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Beyond the Imaginary Barline

 
  Scott McCormick is a professor in Berklee's Harmony Department. He has written the MusicGamesOne software program that teaches music fundamentals in a video-game format.
  Nick Balkin

I admire music theorists who can step back from what they have learned and examine music from a fresh perspective that is separate from the system they have been taught. In his book A Theory of Evolving Tonality, Joseph Yasser offers a fresh, unique, and valuable perspective on the relationships in tonal music. His approach inspired me to look at rhythms in a new way.

In 1999, when I first taught Berklee's Writing Skills course, I was forced to examine the structure of rhythmic notation so that I could teach it. I went back to square one and re-examined rhythmic notational practices-especially the imaginary or invisible bar line concept. The principle of the imaginary bar line is that one should be able to draw a bar line in the middle of a measure of 4/4 meter that divides it into two bars of 2/4. This makes the music easier to understand for those reading it.

My first observation was that there were quite a few commonly used patterns that do not follow the imaginary bar line rule. At first, I identified these rhythmic patterns as exceptions to the imaginary bar line concept. Eventually I abandoned this approach and defined them as acceptable four-beat patterns. This led to defining all one- and two-beat patterns as well. These patterns are shown in examples 1, 2, and 3.

In addition, the imaginary bar line concept is incomplete for the notation of sixteenth-note patterns. With sixteenths, we need to show the beginning of each beat. In effect, we need three imaginary bar lines. (For a demonstration of this principle, see the last bar of example 7.) Because of the limitations of the imaginary bar line concept, I supplemented it with two aspects of music notation: a definition of the essential one-, two-, and four-beat rhythmic vocabulary and the five layout patterns that are discussed below.

I also realized that the distribution of these patterns was consistent with current studies of human perception: we perceive information in chunks rather than in small bits. There are parallels between reading music and reading words. We don't see individual letters; rather, we group letters into chunks of information and see words. Adept music sight readers perceive groups of characters and not the individual characters.* The graphics of music notation are structured to make these chunks of information easily accessible to the music reader.

The One-, Two-, and Four-Beat Rhythmic Vocabulary

Although the design principles explored here are applicable to all meters, this discussion is limited to the most common of all time signatures: 4/4. This idea can be applied to all rhythmic values, but the smallest rhythmic value I use here is primarily the eighth note.

Rather than use the term chunk, I use the terms one-beat, two-beat, and four-beat patterns. I also think of them as rhythmic "words" comprising between one and five music characters. First we'll define and examine the rhythmic words or patterns, and then we'll see the five ways that they are distributed in a measure.

The five one-beat patterns are shown in example 1. The first three patterns consist of one symbol. I view a beamed pair of eighth notes as a single visual symbol. The fourth and fifth patterns consist of two separate musical characters.

The 10 two-beat patterns are shown in example 2. The first three patterns consist of one connected visual symbol, whereas the remaining patterns consist of two or three music characters that the reader must learn to combine into a rhythmic word. Notice the characteristics of each two-beat pattern. Beat two either happens on a note that is beamed from the previous eighth note or has a note that is sustained through beat two. This means that there is no music character happening on the second beat.

The four-beat patterns are shown in example 3. I define these patterns as commonly accepted rhythm patterns in which beat three occurs in empty space. There is no music character visible on beat three.

Unlike the one- and two-beat patterns, four-beat patterns have the possibility of substitutions. In example 4, quarter notes in the third, fourth, and fifth four-beat patterns can be replaced by any of the other one-beat patterns.

  Examples

The Five Layout Structures

There are only five ways that these one-, two-, and four-beat patterns can be arranged in a single bar of 4/4. These possibilities are shown in example 5. Ties have no role in the way the one-, two-, and four-beat rhythm patterns are laid out in a measure. The primary musical information is expressed in the rhythm patterns themselves. Ties are secondary in that they modify the sound expressed by the basic rhythm patterns. A note with an accidental represents a similar situation. The letter name of the note (a D, for example) is the primary information; the accidental is secondary because it modifies the primary information.

Diagramming a Tune

Example 6 features the tune "Paper Doll" that has been diagrammed to show that each measure demonstrates the layouts shown in example 5. Good sight readers unconsciously group musical characters into the rhythmic words defined by the rectangles in this example. Music reading is about comprehending organized groups of notes, not about reading individual music characters.

The Results of Structuring Rhythmic Notation

An important benefit of organizing rhythmic information into the five rhythmic layout structures shown in example 5 is that the possible number of rhythmic patterns is significantly reduced. The patterns shown in example 7 are considered bad notation because they violate the imaginary bar line rule. The rhythmic characters are not arranged in one of the five acceptable layout patterns. All such formations are eliminated from acceptable rhythmic notation, leaving a smaller number of visual patterns for the reader to recognize.

If we want to become fluent sight readers, we have to train ourselves to recognize and perform the basic one-, two-, and four-beat rhythmic words. Awareness of this rhythmic vocabulary and the five layout patterns is absolutely essential in the process of writing music. I like the metaphor of containers: each bar must have the one-, two-, and four-beat containers arranged properly (as in example 5) and filled with valid rhythmic vocabulary. If you fail to arrange rhythmic information in this manner, the result may be severely flawed rhythmic notation.

To test this theory, choose any standard tune in 4/4 and draw rectangles around the one-, two-, and four-beat patterns. I predict that you will find that the notated music follows the guidelines outlined here without exception. You will also probably find sixteenth-note and triplet patterns, which haven't been discussed here. But they fit into this theory as well.

Conclusion

The rhythmic theory presented here is an extension and elaboration of the original imaginary bar line concept. It defines the one-, two-, and four-beat patterns and shows the five ways they can be arranged in a bar. Many of my students have reported that approaching music with this perspective significantly improved their skill in both reading and notating music.

Footnote: *For more on this topic, see the section "Grouping and Structural Perception" in "Cognition and Motor Execution in Piano Sight-Reading: A Review of Literature" by Brenda Wristen, Update: Applications of Research in Music Education, Fall/ Winter 2008, pp. 44-56; http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1005&context=musicfacpub).