Coordinate Systems

To specify the location of a sound source relative to the listener, we need a coordinate system. One natural choice is the head-centered rectangular-coordinate system shown above. Here the x-axis goes (approximately) through the right ear, the y axis points straight ahead, and the z axis is vertical. This defines three standard planes, the xy or horizontal plane, the xz or frontal plane, and the yz or median plane (also called the mid-sagittal plane). Clearly, the horizontal plane defines up/down separation, the frontal plane defines front/back separation, and the median plane defines right/left separation.

However, because the head is roughly spherical, a spherical coordinate system is usually used. Here the standard coordinates are azimuth, elevation and range. Unfortunately, there is more than one way to define these coordinates, and different people define them in different ways. The vertical-polar coordinate system (shown below on the left) is the most popular. Here one first measures the azimuth

as the angle from the median plane to a vertical plane containing the source and the z azis, and then measures the elevation

as the angle up from the horizontal plane. With this choice, surfaces of constant azimuth are planes through the z axis, and surfaces of constant elevation are cones concentric about the z axis.

An important alternative is the interaural-polar coordinate system, shown above on the right. Here one first measures the elevation as the angle from the horizontal plane to a plane through the source and the x axis, which is the interaural axis; the azimuth is then measured as the angle over from the median plane. With this choice, surfaces of constant elevation are planes through the interaural axis, and surfaces of constant azimuth are cones concentric with the interaural axis.

The vertical-polar system is definitely more convenient for describing sources that are confined to the horizontal plane, since one merely has to specify the azimuth as an angle between -180° and +180°. With the interaural-polar system, the azimuth is always between -90° and +90°; surprisingly, the front/back distinction must be specified by the elevation, which is 0° for sources in the front horizontal plane, and 180° (or -180°) for sources in the back. While that is certainly clumsy, we shall see that the interaural-polar system makes it significantly simpler to express interaural differences at all elevations.

On to Azimuth Cues Up to Psychoacoustics