What Are The Elements of Music?

Version 2For as long as any of you reading this have been alive, music has been taught in the context of so-called musical elements. Though one can find variations on just what is included in a list of musical elements, most will agree that it includes rhythm, dynamics, melody, harmony, timbre, texture, and form. Some of those elements have sub-elements within them. Rhythm, for example, has meter and beat as a sub-elements, because meter consists of groups of beats, each group commencing with a relatively strong beat, and beats are the result of patterns of sound durations. There are also categories of elements. Dynamics and timbre, for example are expressive elements, while texture and form are formal elements.

All of this is well and good, until someone starts teaching each element as a discreet entity. While it is true that rhythm without pitch can be found in percussion music of many cultures, it is virtually impossible to find any music in the world that does not contain at least two elements simultaneously. That is, even with a solo West African drummer, one can easily, in addition to the rhythm being played, perceive dynamics, timbre, form , and when more than one drummer is involved, texture. While it is possible to contrive a performance where only rhythm is present, such a performance will invariably be sterile, dull, and unexpressive, all of which completely misses the point of performing music, which after all is to express something. It is inhuman to stoically and artificially stifle all expressive elements for the sake of teaching one of them in isolation. What’s more, I dare say only a computer could be taught to play the sort of sterilized music I have just described without inadvertently slipping in some expressive hint or other.

So while it is useful and essential to understand each element, and to be able to define and recognize each one while listening to music, and manipulate each element while performing or composing music, students must also progress beyond this rudimentary knowledge to being able to see that music exists as an interaction between elements, and in fact cannot exist with only one or the other, just as the human body needs all of its parts to function as a human body, music needs all elements to come off sounding like music.

Now that we understand that musical elements must be combined and must interact in order for music to result, we can now put forth an explanation of just what each of these interdependent elements are. Rhythm is patterns of sound durations. A single note cannot in and of itself be a rhythm; it is only a duration. This must be so because rhythm must have beat and tempo, and neither is discernible from a single note. When there are two or more durations of sound, then a beat and tempo can be perceived and a rhythm can be said to be present. It is unlikely that meter will be ascertainable after only two durations, because meter are patterns of durations that form patterns of strong and weak beats. The listener must hear enough patterns of durations to establish the occurrences of relatively strong beats amid a recurring interval of beats. For example, while we can perceive a tempo and a rhythm from the first three notes of Beethoven’s fifth symphony, we cannot at that point determine the meter. In fact, it is not until two or so bars after the second fermata that the listener can settle into an understanding of the meter as regular duple. I hope that by now you can see how rhythm, beat, duration and meter are all intertwined together, inseparable into discreet elements.

The situation for melody is quite similar. If meter is a by-product of rhythm, then melody is a by-product of pitch and in most cases combined with rhythm. Just as rhythm cannot exist from a single duration, melody cannot exist from a single pitch. A single pitch is only a tone. Tones derive their meaning and thus their melodic property from how they relate to one another. Once a second tone is sounded, we have a relationship between two notes, but do we have a melody? It’s at this point that defining melody becomes tricky. Are two pitches enough to be considered a melody? After all, there’s not enough there to establish tonality, to make a phrase, or to convey a meter. With all of these other elements missing, is it correct to maintain that two tones can make a melody? I would argue that no, this cannot be a melody, and for the very reasons I have just stated. A melody must have meter, tonality, and phrase. It must have these things because our brains require them in order to make sense of what we hear; in order to comprehend those sounds as music. We must be able to ascribe to the patterns of sounds a structure that includes rhythm and tonality, or else it cannot make sense to us, and will likely not sound melodious, which is the correct way of saying melody-like. At this point I must quickly add that I am speaking here of tonal music. Whether or not music with pitches can ever be truly atonal, and whether so-called atonal melodies such as 12-tone rows are truly melodies are good questions which I will blatantly avoid addressing here. Suffice it to say that melody are patterns of notes from which the human brain can extract patterns of durations, pitches, and strong and weak beats.

