Density 21.5
Density 21.5 is a piece of music 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 grammes per cubic centimetre.
Allmusic's Sean Hickey says, "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 (1990) 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 (p.77). The piece uses interval cycles, "inherently non-diatonic symmetrical elements." (p.83) 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." (p.12)
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