Shoegaze generally refers to a style of music that could be said to offer certain aspects of drone and noise rock. Often a dreamy, psychedelic, distorted, wall of sound.
This style of music, it is said, was labelled
shoegaze due to the low energy, motionless way it was played live by its performers. These bands were said to almost be staring at their shoes.
Wikipedia has this to say about the movement.
The heavy use of effects pedals also contributed to the image of performers looking down at their feet (shoegazing) during concerts.
The shoegazing sound is typified by significant use of guitar effects, and indistinguishable vocal melodies that blended into the creative noise of the guitars. A lump description given to shoegazing and other affiliated bands in London in the early 1990s was The Scene That Celebrates Itself. In the 1990s, shoegazing groups were pushed aside by the American grunge movement, forcing the relatively unknown bands to break up or reinvent their style altogether. Recent times have seen a renewed interest in the genre among "nu-gaze" bands.
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Shoegaze.co.uk