The third and final major element to be discussed here is harmony. Harmony is also Music-Feelings-300x197dependent on relationships between notes. It is incorrect to define harmony as tones heard simultaneously. If this were so, then arpeggiated passages such as Bach’s Prelude 1 in C major from the first volume of The Well Tempered Clavier would be said to be without harmony, which would be absurd. As we listen to music, we remember and retain harmonically important tones, and relate them to subsequent tones related to the former by virtue of being part of the same chord. To those who would distinguish between harmony and implied harmony, I would say that is an accurate technical distinction, the former relying on all tones being physically present, the latter relying on tones being audiated while other tones are physically present. In the mind, all tones are present, either physically or cognitively, so in the end harmony exists in either case. So harmony is the combining of tones into combinations that are perceivable as functional harmonies. Those combinations are arranged syntactically into harmonic progressions that we recognize and understand by virtue of familiarity gained from experience listening to tonal music. Again, this definition suits tonal music and not atonal music, though there is a compelling argument to be made for atonal harmony, but not harmonic progressions.

The remaining elements are easily explained. Dynamics is the degree of softness or loudness sounds are heard. Dynamics are dependent on durations and pitch, for without either their is nothing from which to judge a degree of loudness or softness. Timbre is the distinctive tone of a given instrument or group of instruments. Every musical sound has a timbre because it must be produced by a sound source, and every sound source has a characteristic tone quality. Composers manipulate dynamics and timbre to infuse their music with expressiveness. Texture is related to timbre in that discreet voices or layers of musical lines can be assigned to any instrument or group of instrument, producing the desired timbre. When the texture is monophonic, the line may be played by a single instrument or group of like instruments, or by a group of various instruments. In polyphonic or homophonic textures, all lines may be played by multiple instances of the same instrument (all violins or all clarinets, for example), or each line may be played by different instruments. Dynamics are used to create expressive gestures such as crescendos and diminuendos, and to bring out certain lines, perhaps a melody and counter-melody combination, while relegating to the background a harmony part.

Musical elements are best understood in relationships to each other, not as discrete entities. While explanations of each are important, those explanations must highlight the interdependence of the elements. As musics of different cultures are studied, students will find music that has no melody, or has no harmony, yet there will still be multiple elements interacting to create the music to which they are listening.

What Do We Want Children To Be Able To Do In Order To Sing Well?

Version 2Good teaching is largely about stating clear objectives, and then instructing students in how to achieve those objectives. When it comes to singing, often times music educators frame the task in terms of singing on pitch, using a head voice, and maintaining a steady beat. Clearly these items are important to good singing, but as objectives, they do not get at the heart of the matter, which is what do singers do to stay on pitch, stay on beat, and maintain a head voice? If we attempt to get at pitch by matching pitches to a reference source such as a piano or our own voices, we are not teaching accurate singing, we are teaching pitch matching, which requires a reference tone and avoids producing accurate pitches independently. Likewise, if we attempt to get at steady beat by following a conductor, drum, or other reference, we are again teaching beat matching , which requires a reference beat, and avoiding teaching accurate singing. To truly teach students to sing accurately, we must develop what Kodaly specialists call “inner hearing” and what Gordon called “audiation.” Both concepts, though not identical, include hearing aspects of music in the imagination that cannot physically be heard.

The process of developing audiation/inner hearing (which from here on I will simply refer to as audiation) begins with rote learning, progresses through verbally associating tones and rhythms to verbal labels, and associating the connected tones or rhythms with notation. This means that steady beat can be performed for the students to echo at the rote learning stage, but not with the students, and patterns of tones can be performed for the students to echo at the rote learning stage, but not with the students. When students are echoing in groups, they must reproduce what you have performed without using you as a reference, but they still use each other as a reference. Because of this, it is important for students to also echo you individually once they have learned patterns from rote.

If we take a closer look at this learning process, we must examine how students will know if they have echoed the teacher’s models accurately. This comes down to the abilities to make tonal sense of what has just been heard, and to make same/different discriminations. In the first instance, the child must be able to perceive harmonic functions of tones, especially tonic and dominant, must be able to cognitively organize groups of tones into familiar patterns such as chords, familiar motifs or phrases, and so forth, and must be able to make same/different discriminations between what the child has heard the teacher do, and what the child has done in an attempt to echo. The child must ask him or herself, “is what I just did the same as what the teacher did or was it different? If it was different, how and where was it different? What was my error? How can I make it the same next time?” When I am teaching phrases or patterns to the group at the rote learning stage, I will repeat the phrase or pattern several times if noticeable inaccuracies occur. The student know that I have determined that their echo is different from my source and so they listen critically and try to correct their error. Even in a group, they are usually able to detect the difference and improve their accuracy without my telling them what the error was. This ability to self-correct is evidence that learning is taking place. If I were to tell them every error and “fix” them by rote repetition, that depth of learning would not occur.

