Density 21.5 is a composition for solo flute written by Edgard Varèse in 1936 and revised in 1946. The piece was composed at the request of Georges Barrère for the premiere of his platinum flute, the density of platinum being close to 21.5 grams per cubic centimetre. Structure AllMusic's Sean Hickey writes, "According to the composer, Density 21.5 is based on two melodic ideas—one modal, one atonal—and all of the subsequent material is generated from these two themes. Despite the inherent limitations of writing for an unaccompanied melodic instrument, Varèse expertly explores new areas of space and time, utilizing registral contrasts to effect polyphonic continuity." George Perle analyses the piece both harmonically and motivically, and describes its background structure. Formally, he says, the piece consists of two parts of nearly equal length, the end of the first section being bars 24–28. The piece uses interval cycles, "inherently non-diatonic symmetrical elements". The opening ten bars outline a tritone, C–G, itself further divided into minor thirds (by E) with the upper minor third differentiated by a passing tone, F, that is lacking in the lower minor third. Thus the diminished seventh chord, or rather C31, interval cycle, partitions the octave, and "places Varèse with Scriabin and the Schoenberg circle among the revolutionary composers whose work initiates the beginning of a new mainstream tradition in the music of our century". He continues: "the concept of the perfect fourth or fifth as a referential interval relative to which the tritone requires resolution ... has no relevance at all to Density 21.5". However, there still is a reference point, first in the differentiated minor third, C–(E–F–G)–B. The second tritone, created by C31, E–B, C64, is hierarchically related to the C–G tritone, C61. Thus regristral placement is taken into consideration, creating pitches rather than pitch classes. "My reason for stressing this hierchical distinction between C61, and C64 is that there is a constant shifting of such distinctions, a constant reinterpretation of structural notes as passing notes and vice versa, and it is through this ambiguity, this perpetual change of function, that the composition unfolds. This is what the composition is ". The piece proceeds to outline new tritones, D–G, D–A, and then pauses, in measures 13–14, B–E, which is part of C3, "right back where he had started", however, "the relation between the two tritones of C31 becomes not less but more ambiguous". He sees the