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Density 21.5

January 06, 2023

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,[a] the density of platinum being close to 21.5 grams per cubic centimetre.[1]

Edgard Varèse, 1936

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."[2]

George Perle analyses the piece both harmonically and motivically, and describes its background structure.[3] Formally, he says, the piece consists of two parts of nearly equal length, the end of the first section being bars 24–28.[4] The piece uses interval cycles, "inherently non-diatonic symmetrical elements".[5] 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".[6]

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".[7] 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 about".[8]

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".[9] 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-seventh 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".[4]

From the second beat of bar 56 until the end, however, the piece uses an interval-2 cycle, C2, which still produces tritones, but partitions them differently. E–B♭ 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."[10]

In the foreground, the head motif, 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-seventh 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 major 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."[11]

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."[12]

 
Three complete motif occurrences, measures marked above[3]

Timothy Kloth interprets the head motif or, "the molecular 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.[13]

Recordings

George Perle[12] and Marc Wilkinson[14], in writing, and Harvey Sollberger, in recording, all interpret the fourth note in bar twenty-three as a B natural.

The piece has been recorded and released on:

  • Members of the Columbia Symphony Orchestra, directed by Robert Craft – Varèse: Density 21.5, Hyperprism, Intégrales, Ionisation, Octandre, Poème Electronique (1959) CBS Masterworks – CBS 60286.
  • Severino Gazelloni, flute (1967) WERGO WER 60029, Series: Große Interpreten neuer Musik.
  • Ensemble Instrumental de Musique Contemporaine de Paris, directed by Konstantin Simonovitch – Varese: Deserts / Hyperprism / Integrales / Density 21.5 (1971) La Voix De Son Maître 2 C 061-10875 Y.
  • 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.
  • Harvey Sollberger[citation needed]
  • Philippe Bernold, Alexandre Tharaud, The Solo Flute in the 20th Century (2008), Harmonia Mundi Musique d'Abord HMA1951710
  • Claire Chase, Density (2013) New Focus Recordings[15]

Notes and references

Notes

  1. ^ The flute was a 90/10 platinum-iridium alloy with a density of about 21.6 grams per cubic centimetre. It cost US$3,750 in 1935, about US$65,000 in 2014 dollars. The flute was manufactured by Haynes Flutes. See Anon. 1941, Anon. 2018, and US CPI Inflation Calculator 2016-03-04 at the Wayback Machine

References

  1. ^ Chou 1994.
  2. ^ Hickey.
  3. ^ a b Perle 1990.
  4. ^ a b Perle 1990, p. 77.
  5. ^ Perle 1990, p. 83.
  6. ^ Perle 1990, p. 12.
  7. ^ Perle 1990, p. 17.
  8. ^ Perle 1990, p. 71.
  9. ^ Perle 1990, pp. 74–75.
  10. ^ Perle 1990, pp. 79–80.
  11. ^ Perle 1990, pp. 108–109.
  12. ^ a b Perle 1990,[page needed].
  13. ^ Kloth 1991, p. 2.
  14. ^ Wilkinson 1957,[page needed].
  15. ^ Walls 2013.

Sources

  • Anon. (May 6, 1941). "Platinum Flute at $3,750 Best, Barrere Finds". The Milwaukee Journal. Retrieved December 14, 2018.
  • Anon (2018). "Georges Barrère: NYFC President 1920–1944" The New York Flute Club, Inc. website (accessed December 14, 2018).
  • Chou, Wen-chung (1994). Edgard Varèse: The Complete Works (Media notes). Jacques Zoon. Decca London Polygram. 289 460 208–2.
  • Hickey, Sean. Edgard Varèse: Density 21.5, for Flute Solo" at AllMusic
  • Kloth, Timothy (1991). "Structural Hierarchy in Two Works of Edgard Varèse: Écuatorial and Density 21.5". Contemporary Music Forum. 3.
  • Perle, George (1990). The Listening Composer. University of California Press. ISBN 0-520-06991-9.
  • Walls, Seth Colter (2013). "Flutist Claire Chase Has Breath and Breadth in Density". Q2 Music Featured Album: WQXR website (October 14; accessed December 14, 2018).
  • Wilkinson, Marc (1957). "An Introduction to the Music of Edgard Varèse". The Score and I.M.A. Magazine. 19 (17).

Further reading

  • Babbitt, Milton (1966). "Edgard Varèse: A Few Observations of His Music". Perspectives of New Music 4, No. 2 (Spring–Summer): 14–22.
  • Bernard, Jonathan W. (1981). "Pitch/Register in the Music of Edgard Varèse". Music Theory Spectrum 3 (Spring): 1–25.
  • Bernard, Jonathan W. (1986). "On Density 21.5: A Response to Nattiez". Music Analysis 5, nos. 2–3 (July–October): 207–231.
  • Brouwer, Candace (1997–98). "Pathway, Blockage, and Containment in Density 21.5". Theory and Practice 22–23:35–54.
  • Guck, Marion (1984). "A Flow of Energy: Density 21.5". Perspectives of New Music 23, no. 1 (Autumn–Winter): 334–347.
  • Kresky, Geoffrey (1984). "A Path Through Density". Perspectives of New Music 23, no. 1 (Autumn–Winter): 318–333.
  • Marvin, Elizabeth West (1991). "The Perception of Rhythm in Non-Tonal Music: Rhythmic Contours in the Music of Edgard Varèse". Music Theory Spectrum 13, no. 1 (Spring): 61–78.
  • Nattiez, Jean-Jacques (1982). "Varèse's Density 21.5: A Study in Semiological Analysis", translated by Anna Barry. Music Analysis 1, no. 3 (October): 243–340.
  • Siddons, James (1984). "On the Nature of Melody in Varèse's Density 21.5". Perspectives of New Music 23, no. 1 (Autumn–Winter): 298–316.
  • Tenney, James, and Larry Polansky (1980). "Temporal Gestalt Perception in Music: A Metric Space Model". Journal of Music Theory 24:205–241.