The same is true of steady beat. “Was the tempo the same throughout, or did you get faster or slower?” Changing tempo can often be corrected simply by having the students tap the pulse on their knees as they sing. It must be said that simply having students tap a steady beat in the absence of music from which the beat can be extrapolated is of extremely limited value. Rhythm is a complex concept. It is a blending of tempo, duration, and meter. Steady beat is extremely difficult to maintain when meter is not

score

The metrical hierarchy demonstrated

being considered. Patterns of durations, which is what comprises rhythms, are only made meaningful when they are grouped into patterns of strong and weak beats from which we perceive meter. Meter gives us frames of reference that make apparent levels of rhythmic structure and clarify what the beat unit of each level is. Music progresses along beats that can be measures or single note durations. Without these sign posts resulting from the combination of levels, a listener or performer can become lost in an ongoing sequence of indistinguishable beats. It’s as if every person we met had an identical appearance, like twins. We would quickly loose the ability to tell one person from another. So it is with beats. One beat is set apart from others by where it falls within the metrical pattern.

What, then are the implications for teaching singing? Pitch matching must be replaced by pitch echoing within a tonal context, and playing with a provided beat must be replaced by playing with one’s own audiated beat and that beat within a metrical structure. For pitches, it is helpful to establish a tonality before asking the student to sing. This can involve singing or playing for the student a I-V-I progression, either sung in arpeggiated form, or played as chords on a keyboard. After the tonality is established in this way, the student will have a tonal context in which to place the tones he or she sings. For example, if the child is to sing the folksong “Rocky Mountain,” then he or she will begin knowing that the first note is the tonic note, and that the first phrase is entirely comprised of the tonic triad. This fits easily into the I-V-I preparation, and facilitates singing all of the tones in tune, avoiding matching pitches with an external reference, and making it unnecessary to attempt to sing intervallic ally from one tone to the next. Being able to keep the tonality firmly in mind while singing guides the singer in staying on pitch, and also makes more apparent deviations, because they are not gradual distortions of intervals, but dissonances to the tonal environment active in the singer’s mind. Strategies such as interrupting singing to have the student jump to the tonic note, or to identify occurrences of the tonic note while singing help.

For steady beat, the procedure is much the same. First, establish a meter by chanting a rhythm pattern that includes ictus value notes, and next-level beat divisions; that is, that contains, for example, quarter notes and pairs of eighth notes. This rhythm would establish the meter as duple, because the ictus is divided into two sounds. After establishing this, the student will then continue to divide each beat into two parts. Maintaining that meter will facilitate maintaining the steady beat. So when it comes down to it, teaching students to sing accurately is more a matter of teaching inner hearing/audiation, than it is about teaching imitation or matching. It is about building musicianship to the point where the student organizes musical sounds into patterns and structures that demand and facilitate accurate performance to maintain.

 

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.

Musical Meter Is Everywhere

2011 Symposium2

Over the last few years, I’ve noticed that meter is a concept that many of my students really don’t understand. I discovered this because of improved assessment techniques, so I suspect that this has been the case for some time. As long as I was assessing understanding of meter with head knowledge such as asking what the numbers in a time signature mean, they appeared to grasp the concept perfectly. But when I started asking them how many beats were in the pattern of strong and weak beats in music they were listening to, everything changed. Some confused notes for beats, some didn’t hear any beats stronger than others, and only about one  third could correctly perceive a pattern of strong-weak or strong weak weak. As a result of this discovery, I changed the way I teach meter. I started using movement, first prescribed to the meter, then created by the students to a disclosed meter, and finally created by the students to a meter they had to discover. I encouraged them to try different patterns until they found one that felt right in their body. I also stopped teaching time signatures until they could do all of this. Sound before sight, right? Once students have meter in their bodies, the numbers in a time signature make real sense. The big motion “heavy” motion is the beginning of the pattern. The small, lighter motions are the rest of the beats in the pattern. The number of lighter motions plus the one big motion equals the number on the top of the time signature. The number on the bottom is the kind of note they are moving to with their lighter motions.

