Can rhythms be fast?

Version 2Tempo is a deceptively tricky musical concept. On the face of it, it seems straight forward enough. Tempo is measured as the number of beats occurring in one minute given a steady rate, and that beat can be equal to any note duration, such as eighth, quarter, half, or whole note. There are tempo markings that broadly indicate that the tempo should be lively, very fast, moderately fast, moderate, slow, or very slow. There are the more precise metronome markings that indicate a precise number of beats per minute, and the note value that will be used as the unit of measurement. All of this makes tempo uncomplicated and clear to performers, because as the musician plays or sings, they are forming rhythms over a concrete pace of pulses that coincides with the instruction in the printed score or, as in the case of dance music, of the standard convention.

Tempo for the listener is more complicated. The listener does not necessarily know what the unit of pulse is, and so must match a pulse rate with the rhythm patterns they are perceiving. So while the performer may be playing a passage of 32nd notes at a slow 8th note tempo (a common situation in classical slow concerto or sonata movements), those 32nd notes are going by rapidly for the listener, who might organize the music into beats of 16th notes, making the tempo faster than for the performer, who is measuring those same 32nd notes in slowly moving 8th notes. In this case, it would be tempting to say that the tempo (measured in 8th notes) is slow, while the rhythm (as perceived by the listener) is fast. But the difference is not between tempo and rhythm, but instead between the unit used to measure (and perceive) rhythm. The same music can be said to be fast or slow depending on what note value is being used as the unit of the pulse.

A good example of this is the opening of the 4th movement of Mozart’s Symphony no. 41 in C major (Jupiter). The tempo marking is motto allegro, and the pulse is generally around 120 beats per minute. Yet the first four measures are whole notes, and so one note progresses to the next slowly, even as one perceives the pulse to be fast, in contrast to the accompanying eighth notes, which are flying four times faster than the fast pulse, almost to fast to track. Yet if we listen to the same music and track two measures as one beat, though many notes pass by, the tempo now seems extremely slow. It is all in what is perceived as the unit of pulse.

A second factor in the perception of tempo is meter. Meter is part of the rhythmic structure of music, and influences how listeners perceive the unit of pulse. In the Mozart example just cited, the tempo is only perceived as fast if the meter is perceived as alla breve. If the meter were perceived as two or four whole notes per measure, then the tempo is perceived as Andante at most. Meter defines how the listener groups note durations into patterns that can be divided and subdivided into equal parts. There are times when musicians will use a faster, subdivided tempo to improve accuracy, while they intend the audience to perceive a slower, unsubdivided tempo. The introduction to Dvorak’s symphony no. 9 (From the New World) comes to mind. Notice how the conductor conducts eighth notes an an Allegro tempo, while the music, when listen to without following the conductor, is perceived as being Adagio, as Dvorak intended.

I began by asking the question, “can rhythms be fast?” We are now in a position to answer that question by saying no, it cannot. The reason is that tempo is a measurement of degrees of fastness measured in beats per minute, whereas rhythms are a relationship between a beat and a duration which is shorter, equal to, or longer than one beat. Rhythms as they are perceived by a listener are not individual notes, but patterns of note durations perceived as patterns by their relationship to a beat, regardless of tempo. In other words, the rhythm pattern of one quarter note, two eighth notes, two eighth notes again, and  one more quarter note will be heard as such at any tempo as long as the quarter note is used as the unit of pulse. The notes can be made faster by increasing the tempo. The first sound is equal to a beat, the next four sounds are divisions of the beat into two equal parts, and the last sound is again equal to a beat. We cannot say the rhythm is faster or slower, because the fastness or slowness is entirely dependent on the tempo, the speed of the beats, not the durations, which set the interval of time from the end of one note to the beginning of the next.

While it is true that we arrive at the next note sooner if the last note was a sixteenth note than if it were a quarter note, the reason we arrive sooner is a shorter note duration, not a faster tempo. The tempo, which is the measurement of fastness, has not increased, the durations of notes, the measure of rhythm, has decreased. There is more activity within the beat divided into four equal parts than within the beat divided into two equal parts, but that is not an indicator of faster, of tempo, but of duration, of rhythm. Fast does not exist apart from a reference to pulse. Fast is a relative concept that is not dependent on duration, but on pulse. A flourish of 32nd notes is a group of very short durations, not very fast notes. Notes are not fast or slow apart from the pulse to which they are sounded, only the pulse itself can be considered fast or slow.

The Fallacy of Compound Meters

2011 Symposium2

One of the most baffling concepts in music is the idea that some meters are compound while others are simple. Something that is compound is made up of two or more parts each of which is itself a complete entity. In language, a word like lifetime is a compound word because it is a single word with a meaning but made up of two words, life and time, that each have a separate meaning.There are also compound sentences, which are sentences made up of two or more clauses, each of which has a distinct meaning, connected by a conjunction such as and or but. For example, the sentence “apple trees bear fruit, but maple trees do not bear fruit” is a compound sentence.

