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.

A Variety of Music Speed Types

2011 Symposium2

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.”


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.


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.


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.”

Classical Music and Contemporary Culture

2011 Symposium2

Elsewhere on this site, I wrote about the top 25 classical music works, and key words that help explain why they are as popular as they are. After writing that post, I decided to take the results to my eighth grade students and see if the key words in the survey resonated with these adolescents. Some of them are reluctant to listen to classical music, but many of them were surprised to find how much classical music was already familiar to them through the media. For my inquiry, I made a list of 10 pieces from the top 25. These pieces were the first theme from Beethoven’s fifth symphony, the finale from the 1812 overture, allegro from “Eine Kleine Nachtmusik,” the toccata from toccata & fugue in d minor by J.S. Bach, the finale from the William Tell overture, Pachelbel’s canon in d, “O Fortuna” from Carmina Burana, the opening from Richard Strauss’ Also Sprach Zarathustra, “Infernal Galop” from Orpheus in the Underworld by Offenbach, and “Hallelujah” from The Messiah. For each excerpt I had the students circle all choices that applied to complete the sentence “What I like most about this music is…” from the following list: a. the rhythm and the beat, b. I recognize this music from a cartoon, c. I heard it at a wedding I attended, c. I heard it on tv or in a film, d. the melody is easy to remember and/or sing, e. the music evokes a strong emotion in me i.e. joy, scary, sad, excited, etc.

The results indicated to me how important contemporary culture is to the enjoyment of classical music. Thirty students participated (n = 30). The results are given shown in table 1.

Table 1 Tally and Percentage of each choice for each excerpt

  Total Percentage
The rhythms and the beat 116 64
I recognize this music from a cartoon


93 52
I heard it at a wedding


28 16
I heard it on TV or in a film


168 93
The melody is easy to remember and/or sing


82 46
The music evokes a strong emotion in me 58 32

Students indicated that what they liked most about the classical music they heard was that it was familiar to them from television or film. The students gave this as a reason for liking the classical music they heard 93% of the time. None of the other reasons were close. Of the remaining choices, the next most often chosen reason was the rhythm and the beat, which was given as an answer 64% of the time. This also points to contemporary cultural influences, because contemporary popular music privileges the musical elements of rhythm and beat. On other occasions, my students have told me that the absence of a prominent beat (by which they often mean rhythm too) was the reason they did not care for a particular classical music work.

The low placement of “the music evokes a strong emotion in me” is interesting. At one point in the closure portion of the lesson, as student asked how music could be expressive if their were no words. He had not considered that the music itself, that is the musical elements of rhythm, pitch and so forth, could in and of themselves be expressive. With adolescents so focused on the beat and rhythm and after that the lyrics, expressive qualities of the music apparently often go unnoticed. This suggests that even when students are just listening to music, when there are lyrics, much of the music is background to the privileged elements of lyrics, beat and rhythm. This indicates to me the need to teach more instrumental music and to focus on expressive use of musical elements in contemporary popular music when using it in a lesson. To be sure, pop, rap, and rock composers frequently are not trying to be expressive beyond the lyrics, but there are enough songs where the music is expressive, particularly among pop ballads,  to be useful in teaching students to recognize and enjoy the expressiveness of music.

I also see in all this a recommendation for symphony orchestras. They need to take back their music; reclaim their repertoire from the popular media. Many of the works on that list of the most popular ones were orchestral classics long before the movies, commercials and television programs scooped them up and popularized them. These pieces need to graduate from pops concerts and be featured often to young audiences. These new concert goers will delight in hearing this familiar repertoire, and will, I believe, develop a curiosity about other works by the same or similar composers, and in this way be drawn to return to the concert hall.