That made meter more meaningful. Next, I wanted to connect musical meter to other things my students experience or perceive every day, but not necessarily in music. What other things that they use or hear have strong an weak beats? Though digital and computer clocks have largely replaced tic-toc clocks, most of my students still know what the latter are. Just the fact that we give different names to the two clicks suggests that they are different, and we naturally attribute more strength to the tic than to the toc. When we start a pendulum in motion, we have to exert a force onto it to produce the first tic, but it returns on the toc  to its starting position without any effort on our part at all. Many young children are pushed on the swings by a parent. The parent pushes as the child swings away, but the swing and child return to the parent with no effort from the parent–strong going out, weak coming back.

Language is loaded with meter. Orff teachers use this property of language all the time to teach rhythms. Look up any word in a dictionary, and you will find that one syllable has an accent mark on it. That is the strong syllable when the word is pronounced correctly. When the strong syllable is misplaced elsewhere in the word, the word sounds silly and wrong. The word “apple” must have a strong first syllable and a weak second syllable. The word apple is a great illustration of duple meter. The word “pineapple” also must have a strong first syllable, but that first syllable is followed by two weak ones, making the word a great illustration of triple meter. If I’m working on duple meter with my students, I might expand that out with a sentence using the word “apple” and other duple meter words. For example, I might have the children say “apple cobbler tastes so good. I’d eat more if Mama would, let me have another plate, but she says it’s getting late.” Each phrase is chanted to the rhythm of du-de du-de du-de du. The children must audiate the micro beat on the “du” at the end of each phrase.

With older children, I like to use rap music to teach what duple meter is (or quadruple meter for you non-Gordonites). Most rap phrases are four beats long and end with a one-beat rest, so patterns of strong-weak-weak-weak are easily perceived. I italicized the third “weak” because it is at least secondarily strong compared to the beats that surround it, and often common time and 2-4 time are aurally indistinguishable. Nearly any clean rap lyric works well for this. The one on my mind now is Wiz Khalifa’s rap section to the song “See You Again.”

All the planes we flew                                                                                                                         Good things we’ve been thorough                                                                                                   That I’ll be standing right here talking to you                                                                            ‘Bout another path I know we loved to hit the road and laugh                                                  But something told me that it wouldn’t last                                                                                Had to switch up                                                                                                                                 Look at things different, see the bigger picture                                                                        Those were the days                                                                                                                           Hard work forever pays Now I see you in a better place

From the rap song (or part of a song) it is helpful to extract the rhythm from the words. Depending on your class, this can either come off really silly or really fun. I start by chanting the rhythm of the rap on a neutral syllable to the class. My students are used to me doing silly things in front of them, so they either enjoy the performance, or humor me and listen anyway. Often I will draw them in with allowing them to move and/or make a “beat” (rhythm) to accompany me, and gradually students begin to join in chanting the rhythm. With the rhythm the same as the rap, if the rap had meter, the chant must have the same rhythm. From this I make the point that music without words still has meter, just as it has pitch, rhythm, tempo, and other musical elements.

Popular music is a good place to begin teaching meter, because the rhythm section (drums, bass) demarcate the metrical patterns so clearly in their repetition of a rhythm pattern and also with the use of cymbal and bass drum to mark the strongest beats, usually at the beginning of phrases or sections. There is a natural progression of less and less of this as one moves from rap to rock, rock to pop, pop to jazz, and jazz to classical. If I follow this progression in the music I present to my class for listening, then gradually they become more and more accomplished at continuing to perceive the meter, as it becomes less and less obvious. By the time I get to classical, instead of complaining that classical music has no beat, they understand that its beat is simply more subtle, and it is more up to them to catch the beat and audiate it as they listen.

What Do Music Notes Mean?

2011 Symposium2

I searched the title of this post today, and the results were any number of explanations of how to read music; what the note names were, the different kinds of notes, the treble and bass clefs, and so forth. But is this really what those notes on a page mean? Not at all. As you read these words on your phone or computer, what do the letters mean? Would you say that in the word “ice cream,” the individual letters mean anything? Of course not. The letters mean nothing unless they are in a string with other letters so that the string of letters spells a word. It is the word that has meaning, not the letters from which the word is formed. It is the same with music Each note has a sound of its own, just as letters have sounds of their own, but an isolated note means nothing. It must be part of a group of notes which one can understand as expressing some human quality that the creator of that group of notes intended to express. Leonard Bernstein, in his Young People’s Concert “What Does Music Mean,” said  “if I play a note, one note all alone means nothing. It’s just a plain old F sharp or a B flat.

