat in half notes is going to find the music has a moderate tempo and a fast speed; it has a moderate (half note) tempo, and mostly durations that are further divisions of that beat. The speed is still fast because the notes are moving at the same rate per second, and are divisions of divisions of the  half note beat.While rare in practice, it is even possible to perceive the music with a whole note beat, giving the music a slow tempo but still fast speed. Listening to, conducting, or performing music with a slow tempo beat is valuable because it reveals rhythmic structure at a deeper level, focusing our perceived organization of the music over longer time spans compared to zeroing in on beats that occur over shorter time spans of music. For musicians, it is useful to be flexible in this matter so that listening comprehension is enhanced, and difficulties adjusting to conductors who use a different tempo beat than the musician is used to are minimized.

I mentioned earlier that tempo is measured in beats, while speed is measured in time. This statement needs some tightening up, because tempo itself is a kind of speed, and tempo is typically defined in units of beats per minute, as revealed in tempo markings and metronome usage. The distinction between beat and speed is necessary, as we have seen, because they can go in opposite directions. Even so, ultimately both are defined by time. This being so, the speed at which music moves must be defined entirely by time, and specifically by the number of musical events, whether they are beats, elongations of the beat, or divisions of the beat, that occur per unit of time. It is useful to define beats in units of occurrences per minute, because that is the established convention, and because beats are slow enough, even at fast tempos, to be so defined. Divisions of the beat, on the other hand, are more conveniently defined in units of occurrences per second. This is useful because knowing only the tempo does not give an accurate description of the speed.

 

Hierarchy in Rhythmic Structure: Meter, Beat and Duration

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For many years, I have been bothered by the usual definition of a time signature. In common time, it is often taught that the top number refers to the number of beats in each measure, and the bottom number refers to the kind of note that gets one beat. So a time signature of four-four supposedly means that there are four beats in each measure, and that a quarter (4th) note gets one beat. But this explanation simply isn’t true all of the time. For example, take the opening of Dvorak’s Symphony No. 9 (From the New World).

Opening of Dvorak's Symphony No. 9 in E minor

Opening of Dvorak’s Symphony No. 9 in E minor

The time signature in this example, by the just stated reasoning, ought to be telling us that there are two beats in each measure and that a quarter note gets one beat. Although a case can be made for this from the notation, no one hears the music this way, and conductors don’t conduct it this way. We hear, and they conduct four beats to the measure, with the eighth note as the unit of measurement. Time signatures do not necessarily correspond to what he music actually sounds like, and are to some extent arbitrary. We don’t really hear a time signature like we hear notes or silences during rests.

Time signatures, like beats, have no sound, and so cannot be heard. They can only be perceived out of the structural organization we make from the sounds we do hear. The reoccurrences of salient notes evenly spaced over time provides the information we need to ascertain a beat from the music to which we listen. When we are listening to music, we are in fact hearing several beats at once. We are hearing the “conductor’s” beat, called the ictus, and we are also hearing the beat of evenly spaced strong beats that begin each metrical unit, the evenly spaced strong beats that begin every other metrical unit, which gives us the sense of strong measure-weak measure, and evenly spaced strong beats that begin consecutive phrases, which may be four or eight metrical units apart. In the other directions, we are at the same time hearing beats that are divisions of the ictus, such as the sixteenth note beat in the example above. These several beats are understood in a hierarchy of beats. The first beat of a metrical unit is understood as a strong beat because it is strong at all levels simultaneously. The third beat of a measure in common time is heard as stronger than the second, because the former is a strong beat on more levels. This principle can be seen in the following figure, where the dots under the music represent beats at the levels of eighth, quarter, half, and whole note.

The metrical hierarchy demonstrated

The metrical hierarchy demonstrated

In the process of a listener making sense of this melody, all four of the beat levels shown are present in his or her perception of the music, yet only one of them will be adapted as the ictus. It may well be that the preferred ictus in this case will be the half note level, in spite of the time signature that suggests otherwise. The feeling of syncopation in the tied quarter notes is easily overlooked if the quarter note is taken as the ictus. Teachers and students should latch on to the ictus that is most naturally perceived from listening.