Strong Beat and Driving Rhythm Found in Top Classical Pieces

2011 Symposium2

The popularity of classical music is of interest to those who teach music, and to those who run symphony orchestras. One of the things that attracts audiences to concert halls is favorite repertoire being on the program. Contemporary composers of classical music have at times been at odds with audiences, because their music was not what people wanted to hear. Much has been written about the lack of appeal that atonal and aleatoric music has to audiences, but knowing what audiences do like and want to hear is important if orchestras are going to attract and audience outside the tried, true and aging faithful. A list of the top 100 classical music pieces found on kickassclassical provides some interesting food for thought. Let’s look at what is there.Top Ten Classical Pieces

While there are really no surprises on the list, what I find particularly interesting are the keywords associated with each piece. I counted the number of times each keyword shows up in the top 25 pieces; here is what I found. Four pieces or 16% (rank 3, 6, 15, 19) are matched with key words that are or suggestive of life events. Ten of them, or 40% (rank 1, 2, 4, 8, 9, 11, 14, 16, 22, & 23) are matched with key words that are or suggestive of emotions, and half of them are in the top ten. Five, or 20% pieces are associated with the word cartoon. This is born out in my classes. Students will invariably get the most excited and motivated to listen when they hear classical music that they recognize from or that sounds like music they have heard in cartoons.

Another interesting finding from this list is that all of the top five and 8 of the top ten have prominent rhythm in the themes. This produces an overall more driving, active kind of music, and it also results in a more explicit beat. This last point I believe is key. Young people in particular enjoy the heavy rhythm and beat emphasis of popular music. I have observed in my classes that the more rhythm and beat are prominent in a classical work, the more likely it is that they will enjoy that piece. Though not on the list, it is worth mentioning that among contemporary composers, the minimalists, including John Adams and Philip Glass, have been among the most popular, and that minimalist music is much more rhythmic than other styles.

It is also noteworthy that 15 of the top 25 pieces were written in the 19th century, and that the two most popular composers on the list are Beethoven (3) and Tchaikovsky (2). If my students are any indication, it appears likely that Beethoven’s popularity is driven in large part by two works, one of which (surprisingly) did not make the list: the fifth symphony, and Fur Elise. Tchaikovsky gets heavy promotion in the United States every American Independence Day (when the 1812 overture is common fare) and every Christmas season with the innumerable productions of The Nutcracker. 

In general, I could conclude that pieces that have been worked into popular culture are also the most popular in the symphonic concert hall. Between weddings, holiday celebrations and films, many of the pieces on this list are familiar to a large population of people who have rarely or never been to a symphony orchestra concert. That familiarity breeds popularity is a well worn adage in the popular music industry, which relies on heavily promoted concerts and frequent plays on radio stations to popularize its product, and it was well understood by Richard Rodgers, who once explained that he could pick a song from a show and make it popular by placing it in the overture, in the first act, in the n’tract, and reprised in the second act. By the tie the audience left, they had heard the song four times and were humming it on their way home.

Singablility may well be another hallmark of more popular classical pieces. The bottom half of the list also includes many pieces made well known by use in popular media, but many of these have less lyric melodies. These works include Grieg’s Piano Concerto (used in Adrian Lyne’s 1997 film Lolita), Lacrimosa from Mozart’s Requiem (used in a recent DirectTV commercial), Overture to The Magic Flute, “Mars The Bringer of War” from Holst’s The Planets (used often in Carl Sagan’s Cosmos and referenced in the opening bars of (Imperial March” from Star Wars), and even “March” from  The Nutcracker, which comes in at only number 75. In conclusion, it may be that the most popular classical pieces strongly appeal to at least one emotion, are already popular to audiences through popular media, and are comprised largely of memorable and singable melodies.

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.

What Are The Elements of Music?

2011 Symposium2

What are the elements of music? It sounds like a simple question, one to which you’d expect a straightforward answer; perhaps a list of seven or eight items. If you ask this question of most if any music teacher, you’re likely to get such an answer. The trouble is, if you ask several music teachers, you’re likely to get several different answers. There doesn’t seem to be any clear, precise list that everyone agrees is the list of musical elements. Many answers reveal a confusion in just what an element is. To begin our discussion, it is helpful to understand that an element is not the same thing as a concept. In Webster’s dictionary, you’ll find that a concept is “an abstract or generic idea generalized from particular instances.” An element, on the other hand is “a constituent part; the simplest principle of a subject of study: rudiments.” Upon reading these definitions, we immediately realize that a concept is broad and general, whereas an element is narrow and specific. A concept describes the sum of the parts, and an element is one of those parts. 

