The Difference Between Visual Meter and Aural Meter in Music

2011 Symposium2

Of all the structures and elements of music, meter is arguably one the most confusing. This is due at least in part to the fact that unlike rhythm and pitch, and to a lesser extent unlike dynamics and tempo, our Western system of music notation is often vague or imprecise when it comes to representing meter. To illustrate this, consider Beethoven’s famous “Ode To Joy” melody. For a person hearing this for the first time, or for a person hearing this without ever having seen it written down, the meter for this melody sounds like it is organized into alternating strong and weak beats, or what we would call two-four time. Every indication from listening alone supports this analysis. The music proceeds in patterns of strong, weak, strong, weak beats, and strong, weak measures. For us who have seen the melody written out, we know that Beethoven notated it in four-four time. So which is the correct meter, the one we hear, or the one we see? For most people, it is by necessity the one they hear, because most concert goers have never and will never read the printed music. I dare say that a great many classical music lovers don’t read music at all. To all of them, it matters not at all how Beethoven in his score, or Pearson, Sueta, Kinyon, or anyone else who has ever transcribed “Ode to Joy” for band, chose to write it down. All that matters to a member of a concert audience is what he or she hears, and how he or she interprets and understands what is being heard.

Before going on, it will be helpful to define meter. Meter is the grouping of beats into patterns of strong beats and weak beats. If every other beat is strong, then we call that duple meter. If every third beat is strong, we call that triple meter. The problem comes in the fact that any note duration can be heard as a beat. An eighth note can be a beat, or a quarter note, half note, dotted quarter, dotted half, and so forth. Any of these can be considered the beat of a given piece of music. Not only that, but several of these durations can be heard as the beat at the same time. In Beethoven’s Ode To Joy, we commonly consider the quarter note as the beat, but the half note  or even whole note could also be heard as the beat. The designation of a quarter note as the beat is subjective and even somewhat arbitrary, because an equally strong case can be made for any of the other durations. We can choose to insist that the time signature is four-four so therefore the quarter note gets one beat, but of all the choices, that is probably the least musical of them all–it discourages the beautiful flow and friendliness we all love and associate with this tune.

The truth is, we give far too much importance to measures and far too little importance to meter. We can hear and experience meter, we can neither hear nor experience measures–they are a notational convenience that is at best an unreliable indicator of meter.  What we really should be concerned with is how parts beats are divided into throughout the course of the music. No matter which of the durations we choose for “Ode to Joy,” when one beat is divided, it is always divided into two equal parts, and never into three equal parts; therefore, this melody is in duple meter, no matter what kind of note we decide gets one beat, an no matter how many beats we think are in each measure. The quarter note is divided into two eighth notes, the half note is divided into two quarter notes, and therecite-budvjj whole note is divided into two half notes, which is divided into two quarter notes, which is divided into two eighth notes. We see from this that metrical structure is hierarchical, but not in a mathematical sense as implied by those rhythm hierarchy charts found in instrumental method books, but in a cognitive sense in that our human brains intuitively organize rhythm into the very sorts of hierarchies I just described. It is a perceptual hierarchy, not a visual one.

To explain this further, we need to recognize there are two kinds of beats. These were described by Gordon as tempo beats and meter beats. If you suppose that the half note is equal to the beat in “Ode to Joy,” then the half note duration is the tempo beat, sometimes also referred to as the ictus. The duration which is the equal division of the half note, as we have seen, determines what the listener perceives as the meter. In our Beethoven example, this was the quarter note duration, because two quarter notes divide the half note beat into two equal parts. The quarter notes, then, are the meter beats, because they determine the meter. There are two meter beats (in this case quarter notes) for every tempo beat ( in this case half notes), and so the meter is duple.

The difference between tempo beats and meter beats is most evident in the so called compound time signatures. Consider six-eight time, which is often referred to as compound duple. It is duple because there are two tempo beats per measure, and it is compound because each tempo beat is divided into  three meter beats. The word “compound” is meant to point out that there are elements of both duple and triple meter present simultaneously. This is in contrast to “simple” duple, in which there are only elements of duple meter–two tempo beats per measure and two meter beats per tempo beat. But all of this brings us back to talking about measures instead of what the listener hears. No one really perceives the meter of “Barcarolle” from Offenbach’s The Tales of Hoffman and the meter of Strauss’ On The Beautiful Blue Danube to be different, yet the former is written in six eight (compound duple) while the latter is written in  three four time (simple triple). The number of meter beats in relation to one tempo beat is all that matters. The music can be notated in any number of ways, and it will sound exactly the same. The most sensible and uncomplicated way of understanding meter is to think of it as something we hear, an aural meter, and not something we see in notation.

Improvising With Tonal Patterns

2011Symposium_1_2Music is constructed with patterns of pitches and rhythms. As we have seen over the last two weeks, we begin to learn these patterns aurally from birth and even before. Aural learning continues into the school age years, and is necessary before music reading and writing can be taught effectively. Not only are the raw pitches and rhythms learned, but also the meters and tonalities resulting from those patterns. As  a person learns patterns, tonalities, and meters, he or she can begin using them in improvisation. Improvisation can only be done with patterns, meters and tonalities that have been learned.; we do not improvise from nothing, but from ideas that are essentially original orderings and variations on things we have already heard and are familiar with.

