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The traditional two-dimensional line graph is quickly understood, easily designed, and readily completed by most people. Therefore, it has been selected as the basis for notating (creating written representations of) sound events and sound objects.

The line graph will nearly always be used with time as the horizontal (X) axis. In this way, values of states (levels) of the component parts of the sound can be plotted with respect to time. This allows the sound to be observed from beginning to end at a glance, out of real time.

Time Line

The length of the sound event or sound object that can be plotted on a single graph is dependent upon the selected increments of the time axis, or time line. Events of great length (and little detail) may be plotted on a single graph, and events of short duration (and great detail) may be plotted on a single graph. A balance must be found in selecting the appro-priate time increment for the time line. The sound should be easily observed in its totality (from beginning to end) and the graph should have sufficient detail to be of use in observing the qualities of the material.

Time increments will be selected for the X-axis that are appropriate for the sound. Time increments will take one of two forms: (1) units based on the second (millisecond, tenths of seconds, groups of seconds, etc.), and (2) units based on the metric grid (individual or subdivisions of pulses, measures, groups of measures). If the sound material is in a musical context, the metric grid will nearly always be the preferred unit for the time axis. Humans judge time increments most accurately with the recurring pulse of the metric grid acting as a reference.

Horizontal (X) Axis Time

Vertical (Y) Axis

Figure 5-1 X-Y line graph.

In general, when the sound evaluation utilizes the metric grid, a process of analytical listening is occurring. Critical listening evaluations most often use real time increments and not the metric grid. The differ-ence is one of context and focus.

If the sound material being evaluated is not in a musical context, increments based on the second must be used. It will be common to use increments based on the second in the evaluation of timbre relationships (including sound quality and environmental characteristics). While con-ceptualizing the pulse of MM:60 (or an integer or a multiple thereof) will provide some reference to the listener in making time judgments without a metric grid, this activity may not always be appropriate. It may distort the listener’s perception of the material, and the reference may be unstable, as the listener’s attention will rightly be focused elsewhere.

A stopwatch might assist in evaluating larger time units (to the tenths of seconds). The ability to judge time relationships can be devel-oped. It is recommended the reader turn now to the Time Judgment Development Exercise at the end of this chapter. The exercise will, with practice and over time, allow the reader to refine their skills in accurately making time judgments, by learning to recognize the unique sound qual-ities (timbres) of various time units.

With practice, the listener will develop the ability to make accurate time judgments of a few milliseconds within the context of known, rec-ognizable sound sources and materials. This skill will be invaluable in many of the advanced sound evaluation tasks regularly performed by audio professionals.

The time unit used in the line graph will be that which is most appro-priate for the sound event or sound object. The time increment selected must allow the graph to depict the example accurately. The smallest per-ceivable change in the components of sound being analyzed must be readily apparent, and yet as much material as possible should be con-tained on a single graph.

Vertical (Y) Axis

The components of sound to be plotted and the boundaries of levels and activities of those components are next determined. In the initial two stages of the sound evaluation process, the listener determines those components of the sound event that provide it with its unique character.

These components will be the ones most appropriately evaluated by plot-ting their activity on the line graph.

The component of the sound event to be evaluated will be placed on the vertical (Y) axis of the line graph. The second step of the sound eval-uation process (above) is now followed. The listener will now determine the maximum and minimum levels reached in the sound event, in each

of the components of sound to be graphed. These maximum and min-imum levels will be slightly exceeded when establishing the upper and lower boundaries of the Y-axis.

Exceeding these perceived boundaries allows for errors that may have been made during initial judgments of the boundaries and allows for greater visual clarity of the graph. Boundaries should be exceeded by 5 to 15 percent, depending on context of the material and the space available on the line graph.

Next, the minimum changes of activity and levels are determined.

Through Step 3 of the sound evaluation sequence described above, the lis-tener will determine the smallest increment of level change for the com-ponents of the sound event.

This smallest increment of levels will serve as the reference in deter-mining the correct division of the Y-axis. It is necessary for the Y-axis to be divided to allow the smallest value of the component of sound to be clearly represented, just as the X (time) axis of the graph was divided pre-viously so the fastest change of level would be clear.

The division of the vertical axis must allow the graph to depict the material accurately. The smallest significant change in the components of sound being evaluated must be immediately visible to the reader of the graph, and yet the vertical axis must not occupy so much space as to dis-tort the material. The reader of the graph must be able to identify the overall shape of the activity, as well as the small details of the activity of the component the graph represents. A balance between limitations of space and clarity of presentation of the materials must always be sought.