Now let’s apply these definitions to music. When we hear a melody, is what we aremusic_words_large hearing a generalization from particular things we hear, or is it a specific, constituent part of the whole? One could argue that the melody is a constituent part, as is harmony, and when those two are combined, music is formed. One could also argue that the melody is a generalization made from each particular pitch and duration of which it is made. If we accept that both are true, that melody is both a concept and an element, then we must conclude that music, even at the conceptual and elemental levels, is unavoidably hierarchical. Even if this is so, it is still possible to examine the levels of the hierarchy until we reach the level at which everything is an element. If we do so, we will be left with individual notes which by themselves make little or no musical sense, but which are purely elements of music.

So what are the elements from which a melody is generalized? They are pitch, duration, timbre, dynamics, and articulation. Every musical sound that can be included in a melody must have each of these elements involved. When they are combined, they form the concept of a melody. If you have seen other lists whose mathmusicauthors claim to be naming the musical elements, you may wonder where rhythm and meter are. Rhythm is a concept. It is generalized from a sequence of durations, just as melody is generalized from a sequence of pitches and durations. Meter is also a concept, because it is generalized from patterns strong and weak beats, which are in turn generalized from sequences of durations and articulations. So meter and rhythm are concepts, not elements.

What of harmony, key, and mode? What is harmony but the consecutive sounding of pitches; therefore harmony is generalized from simultaneous instances of pitch. In a similar manner, key is generalized form groups of pitches which indicate certain chords and chord progressions which in turn establish a tonic key, such as D or B, and a mode such as major, minor or Dorian. Keys and modes, and harmony in general are all concepts generalized from the elements of pitch; therefore harmony, key and mode are concepts, not elements.

Some claim that tone color, texture, and form are elements of music. Tone color is closely related to timbre, and is indeed an element; it cannot be viewed as a generalization of other elements. Texture cannot, by our reasoning, be an element, because it is the way in which simultaneous parts are presented. Two or melodies sounded at once is one sort of texture, called polyphony, while one melody thinking musicaccompanied by chords is another sort, called homophony. When one melody is played alone, that is another texture, known as monophony. All textures are generalizations of how the various parts are related, and must then be understood as concepts.

I agree with Sylvia Constantinidis that elements of music can properly be called properties of musical sound, and that they include pitch, dynamics, tone color, and duration. In defining musical elements with precision, we can begin to eliminate the confusion over the subject of musical elements. If one learns how these four elements are utilized in music, other vocabulary, including the numerous concepts so often misnamed elements, will become readily understood. Pitch is the property of sound that is measured in vibrations per second, and is perceived to have highness, like the piccolo solo in Sousa’s Stars and Stripes Forever, or lowness, like the opening four measures of Schubert’s symphony in B minor (unfinished), or anywhere in between these extremes of highness and lowness. Tone color is the quality of sound made by an instrument, and is described with words such as dark, bright, shrill, or warm. A musician can vary the tone color of his or her instrument to make the music more expressive, and instruments themselves have characteristic tone colors, also known as timbre. A clarinet in the mid or low register is dark or mellow, whereas the piccolo in its high register is bright or even shrill. Dynamics are simply how loud or soft the music is, and duration is simply how much time a particular note lasts, measured in beats or seconds. These are the elements of music.

Reflective Questions for 5th Grade Music Composition

2011Symposium_1_2Today I am going to discuss questions students can use to reflect on their creative musical work. In Connecticut, these questions are part of the Common Core Assessments for music. Each question gets at an important musical aspect or concept, and helps focus students on more than just getting notes down on paper and singing or playing what they have written. These questions move a student’s musical thinking up to a higher level, and deepen musical understanding. You will see that the questions also go beyond what can be seen on paper, into the realm of what is heard and perceived in the composer’s mind.

The first question is, “what pitch is your tonal center?” An advanced composer will know immediately what the tonal center is, because they had it in mind the whole time they were composing. Even so, this question presents the opportunity to check if the intended tonal center is fact the tonal center a listener hears when the musical work is performed. For the novice composer who has perhaps not audiated what he or she has composed, this question demands that the piece be heard, either in physically present sound or through audiation, and the tonal center determined. After listening to a melody, a tonal center may be poorly established or not present at all, in which case revisions are called for that will establish or strengthen a tonal center. This question alone can bring out substantial learning.