At its beginning stages, original musical thought may be slight alterations to a pattern the student has just heard. When I sing a pattern to a student, and ask that student to sing back to me something different from what I just sang, my youngest students sometimes have trouble thinking of something to sing. I then guide them with suggestions. I may point out that in what I just sang the pitches went down, so he or she could try singing something that goes up. Or I might suggest that the child sing what I did, but add or remove one or more notes. Another idea is to sing the rhythm of the child’s name. All of these strategies coax the child to begin generating musical ideas from musical thoughts. All of it is aurally based, without even a reference to notation.

When notation is brought in, it is only of patterns that the children have already learned aurally. Early on, I will write several tonal patterns on the board, sing one of them, have the class or an individual repeat the same pattern, and then tell me which pattern of those on the board we just sang. This strengthens the connection between what is heard and what is seen. Again, strategies may be needed to shore up this learning. For example, one of the patterns might be “do, mi.” After correctly singing and identifying that pattern, I might move on to “do, mi, so.” I have already made sure that only these two patterns begin with “do,mi,” so I can say to the unsure student, ” what are the first two pitches in the pattern I just sang?” I the sing “do, mi, so” again, and wait for the student’s answer. After finding them to be “do, mi” I then say, “pattern 1 was ‘do, mi,’ can you find another pattern that begins with the same pitches?” Using this question as a guide, the student can then find the pattern that is “do, mi, so.” All of this gives students practice in locating notes on the staff, and thinking in 101terms of patterns or combinations of pitches, instead of individual pitches.

After building proficiency at singing and reading patterns, students can move on to improvising with these same patterns. Students can repeat patterns, sequence several patterns, and alter one or more notes in a pattern to create improvised music. Until rhythm is added, there is no meter, but students are already hearing a tonality form the patterns they are improvising, because the patterns I have taught them for this activity are all in a single tonality. Do, mi can become do, mi, mi; so, fa, re can become so, fa, re, so; so, mi, do can become so, do, and so forth. I can use the same approach with rhythms, beginning with rhythm patterns aurally, then going into notation, and leading into improvisation. After using rhythm patterns in this way, I then reinsert pitches, and have students play with both tonal and rhythm patterns at the same time; that is, they can now change pitch, rhythm, or both as they improvise.

Although improvisation is not usually thought of as including notation, I find that including notation in these improvisation activities helps students strengthen their audiation and reading skills. By seeing what they are improvising off of in the small segments of tonal and rhythm patterns, they are connecting what they see to the changes they are making to it. It is also a kind of readiness exercise for improvising off of a lead sheet, where musicians have entire melodies notated. Learning to read in patterns first transfers to reading whole melodies, preparing students to see patterns in notated melodies, and isolate them as materials for fruitful improvisation. It also takes some of the mystery out of improvisation for inexperienced improvisers, because it feels less like they are making music out of thin air, and more of what it really is: making music out of patterns they already know.

Teaching Antecedent and Consequent Phrase Structure in Music

2011Symposium_1_2One of the musical structures we must teach our students is that of phrasing, or what Lerdahl & Jackendoff refer to as grouping. Basic to musical phrases is the concept of antecedent and consequent phrases. Antecedent phrases are complete phrases that end on a pitch of relative instability or tension, resulting in the listener expecting continuation, even after the performer takes a brief pause or breath. Consequent phrases are also complete phrases, but they end on a pitch of relative stability or relaxation, resulting in the listener recognizing the conclusion of the musical thought. Themes, sections, movements and works end on consequent phrases. Very often, consequent phrases end on the tonic, and antecedent phrases end on the dominant. Because antecedent or consequent phrases are defined primarily by the harmonic function of the last note, they are most effectively taught by holding rhythm constant while giving students creative license with pitch. The only stipulation is that the consequent phrase must end on the tonic. It is also possible that students can use elaborative notes in the consequent phrase. Take the melody “Mary Had A Little Lamb” as an example.

Mary

Structurally, the first line is a reduction of the second. The quarter notes on beats 3 and 4 of the second measure of the second line reduce to one half note in the first line, and the quarter note on beat 3 of the third measure in the second line is an upper neighbor tone that is omitted in the reduction, in which a half note on D occurs. The last measure of the first line could be reduced further to a whole note on G, the dominant. In its reduced form, the second line is identical to the first except for the last note; the antecedent ends on the dominant and the consequent ends on the tonic. Students can be given the first line, with the further reduced last measure, and then asked to write a consequent phrase ending on the tonic pitch. They would be at liberty to write any diatonic pitches, but to maintain the rhythm of the first line exactly. One possible solution is given below.

Mary2

Prior learning will include voice leading, analysis of stylistic elements, and skill at audiating so that students do not write down random notes, or notes that are stylistically incompatible with the antecedent phrase provided. Doing this activity with antecedent phrases of different styles and genres provides the opportunity for students to learn about and compare each style or genre represented. Assessment would include ending on the tonic, maintaining the same rhythm  preserving the same style, using diatonic pitches, and observing good voice leading. If student work is handwritten, assessment could also include accurate forming of note heads, stems, measures, clef, and time signature, and the correct number of beats in each measure. Students who do the work on music notation software should nevertheless be asked to demonstrate understanding of notation conventions such as correct length and direction of note stems, and of the metrical arrangement of notes within measures. Technology should never allow students to bypass the learning of concepts.

A great deal of learning can result form this one activity. Phrase structure, style, genre, and notation are all closely related issues in music. This activity fosters an efficient use of time because all of these can be addressed at once in a practical, relevant way; students need to know about and apply their knowledge of style, genre and music notation in order to gain a deep understanding of the target concept, that of antecedent and consequent phrases.