In music, six-eight meter is considered compound, whereas two-four meter is considered simple or not compound. If this is so, then we would expect to find two or more distinct patterns of strong and week beats joined together in six-eight but not in two-four. The problem is, this simply isn’t the case. Either meter could be considered simple or compound, depending on how one defines the elements that are or are not present. In six-eight meter, there are both eighth note beats and dotted half note beats occurring simultaneously; two dotted quarter note beats per measure, and three eighth note beats per dotted quarter. With these two elements joined together, this could qualify six-eight time as being compound. But in two-four meter, there are eighth note beats and quarter note beats occurring simultaneously; two quarter note beats per measure, and two eighth note beats per quarter note–so why isn’t that considered compound? In music, rhythmic and grouping structure can be perceived at any note value level. There are eighth note, quarter note, half note, and even whole note beats perceived by both performers and listeners, and theses beats are always present simultaneously, even in so-called “simple” meters.

The standard explanation for compound meter really has nothing at all to do with the concept of compound. That explanation is that when a beat is divided into three equal parts, the meter is compound, and when it is divided into two equal parts, then it is simple. While this agrees with the designations of six-eight as compound and two-four as simple, there is nothing there that is truly compound. With this definition, there are not recite-16rpklktwo or more elements joined together. Whatever six-eight time is, three divisions of each beat cannot qualify it as compound. It would be more palatable if the word complex were used instead of compound. Researchers, including Temperley and Lerdahl have found that people prefer duple meter to triple meter, so it may be that in some way a beat divided into three equal parts is more complex to our human minds, but that does not make it compound.

If all of this is so, then why is six-eight meter called compound? What are the two elements joined together to warrant that designation? Many students and even some teachers miss this because they are devoted to the idea that the bottom number in a meter signature indicates the kind of beat that gets one beat; however this is not always true, and is the key to understanding what compound meter really is. In all of the compound meters, the bottom number in the meter signature is never the number of beats in each measure. The bottom number indicates one type of note, but performers and listeners alike treat another kind of note as the pulse or ictus as it is often called. In six-eight time, the bottom number indicates an eighth note, but the kind of note getting one note is a dotted quarter note. Here we finally have our two elements: the note value shown in the bottom number of the meter signature, and the note value that is actually the beat. In meters that are not compound, the bottom number in the meter signature is always the same as the kind of note that gets one beat. Because the bottom number indication and the ictus are the same, there are not two elements joined together, but one shared by both the meter signature and the ictus.

With this problem solved, we now move on to the other area of confusion concerning meter designations. What determines if a meter is duple or triple? Traditionally, the number of beats in a measure was the determining factor. Two beats per measure are considered duple meter, and three beats per measure are considered triple. Some add to this quadruple meter, which is four beats per measure, while others hold that four beats per measure is to the listener indistinguishable from two beats per measure, and so is also considered duple. Then there are others, most notably Gordon, who have argued that the number of beats in each measure has nothing to do with determining a meter to be duple or triple, but rather it is the number of divisions within each beat. By this reasoning, six-eight time is not compound duple, but usual triple, while two-four meter remains duple, though because the quarter note beats are divided into two eighth notes, not because there are two beats in each measure.

In the end, it all comes down to grouping. Meter, by definition, is a pattern of strong and weak beats. The key to perceiving any meter is into what groups do our minds organize the music we have just heard? Do we hear patterns in which a strong beat occurs every three beats or every four beats? If number of beats per measure is the deciding factor, then we must be hearing only the first beat of each measure as a strong beat, and all other beats within the measure as weak. Because this is not always the case, it must be admitted that number of beats per measure is not always an indicator of meter. Although Richard Strauss’ Til Eulenspiegel’s Merry Pranks is written in six-eight time, which should be compound duple meter, anyone is hard pressed hear those opening bars in groups of two beats while overlooking the rapidly moving groups of threes played by the horn. Nor do most hear the Andante Cantabile in the Fifth Symphony of Tchaikovsky and perceive duple or quadruple meter. That glorious music can only be heard in metrical groups of three.

We now understand the meaning of the terms compound and simple in regard to musical meter, and we have also seen that these designations can be misleading or inaccurate, particularly in cases where the meter is designated as compound. Relying on the number of beat divisions instead of the number of beats in a measure is more accurate. There are times when the two will agree, and those times will invariably be when the perceived ictus is found to equal one measure, as with a waltz or very quick march. But this is not always the case, and so cannot be a reliable method. Because of this, the terms compound and simple do not add much to most people’s understanding of music they hear, and more often unnecessarily confuses them. Because they are often used terms, it is necessary to understand them, but also to understand their limitations. Always let your performing and listening be guided by what you audiate, and remember that the notation is the composer’s best effort to pass on to others what he or she audiated when creating the music. Theory is inferred from practice and not the other way around.

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.