The next two questions are follow ups to the first: “Where is the first time the tonal center pitch occurs in your composition?” and “where is the last time the tonal center pitch occurs in your composition?” These questions require that the student composer not only know what the tonal center is, but also where it occurs. It is relatively easy to recognize a tonal center when it is the last note of a melody; the closure that the tonic pitch brings is highly noticeable. But recognizing it in the midst of a melody, especially if it does not occur at the end of a phrase, is more challenging, especially for less experienced students. These questions make the student composer aware of where and how the tonal center has been used, and how the tonal center brings relaxation to a melody, between instances of relative tension from other tones. Although not included in the Connecticut set of questions, locating all occurrences of the tonal center can also be instructive, especially if there is too much or too little tension in the overall melody.

The next two questions address matters of rhythmic structure. First, “what rhythmic values did you use?” For this question, the student is to identify note values employed. As with the tonal center, these should have been audiated during the composing process, and should be recognizable by composer and audience alike upon hearing the work performed. Unless the rhythm is audiated, students will have difficulty in determining where the beats are, which in turn is needed for audiating the meter. Equally important is that the written symbols be correctly identified as representing the audiated durations. .After identifying the rhythmic values, the student is then asked, “How many beats are there in each measure of your composition?” In all likelihood, a number was determined as part of the assignment, but this still needs to be checked by the student as part of his or her reflection. This is also where identifying rhythmic values in the context of a beat is useful. Students must not mistake two eighth notes as two beats, or a half note for one beat. As students answer this question, the teacher can check for any misunderstandings of beat due to flawed audiation or understanding of the concept of beat itself.

Upon completing these reflective questions, students will have a well-grounded and thorough understanding of the musical elements of tonality, beat, rhythm, and meter, and will in many cases have been challenged to “think in music” to a much greater extent than they would have otherwise, even while and in response to composing music. Tomorrow, I will discuss reflective questions having to do with the actual performance of the composed musical work.

Describing Music and Teaching Music

2011Symposium_1_2If you are a music reader, want you to pretend you know nothing about music notation. If you don’t read music, you’re all set. Now take what I’m about to write absolutely literally. “A quarter note gets one beat, and a half note gets two beats.” Just from that description, do you know that the duration of a half note is twice as long as the duration of a quarter note, or did it sound like you should play two quarter notes, which are two beats, every time you see a half note? The latter is what many novice music students take the statement “a half note gets two beats” to mean. If one beat is a quarter note, it’s logical to think that a note that gets two beats gets two quarter notes. This misunderstanding is possible because note values are often defined as mathematical quantities and not durations. Children are used to seeing pictures of apples and pencils and ice cream cones on their math worksheets. Two pencils in one picture equal two apples in another. So it is reasonable to transfer mathematical logic to music when it is presented mathematically. A quarter note equals one beat. A half note equals two beats. Sing a half note. The child does two quarter notes because he or she was asked to sing two beats. It makes all the sense in the world.

Durations are measured with numbers, but they are measurements of  how long something we hear lasts over time, or how long an object takes to move from one point to another, or how long we waited at the doctor’s office in the waiting room. We can’t see time, we can only experience it and represent it abstractly with numbers. A duration is not how many of something there is, like apples in a basket, but of how long it takes for something to occur, from onset to offset, from start to finish, from beginning to end. You can have two quarter notes and two half notes. There are two of each, but knowing that is not helpful in knowing how to perform either, and although there are two of each, and they are all notes, they are not the same notes; they have different durations. The half note has a duration of two beats and the quarter note has a duration of one beat. Both are single notes, but they last for different amounts of time, measured (usually) in beats.

In music, we generally have a reference note that is equal to the duration we consider the beat. This duration isnote_hierarchy called the ictus. Where the quarter note is the unit of measure, a half note is an elongation of the beat. This is a helpful term, because it describes something longer than something else, not bigger or in greater quantity. Elongation means to make longer, so a half note is longer than a quarter note, not multiple reproductions of it. A whole note is also an elongation of the beat, but also an elongation of a half note. How much longer? Two beats longer. Beats is the unit of measuring the duration of a note.

