Minimalism

Minimalism began in the USA in the 1960s.
Key composers include Terry Riley, whose In C (1964) is made of 53 short phrases; Steve Reich (born 1936); Philip Glass (born 1937); and John Adams.
The music is built from short repeated patterns called cells or loops, with very gradual change.

Repetition and ostinato: short cells repeat many times.
Layering: new parts are added one at a time, building up the texture.
Phasing (Reich): two parts play the same pattern, and one gradually moves out of step and later back in. In Reich's Clapping Music (1972), one performer keeps a pattern while the other shifts it by one quaver at a time, until they meet again.
Additive process (Glass): notes are added to a pattern one at a time (and subtractive takes them away).
Metamorphosis: a pattern changes gradually, one note at a time.
Harmony often changes slowly and stays consonant.

Minimalism has influenced film scores, electronic and dance music, and pop.
Music technology made it easier: Reich's early phasing pieces used tape loops, and today a DAW makes looping and layering simple.
To compose a minimalist piece: write a short cell, layer ostinatos, and change one thing at a time.