If a person knows that a particular note on a musical staff is g, or a, b-flat, or whatever, then good for him or her, but that knowledge alone, or even in combination with hearing or performing that one note, won’t result in an expressive musical experience. It will result in a pitched sound being heard. Music must be a musical creator’s  expression of something. The creator can be a composer, improvisor, or sage passing along an oral tradition in song. One note all by itself cannot possibly be so expressive. People innately understand music by grouping perceived sounds into rhythmic or melodic groups often called rhythms, measures, motifs, phrases, themes, and so forth. Whether it is a West African drum pattern, an Indian raga, or a marching band drum cadence, music makes sense to us when we are able to aurally organize it into groups. Music that purposefullyBernstein impedes or blocks a listener’s ability to do so is perceived as confusing or unintelligible. Listeners find it difficult to determine what such music means, because they do not have a familiar way of responding to it emotionally or kinesthetically.

There is, however, a sense in which an individual note, if it is one among other notes,  can have meaning. In Western tonal music, individual tones can have meaning according to a harmonic function. We have names for these individual notes which give us a clue as to what their function is. These names include leading tone, tonic, supertonic, dominant, subdominant, mediant, and submediant. The leading tone has meaning in that it draws us to the tonic a semi tone above. It compels us to anticipate the arrival of the tonic, and in so doing creates tension and forward motion in the music. But without other notes to establish it as the leading tone, it is powerless to do any of this. So even an individual note relies on relationships to other notes to give it meaning. So what music notes mean has nothing to do with note names or where a note happens to be placed on a musical staff; it has nothing to do with what a note is named, it has to do with what a note does. There are leading tones, dominant tones, tonic tones. There are blue notes, altered notes, dissonant notes and accented notes. These characteristics are closer to the mark; they describe what a note can mean. An altered note is one that becomes a leading tone, or dominant tone within a tonality where this ordinarily is not the case. Altered notes introduce tension because they have strong tendencies to move us toward another note, and because they are often dissonant in the current tonality. The name of a note–b-flat or f-sharp–is merely a convenience; it tells a musician which pitch ought to be played or sung. The names themselves have no meaning, only the sounds one produces by reading a particular pitch in written music.

snare drumWhat of notes that have no pitch? Do notes that are for non-pitched instruments such as a snare drum or high hat have any meaning? Yes they do. Just as pitched notes have tonal meaning, non-pitched notes have metrical meaning. Meter the ordering of beats into patterns of strong and weak beats. Like pitches, these different strengths of beats have names, like crisis and anacrusis. The note at the beginning of one of these patterns is the strongest, and the note at the end of one of these patterns is the weakest. This kind of note meaning gives a waltz its characteristic lilt, and a march its orders to step LEFT right, LEFT right. Like pitches, non-pitched notes have no meaning apart form relationships with other notes. One note cannot be perceived as strong unless it is surrounded by other notes that are less so. Conversely, one note cannot be perceived as weak unless it is preceded or followed by one that is strong. Syncopated notes, relatively long notes or loud notes, accented notes all have meaning because of the relative importance duration and articulation assign. As with pitches, rhythms have names. These names are called rhythms syllables, and include Curwin, Eastman, and Gordon rhythm syllables. These syllables, like pitch names, help identify durations and in some cases also rhythmic function, but they are not the meaning of the rhythms. The meaning, again, is in how the notes sound in relation to other notes, and in how groups of notes sound. Bernstein summed all of this up well when he said, “the meaning of music is in the music, in its melodies, and in the rhythms, and the harmonies.”

The Problem With Using Math to Teach Rhythm

2011 Symposium2

As I write this, I’m looking at a page from a popular band method book. There is one of those boxes at the top of the page that directs students’ attention to an important concept or new learning. There is a pair of eighth notes followed by an equals sign followed by a quarter note. Next to these symbols is printed, “two eight notes equal one quarter note.” We know what is meant by this; that both two eighth notes and one quarter note occupy the same duration in time. But there are important ways in which two eighth notes do not equal one quarter note. With the two eighth notes, there are two sounds made within a single beat, whereas with one quarter note, there is only one sound made within a single beat. The duration of the beats is equal, but not the notes. One is a duration equal to the length of one beat, the other is a division of that beat into two equal parts. When someone looks at two eighth notes, they do not see something that looks like one quarter note. They look different, and when a person hears two eighth notes and then one quarter note, they sound different, so how can they be equal?