If there are notes (durations) that are longer than the beat, there are also notes (durations) that are shorter than the beat. If the unit of one beat equals a quarter note, then an eighth note is a division of the beat. Once again, we want to avoid language like, “a quarter note gets two eighth notes.” This can lead to children playing two notes when they see a quarter note, just as they did with the half note. Describe eighth notes as durations. Eighth notes last only half as long as quarter notes, so two of them can be sung or played in the same time as one quarter note. Children can tap quarter notes with their heels while chanting eighth notes, and experience the durational relationship between them. As students get older and more advanced, the same approach should be taken with other note durations that are both smaller and larger than those discussed here. The important thing to remember is that notes have duration measured in beats; they do not have beats. Through hearing patterns of durations, which we call rhythms, we are able to detect a beat, but that beat is made manifest by the pattern of durations. Keeping the concepts of duration and beat separate will clear up many rhythm problems commonly encountered in our teaching.

What’s In A Name?

2011Symposium_1_2Although we humans rely heavily on our senses of sight and hearing, our world would not make much sense to us if we did not have language in which to think, and words with which to know things. By naming something, our minds are able to categorize, connect, apply, analyze, evaluate, and represent everything that enters into our consciousness. For those of you that know your bible, one of the first things God does after creating Adam is to see what Adam would call the living creatures God had made (Gen 2:19). We intuitively name things in order to know them and use them.So it is with music.

Once a person has learned musical patterns from his or her musical environment, those patterns are given names so that they can be known and used to knowledgeably listen to, perform, and respond to music. We call the notes by solfege names, and we call durations by rhythm syllable names. We call pitch sequences chords, scales or intervals and further refine our naming with words like major and minor, dorian and mixolydian. When we are able to associate these names with musical sounds, then our hearing and performing of them becomes more accurate, musical, and expressive.

Yesterday, one of my first grade classes was singing the song, “Ebeneezer Sneezer.” The song is useful for teaching solfege, because it ascends the do major scale one phrase at a time, and then ends with a quick descending scale. Ebneezer_SneezerI heard that re and la were out of tune, whereas the other pitches were sung accurately. I stopped them and told them those notes were not correct, and then had them sing the song using solfege. Because they had a grounding of doing tonal patterns with solfege, they immediately sang accurately what they were unable to sing accurately singing the lyrics. I then told them to sing the lyrics, but think about the solfege while they sang, connecting the two. On their first attempt, the inaccuracies were corrected. The mind connected the patterns learned with solfege (after learning them on a neutral syllable) with the notes in the song, even when the solfege was no longer being sung. That is the power in a name; it makes information applicable and usable.

Here is another example, this time one with rhythm. I had taught my third graders the song, “Too Ra Loo.” TheyFeed Your Brain Music have proficiency in sight singing but they were not familiar with the rhythm of dotted eighth and sixteenth. I wrote the melody on the board, and had them quietly sight sing it, concentrating on the pitches. Their  goal was to “name that tune.” After a few incorrect attempts, four children almost at once recognized the song. The class sang the song, and then I drew attention to the dots and sixteenth note beams on most of the pairs of notes beamed together. I reminded them of the rhythm of four sixteenths, and had them sing it with the rhythm syllables “du-ta-de-ta.” Then I told them that the dotted eighth and sixteenth rhythm was simply the first and last syllable, “du___ta.” That wonderful “ah-ha” look appeared on most of the faces, and they immediately were able to connect the rhythm they had already been singing, to the notation they were now seeing. The connection came through a name,”du___ta,” which in turn was understood by connecting it to another name, du-ta-de-ta.”

The amount of information we process while performing music from standard music notation is immense and remarkable. A novice can easily be overwhelmed by the sheer volume of data that must be cognitively handled. Only by organizing that data into comprehensible structures, patterns, and groups can a person hope to become accomplished at music reading. Luckily, most of that organizing and processing happens subconsciously, or else the very act would hopelessly bog us down. But knowing that processing is occurring, and teaching music in such a way that music can be understood in the way our brains naturally make order of our world, is essential to effective music teaching.