The piece's extensive use of slow-moving string clusters prompted the composer György Ligeti to proclaim himself a "Langgaard-epigone" when presented with the score in the late 1960s.

[4][5] According to the music researcher Eric Christensen – in an analysis of works utilizing the "spatial dimension" as a fundamental concept – the space of Music of the Spheres is limited at the upper level by repeated lines of high notes on the violins and flutes, and at the lower level by timpani and deep horns.

[6][4] The following instruments and voices are positioned on-stage: In addition, several instrumentalists are positioned off-stage as the so-called "orchestra at a distance": Music of the Spheres received its premiere performance on 26 November 1921 in the Konzerthaus, Karlsruhe, Germany, with Ellen Overgaard (soprano), Badisches Landestheater-Orchester and Choir, conducted by Hans Seeber-van der Floe.

[4] The first performance in Denmark took place in 1969 in "Rundhøjhallen" in Holme with Aarhus Symphony Orchestra and Choir, conducted by Per Dreier.

[7] In 2010, Music of the Spheres received its British premiere at the BBC Proms, with the Danish National Symphony Orchestra and Choir, conducted by Thomas Dausgaard.