For those that use Curwin/Kodaly rhythm syllables, two eighth notes have a different name than one quarter–yet another way in which they are different. Two eighth notes are called ti-ti, and one quarter note is called ta. There’s no equality in that. So two eighth notes don’t look the same as one quarter note, they don’t sound the same, and they often aren’t given the same name, so how can we expect children to understand the statement “two eight notes equal one quarter note?”

Those of us who don’t use the British nomenclature of quaver, semi-quaver, and so forth, run into another problem when trying to use math to teach rhythm. We call a note in common time with a duration of 4 beats a whole note, a note with a duration of 2 beats a half note, of one beat a quarter note, and so forth. This makes perfect sense in only one meter signature–common time. In three-four time, a half note is two thirds of a measure,  a quarter note is one third of a measure, and an eighth note is one sixth of a measure.  Whole notes completely disappear–or should we call a dotted half note a whole note in three-four time? It a pretty sloppy thing to call something a half when it’s really two thirds.

Meter isn’t supposed to be about counting and fractions, it’s about recurring patterns of Musical-Balancestrong and weak beats. Our teaching must show students how the notion indicates the beats, beat elongations (durations longer than one beat) and beat divisions (durations shorter than one beat). We don’t make the first beat of each measure stronger than the others because that’s how it’s notated, we notate it that way because that’s what we hear when we listen to or audiate that music. Math is important to music because we naturally perceive patterns of strong and weak beats, beats, divisions and elongations. It is the beats that are equal, not the configuration of notes that occur within the beats.

I like to illustrate this to my students in this way. I have four (for common time) or three (for triple meter) students come to the front of the class and stand apart, with equal distances between them. These students represent beats. I then walk from in front of one student to the next, taking one step. My single step represents a quarter note, and the students represent beats. I have a time keeper clap each time I arrive at the next student. Then I go back and walk again, this time taking two equal steps to get from one student to the next. Now my steps represent eighth notes. The time keeper will report that I still got to the next student in one clap, and that he or she clapped at the same tempo as I moved across in front of the students. The class will observe that in order to make it to the next student in the same amount of time, I had to make my smaller steps faster. The steps were half as big so I had to walk twice as fast. I then have the class do a walk around the room. When I play quarter notes, they take single big steps. When I play eighth notes, they take half-sized but twice as fast steps. They listen to me play the rhythm first, then they step it. This teaches them that the beats are equal, but not the notes, and that every beat is the same, but that some beats have divisions within it and some beats don’t.  So the next time you see or are ready to say “two eighth notes equal one quarter note,” remember, in the words of Ira Gershwin, “It ain’t necessarily so.”

A Fable from the Land of Music Notes

2011 Symposium2

Children love stories. Sometimes stories can be used to teach difficult concepts. I remember a story that a music teacher used to tell to explain dotted quarter notes, and some 58 years later, I still remember it. Here’s is another story about note values. I hope you enjoy it.

There once was a land where all who lived there were musical notes. They were not wealthy, but they had all they needed. They lived in common time, and followed all the rules of governor measure. As many are wont to do, they would at times enjoy the company of only others like themselves; quarter notes stayed together, half notes stayed in their own groups, and so forth. This pleased them for a time, but eventually they became quite board with themselves, and decided to try meeting with notes that were different from them. Quarter notes spent time with half notes, and even the sixteenth notes, though they were always in a hurry and didn’t stay anywhere very long, began to accept invitations to spend time with some eighth note acquaintances. The notes realized that they could do things and make things with notes that were different from them that they could not make with only those of their own kind.

The notes became excited about their new friends and what they could do with them. They began to become adventurous and tried new things. Then one day, a quarter note named Willy asked another quarter note whose name was Fred if he could spare him some time. His fellow quarter notes gasped at the thought. How dare Willy ask Fred to give him part of himself? What would happen to Willy? Then they were even more astonished when Willy said yes. He broke off part of himself and gave to Fred. Fred placed the part of Willy right next to him, and suddenly Fred was half of a beat longer. Meanwhile, Fred grew a funny looking curvy line out of the top of him that kind of flowed down his right side. Fred stood in front of Willy, and they were surrounded by curious quarter notes wondering what would happen. They were all delighted to learn that Willy and Fred now made a pretty cool rhythm.

