Hierarchy in Rhythmic Structure: Meter, Beat and Duration

2011Symposium_1_2

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

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

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

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

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

The metrical hierarchy demonstrated

The metrical hierarchy demonstrated

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

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

What is a Convenient Shorthand for Music Notation Within Word Processing Software?

2011Symposium_1_2When writing lesson plans, I frequently have wished that I had a way of writing melodies quickly and easily on my computer within my word processing software. After attempting to use available symbols on the computer keyboard to contrive stick notation, and then line up solfege syllables I found all of this too time consuming and inconvenient. Some time later, I finally thought of a system that, with practice reading it, would serve my purpose well. I may not be the first to use this system for notating music within word processing software, but I don’t recall being informed of it from any other source.

 

For many years, I have used Finale music notation software. In the speedy C-Major-Scaleentry mode, entering notes without a midi instrument, numbers are used for note values, and pitches are indicated with the click of the mouse on the desired line or space of the musical staff. In my music notation for word processing, I adapted the numbers, combining them with solfege syllables. Dotted notes have a period following the number, and rests are a dash followed by a number. Time signatures are indicated with a fraction, and key signatures are indicated with linearly placed bs or #s. Tied notes have a number for the second note of the tie, and the tied notes are connected by an underscore.  I will demonstrate the system with the well-known horn solo from the movement “andante cantabile” from Tchaikovsky’s fifth symphony.

Figure 1

Andante cantabile from symphony no. 5 by Tchaikovsky

bbb 12/8 mi4 re4 do4| mi5. re6. ti4 do4 re4| fa5. mi6. mi4 fa4 so4| la5. la5 la4 la5._5 la4| la5. so5.—5 –4 mi4 re4 do4| etc.

the three bs indicate three flats in the key signature. 12/8 is the time signature. The first note is mi4. Mi in fixed do solfege is E, and because of the key signature, it is E-flat. Solfege syllables continue in the same way. Measure lines are given with a vertical line

( | ). In the fourth measure, there are two A-flats that are tied; a dotted quarter note tied to a quarter note. These tied notes look like this: la5._5 with la5. being the dotted quarter note A-flat, the underscore being the tie, 5 being the tied quarter note. I am able to type all of those notes quickly, and with practice, can read the solfege for pitches and the number for rhythms, just as I read note heads for pitches and stems and connectors for pitches and rhythms respectively in standard music notation. Using this system also has the advantage of keeping me from seeing standard music notation, just as my students are unable to view it, as I sing to them in solfege, and then have them repeat what I sang. It reminds me of the position I place them in, and it also gives me extra practice using solfege in a purely aural/oral way. If you are working on your fixed do solfege, as I have been this year, writing out and then singing melodies using this system is good practice. For those times when I need to remind myself of a melody I will be teaching, this short-hand system works quite well.