Density 21. 5 is a piece of music for solo flute written by Edgard Varèse in 1936 and revised in 1946. The flute is a Musical instrument of the Woodwind family Unlike other woodwind instruments a flute is a Reedless wind instrument that produces its WikipediaWikiProject Composers#Lead section --> Edgard Victor Achille Charles Varèse, whose name was also spelled Edgar Varèse 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. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Platinum (ˈplætɪnəm is a Chemical element with the Atomic symbol Pt and an Atomic number of 78 5 grammes per cubic centimetre (Chou, 1994).

All Music Guide'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. In Music, a melody (from Greek μελῳδία - melōidía, "singing chanting" also tune, voice, or In Music, a scale is an ordered series of Musical intervals which along with the key or tonic, define the pitches However mode In Music, a theme is the initial or primary Melody. The Encyclopédie Fasquelle (Michel 1958–61 defines a theme as follows "Any 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. In Music, a register is the relative "height" or range of a Note, set of pitches or Pitch classes Melody In Music, polyphony is a texture consisting of two or more independent Melodic voices, as opposed to music with just one voice ( Monophony "^[1]

George Perle (1990) analyses the piece both harmonically and motivically, and describes its background structure. George Perle (born May 6, 1915 in Bayonne New Jersey) is a Composer and music theorist. In Western music, harmony is the use of different pitches simultaneously and chords actual or implied in Music. In Music, a motif or motive is a perceivable or salient recurring fragment or succession of notes that may be used to construct the entirety or parts Formally he says the piece is in two parts of nearly about length, with the end of the first section being bars 24-28 (p. The term musical form refers to two related concepts the type of composition (for example a musical work can have the form of a Symphony, a 77). The piece uses interval cycles, "inherently non-diatonic symmetrical elements. In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or " (p. 83) The opening ten bars outline a tritone, c#-g, further divided into minor thirds, by e, with the upper minor third differentiated by a passing tone, f# between e-g, lacking in the lower minor third, c#-e. The tritone ( Tri - or three and tone) is a Musical interval that spans three whole tones. A minor third ( is the smaller of two commonly occurring musical intervals compounded of two steps of the Diatonic scale. A nonchord tone, nonharmonic tone, or non-harmony note is a note in a piece of Music which is not a part of the chord that is formed 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. In Music theory, a diminished seventh ( is an interval encompassing nine Semitones or a particular chord containing this interval In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical In Music using the Twelve tone technique derivation is the construction of a row through segments In Music, an octave ( is the the use of which is "common in most musical systems Alexander Nikolayevich Scriabin (Алекса́ндр Никола́евич Скря́бин Aleksandr Nikolaevič Skrjabin; sometimes transliterated as Skriabin The Second Viennese School is the term generally used in English -speaking countries to denote the group of Composers that comprised Arnold Schoenberg At the turn of the 20th century classical music was characteristically late Romantic in style while at the same time the Impressionist movement spearheaded by Claude Debussy The common practice period, in the history of European Art music (broadly called Classical music) spanning the Baroque, Classical, and " (p. 12)

He continues later, "the concept of the perfect fourth or fifth as a referential interval relative to which the tritone requires resolution. The perfect fourth () is a Musical interval which spans four scale degrees The perfect fifth ( is the Musical interval between a note and the note seven Semitones above it on the musical scale . . has no relevance at all to Density 21. 5. " (p. 17) However, there is still is some reference point, first in the differentiated minor third, c#-(e-f#-g)-bb, the second tritone created by C3₁, e-bb, C6₄, is hierarchically related to the c#-g tritone, C6₁. @@@ main@@@ - title Hierarchy@@@ keywords structure; sociology; information@@@ review@@@ - Thus regristral placement is taken into consideration, creating pitches rather than pitch classes. Pitch represents the perceived Fundamental frequency of a sound In Music, a pitch class is a set of all pitches that are a whole number of Octaves apart e "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. Ambiguity (Am-big-u-i-ty is the property of being ambiguous, where a Word, term notation sign Symbol, Phrase, sentence, or any This is what the composition is about. " (p. 71)

