Coordinate Systems

4.2. COORDINATE SYSTEMS FOR SPATIAL AUDIO

To precisely specify the position of a virtual sound source relative to the listener, spatial audio systems use spherical coordinate systems centered at the midpoint between the listener’s ears:

The Three Spatial Dimensions:

1. Azimuth ($\theta$): The angle in the horizontal plane, measured from the frontal line of sight ($0^\circ$).

   • $0^\circ$: Directly in front
   • $+90^\circ$: Directly to the right
   • $180^\circ$: Directly behind
   • $-90^\circ$ (or $270^\circ$): Directly to the left

2. Elevation ($\phi$): The vertical angle relative to the horizontal plane.

   • $0^\circ$: Eye level (horizontal plane)
   • $+90^\circ$: Directly overhead (zenith)
   • $-90^\circ$: Directly below

3. Distance ($r$): The radial distance between the center of the head and the acoustic source:

   • For distances beyond ~1 meter (acoustic far field), the sound pressure level decreases by 6 dB per doubling of distance ($1/r$ law).
   • For distances under 1 meter (near field), ILD cues increase dramatically, especially at low frequencies, creating strong proximity effects.