Horizontal Graph Analysis

Dr. Michael R. Dilthey

Bridgewater State College

Bridgewater, Massachusetts

Presenting horizontal graph analyses of major compositions to music appreciation students illuminates fundamentals of the pieces, facilitates listening, and promotes independent study. With a prerequisite of basic music vocabulary students will assimilate information in compositions aurally and visually. The graphs are created on Superpaint and transferred into Quick Time on the Director Program and aligned with the recording. This creates a library of scrolling graphs with compact disc recordings of performances which may be used in the classroom, listening library or privately for home study.

example 1

This is a horizontal graph of the beginning of Johann Sebastian Bach's Fugue in G Minor (example1). The primary target for this graph is the music appreciation student. With a prerequisite of approximately two weeks of basic music vocabulary (ie. music parameters) the student may use the graph as a study guide to the composition by observing the various parameters and their placement in the piece. The graph is designed to provide the student with conclusive information gained in a manner similar to reading and studying a musical score without the student’s necessarily having the ability to read music notation. The horizontal graph is incremented by units which coincide with the measures in the score. The student reads through the graph in much the same way he would read through the original score. All of the basic parameters of music are included and described: form and thematic material, harmony, rhythm and melody. The graph is organized by the four voices of the fugue with information regarding form and harmony given above each line representing a voice and information on rhythm and melody given below each voice line. As each voice of this four voice fugue enters, descriptive boxes appear above or below the voice line providing the information on these parameters.

The graph illuminates each of the parameters and their integration. As each description of a parameter appears throughout the piece the student can observe the description and significance to higher level formal divisions. For example: the student may observe that harmonic key changes are aligned with entrances of the subject; or that sixteenth note scale passages are intricately associated with the countersubject. The student may observe relationships between parameters such as the general interaction between rhythm and formal divisions. The student can more readily place formal divisions in the context of the overall work, visually marking the length of sections like the exposition as compared to the entire piece.

The information presented includes the formal divisions of this fugue: the exposition, episodes and subsequent entrances of the subject. The parameters described are harmonic (key areas), rhythmic(note value) and melodic (directions of skips or steps, scales, etc....). Through graphic presentation the parameters of pitch and texture are illustrated by the use of the voice lines. A high pitch is inferred with material presented in the soprano voice and a low pitch in the bass voice. Similarly, when one or two of the voice lines are active the texture is thin and when all four lines are active there is a thick texture. The measure line sequences the information with the score and acts as a reference for discussing the various parameters.

The graph is organized in levels to be read top to bottom around each voice line, including parameters together by ease of perception. The information concerning formal divisions of the fugue is primary to understanding contrapuntal concepts and is placed above each voice line. As the change of tonal centers is connected with these formal divisions, The harmonic parameter is also placed above each line. Rhythmic and melodic information is more closely associated with an in-depth analysis of the composition rather than a basic understanding and this information is grouped together below each voice line. The student can focus his analysis to a general understanding or more complete comprehension of the work.

The graph is designed to be read in real time. Providing the student has a command of the vocabulary, he can observe all of the information while listening to a performance. Further, while listening and reading about one section, the student can look forward to events and/or easily move forward and backward for a comparative analysis.

The graph is complete for independent study and use in the classroom. The student may hear and view the work at once for an augmented understanding of the information and concepts. The student may study formal divisions on the graph before hearing the work in preparation of that first hearing. He may study rhythmic and melodic information after the performance to internalize the information. The instructor may clarify, personalize or prioritize information presented in the graph by pointing out significant divisions or reinforcing connections in the development of the piece (see example 2).

example 2

The instructor may also highlight a section such as a sequence and further display the material in class to demonstrate the melodic and rhythmic connection with main themes. Thus the graph allows for expansion. The information presents the parameters with a certain level of activity. The Instructor may expand the description of a section for a closer analysis of the given parameters or closer explanation of information excluded from the graph such as harmonic implications of sequential material. The Instructor may use the graph to present this fugue or the general concepts of fugue in a generic sense, or for comparing this fugue with other fugues.

This graph was developed as an alternative to the vertical time-line listening guides found in most music appreciation texts. With information presented in paragraph form, the guide either becomes too wordy or limiting by only presenting the information for one or two parameters. If the student doesn't happen to hear those particular parameters, the minutes and seconds time-line provides a less than adequate reference. The common practice of the instructor calling out themes over the recording is disruptive of any aesthetic experience and somewhat rude. The Horizontal Graph allows the individual student to focus on what they want to listen to, while keeping a sense of the whole. The intent of the graph design is to recreate the score reading experience by including information found in the score. The instructor may require the student to watch and listen for different parameters at different times while retaining the sense of the simultaneity of all that is happening. The student discovers fundamental information on form and structure by learning how the various parameters fit into the over-all flow of the piece. The student also improves his ability to hear a composition by understanding the integration of the elements in the music.

The graph is useful in an undergraduate theory course for music majors studying form and analysis. While such a student is able to read music from the original score, the graph offers a clear and concise analysis, presenting the principles of form in the composition. The student can see at a glance the structure of the work and the interaction of various parameters in the construction of the composition. With additional graphs, the student sees in a similar format how different composers use parameters in a variety of ways and how the use of these parameters progresses through historical periods. In addition, the student learns successful analysis techniques for application to the study of other pieces.

Graphs of compositions in other genres will present information in a different format; an analysis of a symphonic work will include timbral and dynamic information as well as adjusting formal discussions to best illustrate the form. Example 3 is a graph of the beginning of the Incidental Music to A Midsummer Night's Dream, by Felix Mendelssohn. The arrangement of the various parameters coincides with the listening experience: the upper portions of the graph include basic information such as texture, timbre, pitch and dynamics, information obtained in the first or second hearing of the work. As the student works down through the graph, more detailed information is delineated such as thematic material, form, harmony and phrasing.

There are significant applications of this graph to the current and new CD-ROM technology. With Multimedia, the graph and recorded performance are combined into one program. The Horizontal Graph Analysis scrolls across the computer screen as the recorded piece is performed. When the pertinent parameters of the piece appear, the labeling of those parameters on the graph are highlighted on the screen, giving the student the information of the graph and further assurances of location in the performance. In addition, with new Audio-Visual technology, videos of live performances may be included as part of the scrolling graphs. The student will have a library of works to study on CD-ROM in the computer laboratory. Further applications of this procedure include Schenker analysis for graduate and undergraduate study. Detailed graphs which are created using the Schenker method will be aligned to recorded performances of the corresponding analyzed works. The student has the opportunity to study the analysis in conjunction with the recorded performance.

example 3