A whole note who happened to be watching the whole time called allchoosing-beautiful-music the other notes around him so that he could speak to them. Whole notes often did this; they always had something wise to say because they always had so much time to think before they had to move no. “I have observed a valuable lesson from what just happened” he said. “In order for Fred to get more, Willy had to give up part of what he had. We can’t grow longer unless someone else pays the price for us by getting shorter. No one can have more unless someone else has less.” One of the whole note’s twin half note sons chimed in, “but by giving to Willy, Fred and Willy together became better.” “Very good, my half note son” replied the whole note. That is how it is sometimes. It is sometimes better to give what you can do without to someone who needs it more than you do. The result is that both are the better for it, and are connected in a new a wonderful way.

Once the notes had let this profound truth sink in, they began looking for ways to make all of them sound better by giving and receiving time from each other. Of course, it wasn’t always harmonious. Fights broke out about who got more time, and there were from time to time thieves who stole time and gave it to others or kept it for themselves. But eventually these criminals were caught when they exceeded their measure’s allotment of beats, or came up short. When this happened everyone knew there had been a theft, and the criminal was usually caught and brought to justice. In spite of this, music became ever more interesting as all kinds of combinations of note lengths began mixing with each other. Over time, the measures relaxed their laws somewhat and an occasional five or even seven beats was allowed to stand. The whole notes made sure things didn’t get too far out of hand, and they always hoped that humans would someday see what good could come of being generous and kind to others.

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.

The Truth About Meter in Music

2011Symposium_1_2I don’t think many of my students think about meter when they are listening to music. They are aware of a melody, of the tempo, of the beat and rhythms, but they are not so aware of the meter, at least not consciously. I’ve noticed that meter is not so much something that must be taught as something that students must be made aware of. Music exists rhythmically in several levels all at once. A child listening or singing a song and asked to show the beat with his or her hands may move to a quarter note, eighth note, or even sixteenth note beat without any prompting. I am often fascinated to watch my four-year-old students when I ask them to show me the beat with a patsch. Most will show me the quarter note beat, but some will intuitively patsch eighth notes. This is especially true if the song begins with eighth notes as, for example, the French folk song “Pierrot” does. If the child taps the rhythm, tapping quarter notes when they occur and eighth notes when they occur, then that is a different thing; but when the child maintains the eighth note patsch through the quarter notes, he or she is audiating the eighth note beat; what Gordon calls the micro beat.

Micro beats are divisions of the beat. Going in the other direction, their are elongations of the beat. Both of these terms assumes a single “beat” to which shorter and longer durations are compared in determining whether they are divisions or elongations; however, another way of looking at this is that there are several levels to the music. There is an eighth note level, a quarter note level, and half note, whole note (in common time), one-measure, two-measure, phrase long levels, and so forth. This view was stated in A Generative Theory of Tonal Music by Lerdahl and Jackendoff. In establishing the one-measure level, the listener intuitively perceives a recurring pattern of strong and weak beats, and assigns a metrical structure to the music based on the perceived pattern. Because much of our Western music is in duple meter, Westerners tend to have a bias toward duple meter, and will favor duple meter in the seconds it takes to establish a pattern. If duple doesn’t “fit” the listener will try another way of organizing the beats, continuing until the right match is found. When I am teaching the concept of meter to my students, I try to bring this intuitive process to the surface; instead of telling them what the meter is of the music they are singing or listening to, I have them try both duple and triplemeter signatures patterns either with conducting or chanting, and let them discover which pattern fits and which one does not. The wrong meter is usually obvious to nearly everyone, because the perception of metrical structure is, as I said, intuitive and therefore subconscious for a listener familiar with the musical genre to which he or she is listening.

Familiarity then, becomes the most important strategy for teaching meter. In other words, as students listen to more and more music of a particular idiom, they will intuitively become more and more successful in detecting the meter of music from that idiom. They can be helped with singing, chanting, playing, and movement activities, but the basic ability to perceive metrical structure is already there. This is important to keep in mind, because meter in this context is natural and self-evident through the music. Meter should never be an unnatural concept that is taught with a theoretical definition and a forced demonstration of unmusically exaggerated strong beat, distorted to make an obvious demonstration of the definition. Strong beats are not just the product of performed accents. Although nearly all music has meter, very little of it has explicitly accented notes on the first beat of each measure. Remember, the music is what is heard, not what is written. Strong beats are more the product of relative duration, parallelism, articulation, and rhythm patterns, than just accents.