Multitiered Graphs

It is not always desirable for each component of the sound event to have a separate line graph. Many times several components of a sound event can be included on the same graph and plotted against the same time line.

Multitier graphs allow several components to be represented against the same time line. With the advantage that all characteristics can be more easily related to one another, which will lead to greater understanding of the sound.

The vertical (Y) axis of the line graph is divided into segments. Each segment is dedicated to a different component of sound. Each segment will have its own boundaries and increments.

Plotting a number of components of sound against the same time line not only makes efficient use of space on the graph, it also allows a number of the characteristics of the sound (perhaps the entire sound) to be viewed simultaneously. By placing a number of the components of the sound against the same time line, it is possible to give a more complete and a more easily understood representation of the sound event or sound object.

The person reading the graph will be able to extract information more quickly from a multitier graph than from a series of individual graphs. In addition, when several components of sound appear against the same time line the states and activities of the various components of the sound event/object can be compared in ways that would be difficult (if not impossible) were these components separated.

Specific multitier graphs will be used for certain evaluations in later chapters. In those cases, the graphs will always appear in a predetermined format, and greatly assist evaluations of components such as sound quality, musical balance versus performance intensity, and environmental characteristics.

Graphing Multiple Sound Sources

Multiple sound sources within the same component of the sound will also need to be graphed. It is quite common for more than one aspect within a component of the sound to be taking place at any one time (such as the sound of harmonics and overtones within the spectrum of a sound). This

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Figure 5-2 Multitier graph.

activity would require a separate tier of a multitier graph for each sound source in each component of the sound event/object being evaluated. The line graph would quickly become large and unclear.

As long as the segment of the graph can remain clear, it is possible for any number of sound sources to appear on any graph. When more than one sound source appears against the same two axes, the activities of each sound source must be clearly differentiated from the others. Sound sources may be differentiated in a number of ways. Each of these ways may be useful depending on the situation—what is available to the reader, the nature of the sound, or the context of the sound event.

The lines that denote each sound source may be labeled. The labeling of lines is accomplished by placing a number or the name of each sound source in or near the appropriate line on the graph. This type of differen-tiation is useful for graphs that contain relatively few sound sources.

Providing a different line configuration for each sound source is sometimes a suitable way of differentiating a number of sources on the same tier of an X-Y graph. Combinations of dots and dashes, or the inser-tion of geometric shapes into the source-lines may be useful for differen-tiating sound sources on the same graph—again for graphs with relatively few sources.

When sound sources are assigned lines of different colors, the graph can clearly display the largest number of sources. Only the number of easily recognized colors available then limits the number of sources that can be placed on the same graph.

The use of different colors has the further advantage of being able to define groups of sound sources by assigning a color to the group and assigning a different line configuration (combination of dots and dashes) to the individual sound source.

Using lines of various thickness to differentiate sound sources is not an option. This approach will obscure the information of the graph.

Varying line thickness will cause the sound to visually appear to occupy an area of the vertical axis. This is a state that is only accurate for a few select components of sound.

The use of color is not always feasible, but it is the preferred method of placing a number of sound sources on the same graph. Using num-bered lines or using varied and distinct line configurations for each sound source are the next, most flexible and clear methods of differentiating sound sources. Combinations of color and line configurations will pro-duce the most organized and most useful graphs. Individual sound sources must always be easily distinguished on line graphs. Readily iden-tifiable lines that have been precisely defined (by using a key, as described below) will ensure the clarity and usefulness of the graph.

The same sound sources may be depicted on a number of tiers of a multitier graph. In this case, care must be taken to define each sound

source and to depict the sound sources in the same way on each tier (either by the same number, color, or line configuration). This will allow someone reading the graph to quickly and accurately determine the states and activities of all of the sound sources (or aspects of the sound sources) over time. A key of the sound sources plotted should be created to ensure this clarity.

A key is the listing of sound sources of the sound event, coupled with a chart of how the individual sound sources are represented on the line graph (see Figure 5-2). This listing of sound sources with their designa-tions must be included in each line graph that contains more than one sound source (unless the lines are labeled).

The listing of sound sources is one of the first activities undertaken in the entire evaluation process. Sound sources are the individual ele-ments of activity within the level of perspective that is the focus of the sound evaluation. A listing of the sources (elements to be analyzed) will draw the listener into the evaluation process quickly and directly, and it should become one of the very first steps in evaluating sound.