Introduction to Auditory Graphs

Introduction to Auditory Graphs

Before the test begins, a short explanation about Auditory graphs is necessary for those who will be listening to the graphs instead of seeing them. It is a random process as to who gets which graph type, so everyone should understand how to listen to these graphs.

The basic auditory graph involves mapping the Y axis data to pitch, and the X axis data to time. So the greater the Y value, the higher the frequency of the sound, and the greater the X value the later the sound will be played. As an example, in the following graph there are two (X,Y) data points: (1,1) and (2,4). The (1,1) point can be heard first, and has a low tone, the (2,4) point is played second and has a higher tone.
Intro graph 1: Points (1,1) and (2,4) image. 

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Please play this graph now.

Note: The concept of 0 is difficult to represent in an auditory graph. We have used the following tone to represent 0 in all of the graphs in this test:

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For most of the graphs that you will encounter, the lowest tone played will represent 0.
A series of points would be played as a series of tones. The following graph gives an example of a series of points that increase in both X and Y values:
Intro graph 2: Y = X image. 
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Please play this graph now.
In previous studies, it was noticed that it is difficult to tell when a graph is linearly increasing (i.e. Y = X), vs. when there is some curvature to the graph (i.e. Y = X^2). For this reason, a sound to alert the listener to the slope and curvature of a graph has been added. This sound is heard as a series of "drum" beats.

The slope of a graph is defined as the rise/run or dY/dX. The greater the slope, the more rapid the beat.

Please listen to the following graphs to determine which one has the greatest slope. 

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2:     MIDI     WAV
(The second graph has a greater slope)
The pitch of the drum beat indicates the curvature of the graph. The curvature is defined as the change in the slope, or d^2 Y/dX^2.

When the curvature is positive ( d^2 Y/dX^2 > 0), as it is for the graph of Y = X^2, the graph is bowl shaped, and is represented with a low pitched drum beat. This graph looks and sounds like the following:
Intro graph 3: X^2, positive curvature. 

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Please play this graph now.

When the curvature is negative ( d^2 Y/dX^2 < 0) as in Y = sqrt(X), the graph is hat, or hill shaped. This type of graph has a high pitched drum beat. This graph looks and sounds like the following:
Intro graph 4: sqrt(X), negative curvature. 

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Please play this graph now.

When there is no curvature ( d^2 Y/dX^2 = 0), as was seen in the linear graphs above, (remember, the graph can still have a non-zero slope) the pitch of the drum beat is between those of the positive or negative curvature graphs.

If you would like to see and hear more examples, please go to the Sonitype page.
If this method of auditory graphing is clear, you're ready to

Start the Test