The piece proceeds to outline new tritones, d-g#, d#-a, and then pauses, in measure 13-14, bb-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. " (p. 74-75) He sees the close of the first section as the attainment of the e-c# missing from the e-g of bars 13-17. However, the b which divides g#-d require an f, "if we assume that the g#-b-d collection represents an incomplete diminished-7th chord, that the work is based on structural relations derived from the interval-3 cycle, and that this implies a tendency for each partition of the cycle to be completely represented. " (p. 77)

From the second beat of bar 56 till the end, however, the piece uses an interval-2 cycle, C2, which still produces tritones, but partitions them differently. e-bb is paired with d-(g#) and c-f#, rather than c#-g. The only odd interval (outside the interval-2 cycle) is the f#-c#, "which transfers us from C2₀ to C2₁. And here, in the last two notes of Density 21. 5 we at last find b paired with its tritone associate. . . only as a consequence of an entirely new harmonic direction that the work takes in its closing bars. " However, "the music of the 'common practice' offers many exemplars of such altogether unexpected digressions just as a work is drawing to its close, followed by a return, for the final cadence, to a consequently more emphatic confirmation of the structural relations implied in the body of the work. The common practice period, in the history of European Art music (broadly called Classical music) spanning the Baroque, Classical, and " (p. 79-80)

In the foreground, the head motiv, presumably Varèse's atonal "idea", does not contain a minor third or tritone, and thus each pitch, f-e-f#, is a member of a different interval-3 cycle or diminished-7th chord. The structural importance of each pitch is then dependent on its context, at which level it partitions the octave, the tritone which divides the octave, the minor third which divides the tritone, the major second which divides the minor third, the minor second which divides the major second. "This variable relation of the basic motive of Density 21. 5 to the harmonic structure of the piece, and its function in articulating and clarifying the formal design, are exactly what we would expect and take for granted in the relation between motive and background in traditional tonal music. " (p. 108-109)

Defined by the head motif and its repetition in bar 3, is "characterized by its relative pitch content (a three-note segment of the semitonal scale), by its interval order--down a half step and up a whole step--and by its rhythm (two sixteenth-notes on the beat followed by a tied eighth-note). This definitive version of the motive, combining all three attributes, occurs at only three different points (not counting the repetition in bar 3), each initiating a new and major formal subdivision of the piece. " (Perle, 1990)

Three complete motif occurrences, measures marked above (Perle, 1990)

Timothy Kloth (1991, p. 2) interprets the head-motive or, "the molecuar structure around which the entire composition is cast," as being the five-pitch-class motive which opens the piece, f-e-f#-c#-g. This is divided into two trichords, cell X, also Perle's head-motif, f-e-f#, and cell Y, f-c#-g.

George Perle and Marc Wilkinson, in writing, and Harvey Sollberger, in recording, all interpret the fourth note in bar twenty-three as a b natural. George Perle (born May 6, 1915 in Bayonne New Jersey) is a Composer and music theorist. Harvey Sollberger (b Cedar Rapids, Iowa, 1938) is an American composer flutist and conductor specializing in Contemporary classical music

The piece has been recorded and released on:

• Edgard Varèse: The Complete Works (1994/1998). Performed by Jacques Zoon. Decca London Polygram 289 460 208-2. Assistance and advised from Professor Chou Wen-chung, who worked closely with Varèse. Chou Wen-chung ( 周[[wikt
• Harvey Sollberger

References

1. ^ All Music Guide, Sean Hickey

• Perle, George (1990). Harvey Sollberger (b Cedar Rapids, Iowa, 1938) is an American composer flutist and conductor specializing in Contemporary classical music The Listening Composer. California: University of California Press. ISBN 0-520-06991-9.
• Kloth, Timothy (1991). "Structural Hierarchy in Two Works of Edgard Varèse: Écuatorial and Density 21. 5, Contemporary Music Forum Vol. 3.
• Marc Wilkinson. "An Introduction to the Music of Edgard Varese", The Score and I. M. A. Magazine 19 (1957):17

Listening

• Density 21.5: John McMurtery, flute