Durations placed onto the grid of this hierarchy create patterns that we commonly refer to as rhythm. When a rhythm rubs up “against the grain” of the beat hierarchy, things like elisions and syncopations result, creating rhythmic tension and capturing the listener’s imagination. I have found that while my brain has been processing this hierarchy all along, when I consciously attend to it while listening or performing music, my enjoyment and interest in the music increases. I also have found music easier to perform and understand when I realize that music can be understood with any of several incti. Try shifting form quarter note beats, to half note beats, to eighth note beats to whole note beats while listening to music, and have your students shift movements to the beat in this way. It is fun and ear-opening all at once.

Rhythmic Structure of Music: It’s More Than Syllable and Counting Systems

2011Symposium_1_2I have observed among students and colleagues alike that there is a good deal of confusion when it comes to rhythm in music. Students are frequently confused about what rhythm is, and teachers are often confused about how to teach it. From the teacher’s point of view, much of the confusion seems to come from how we were taught rhythm. As a child, I was taught to count and tap my foot. As an undergraduate, I still counted and tapped my foot in ensembles and applied music lessons, but Kodaly specialists taught me to use rhythm syllables, and Dr. Gordon taught me to use his rhythm syllables. I have discussed the difference between these systems in a separate post. While it is no doubt important for music teachers to be trained in all of these systems, they all tend to impart an incomplete sense of what rhythm really is, especially if they are not implemented with skill. Today I will discuss what rhythm is and what aspects of rhythm the counting and syllables systems overlook.

Grouping

There are essentially two components to rhythmic structure in music. One is grouping, and the other is meter. When a person perceives a sequence of sounds as a motive, theme, phrase, theme-group or section, that person is grouping those sounds together, sensing them as a single unit. Rhythmic factors determine which notes belong together and which ones don’t. A relatively long note among shorter ones tells a person that the end of a group has arrived, and a new one is about to begin. Changes in articulation, or recurring patterns can also demarcate groups. While pitch factors may also influence how sequences of sounds are grouped, grouping is understood as a function of time, and is therefore part of rhythmic structure, that is, the part of music that is perceived over time. Groups occupy a given time-span, such as a measure, two measures, four measures, and so forth, and are heard hierarchically; that is, two one measure groups are nested into one two measure group, and two two measure groups are nested into one four measure phrase. It is from sensing these hierarchical time units that a person perceives symmetry, and antecedent and consequent phrases; and when the symmetry is disrupted by an elision, without the listener having been “counting beats,” he or she intuitively knows that the established length of groups music and the brainhas been shortened, and excitement builds in the music as a result.

Meter

The other component to rhythmic structure in music is meter. Meter is the means by which a person marks off music into equal time-spans. Beats that are equidistant from one another are the units of measurement, and are combined into recurring patterns characterized by a relatively strong beat followed by some number of weaker beats before the next strong beat occurs. The strong beats recur at regular time intervals, and by this recurrence the meter is established. For example, a minuet or scherzo is in triple meter, because there are recurring patterns of one strong beat followed by two weaker beats, making three beats in all. Meter and grouping interact in the sense that at certain critical points in the music, both the group and the metrical unit begin or end at the same time, as at the beginning or ending of a theme or section.

Duration

Within both groups and meters there are any number of notes, each of which has a specific duration. These durations are what are most commonly thought of as rhythm, though in fact as we have seen they are actually contributors to grouping and meter. Durations help define groups and can also define strong beats, and so are obviously critical to both grouping and meter; however, if only durations are considered apart from grouping and metrical contexts, most of the significance of the durations to the music goes unnoticed. It is even possible to recite rhythm syllables outside the context of beat, and find oneself even further removed from the musicality of the rhythms being chanted. Try this experiment. Chant out loud ti ti ti tow. What meter does this rhythm indicate to you? Did the rhythm start on the beat or on the half-beat? Did it start at the beginning of a metrical unit or after a rest? If it started after a rest, what was the duration of the rest? We can begin to see from these questions that rhythm syllables alone can be as misleading as they are helpful. A beat and meter must be established so that musical context can be understood. When students are taught durations only, without meter or grouping, they cannot possibly make anything musical out of what they are learning. What’s more, retaining what they are chanting becomes difficult because the brain has not been given anything to attach it to; it is like learning a new word without ever learning what the word means. Try memorizing a few words in a language you don’t understand. It’s next to impossible. So when you teach rhythm, teach the whole structure–yes, durations, but also the meter and durations made from those durations.