The title signifies the fact that the thematic material consists of three melodies originating from native-American tribes of northern Mexico.
The Sinfonía india was begun in December 1935, during the composer's first tour of the United States as a conductor, and finished early in the following year.
The percussion section originally included a large number of indigenous Mexican instruments, for example the jicara de agua (half of a gourd inverted and partly submerged in a basin of water, struck with sticks), güiro, cascabeles (a pellet rattle), tenabari (a string of butterfly cocoons), a pair of teponaxtles, tlapanhuéhuetl, and grijutian (string of deer hooves).
When the score was published, the composer substituted their nearest equivalents in commonly used orchestral percussion, but requested that the originals be used wherever possible.
[1] The composer regarded this as a condensation of the traditional three-movement variety of the symphony, in which a third theme takes on the function of a slow movement.