The offset phases produced by second order beats (bottom) as compared with the amplitude modulation that occurs in first order beats (top), which I first wrote about here.
American composer Maryanne Amacher created what she called "Third Ear Music", often making use of psychoacoustical effects such as second order beats and otoacoustic emissions, tiny sounds that our ears emit in response to – as well as in the absence of – sound. Second order beats play with our perception of phase, which is often used during localization to tell which direction a sound is coming from. In this case it's possible to misinterpret the tonal information of a mistuned interval as spatial information. The nature of this particular piece is such that, when played loudly in a room, it can appear to sound like a rotating tone inside each listener's head. Some people find that their perception of the melodic sequence actually changes by tilting their heads from side to side and moving around the room.
Amacher said of these compositions: "when played at the right sound level, which is quite high and exciting, the tones in this music will cause your ears to act as neurophonic instruments that emit sounds that will seem to be issuing directly from your head ... (my audiences) discover they are producing a tonal dimension of the music which interacts melodically, rhythmically, and spatially with the tones in the room. Tones 'dance' in the immediate space of their body, around them like a sonic wrap, cascade inside ears, and out to space in front of their eyes ... Do not be alarmed! Your ears are not behaving strange[ly] or being damaged! ... these virtual tones are a natural and very real physical aspect of auditory perception, similar to the fusing of two images resulting in a third three dimensional image in binocular perception ..." Note: This illusion does not work over headphones.
Recording: Dense Boogie from Sound Characters by Maryanne Amacher, Tzadik Records, 1999