The precedence effect is another name for the Haas effect. If delayed sounds reach the ear between 20 and 40 milliseconds after the direct sound, they are assimilated. The apparent level of the sound is influenced by the level of the delayed components.

Ah yes, but the often quoted 40ms is not absolute because the brain also takes into account direction, with two ears, so the integration falls apart. Especially prevalent in old churches with column speakers on each pillar and vertical surface. The multitude of audio paths prevents the Haas effect establishing itself. 

The Haas effect, also known as the precedence effect, is a psychoacoustic phenomenon where a sound source presented to the listener's ears with a slight time delay creates the perception of a single auditory event originating from the direction of the leading sound. This effect enhances stereo perception and spatial localization in audio reproduction.