External links

  • Performance of Density 21.5: John McMurtery, flute

January 06, 2023
density, composition, solo, flute, written, edgard, varèse, 1936, revised, 1946, piece, composed, request, georges, barrère, premiere, platinum, flute, density, platinum, being, close, grams, cubic, centimetre, edgard, varèse, 1936, contents, structure, record. Density 21 5 is a composition for solo flute written by Edgard Varese in 1936 and revised in 1946 The piece was composed at the request of Georges Barrere for the premiere of his platinum flute a the density of platinum being close to 21 5 grams per cubic centimetre 1 Edgard Varese 1936 Contents 1 Structure 2 Recordings 3 Notes and references 4 Further reading 5 External linksStructure EditAllMusic 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 Varese expertly explores new areas of space and time utilizing registral contrasts to effect polyphonic continuity 2 George Perle analyses the piece both harmonically and motivically and describes its background structure 3 Formally he says the piece consists of two parts of nearly equal length the end of the first section being bars 24 28 4 The piece uses interval cycles inherently non diatonic symmetrical elements 5 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 Varese 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 6 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 7 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 about 8 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 9 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 seventh 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 4 From the second beat of bar 56 until the end however the piece uses an interval 2 cycle C2 which still produces tritones but partitions them differently E B 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 10 In the foreground the head motif presumably Varese 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 seventh 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 major 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 11 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 12 Three complete motif occurrences measures marked above 3 Timothy Kloth interprets the head motif or the molecular 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 13 Recordings EditGeorge Perle 12 and Marc Wilkinson 14 in writing and Harvey Sollberger in recording all interpret the fourth note in bar twenty three as a B natural The piece has been recorded and released on Members of the Columbia Symphony Orchestra directed by Robert Craft Varese Density 21 5 Hyperprism Integrales Ionisation Octandre Poeme Electronique 1959 CBS Masterworks CBS 60286 Severino Gazelloni flute 1967 WERGO WER 60029 Series Grosse Interpreten neuer Musik Ensemble Instrumental de Musique Contemporaine de Paris directed by Konstantin Simonovitch Varese Deserts Hyperprism Integrales Density 21 5 1971 La Voix De Son Maitre 2 C 061 10875 Y Edgard Varese 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 Varese Harvey Sollberger citation needed Philippe Bernold Alexandre Tharaud The Solo Flute in the 20th Century 2008 Harmonia Mundi Musique d Abord HMA1951710 Claire Chase Density 2013 New Focus Recordings 15 Notes and references EditNotes The flute was a 90 10 platinum iridium alloy with a density of about 21 6 grams per cubic centimetre It cost US 3 750 in 1935 about US 65 000 in 2014 dollars The flute was manufactured by Haynes Flutes See Anon 1941 Anon 2018 and US CPI Inflation Calculator Archived 2016 03 04 at the Wayback Machine References Chou 1994 Hickey a b Perle 1990 a b Perle 1990 p 77 Perle 1990 p 83 Perle 1990 p 12 Perle 1990 p 17 Perle 1990 p 71 Perle 1990 pp 74 75 Perle 1990 pp 79 80 Perle 1990 pp 108 109 a b Perle 1990 page needed Kloth 1991 p 2 Wilkinson 1957 page needed Walls 2013 Sources Anon May 6 1941 Platinum Flute at 3 750 Best Barrere Finds The Milwaukee Journal Retrieved December 14 2018 Anon 2018 Georges Barrere NYFC President 1920 1944 The New York Flute Club Inc website accessed December 14 2018 Chou Wen chung 1994 Edgard Varese The Complete Works Media notes Jacques Zoon Decca London Polygram 289 460 208 2 Hickey Sean Edgard Varese Density 21 5 for Flute Solo at AllMusic Kloth Timothy 1991 Structural Hierarchy in Two Works of Edgard Varese Ecuatorial and Density 21 5 Contemporary Music Forum 3 Perle George 1990 The Listening Composer University of California Press ISBN 0 520 06991 9 Walls Seth Colter 2013 Flutist Claire Chase Has Breath and Breadth in Density Q2 Music Featured Album WQXR website October 14 accessed December 14 2018 Wilkinson Marc 1957 An Introduction to the Music of Edgard Varese The Score and I M A Magazine 19 17 Further reading EditBabbitt Milton 1966 Edgard Varese A Few Observations of His Music Perspectives of New Music 4 No 2 Spring Summer 14 22 Bernard Jonathan W 1981 Pitch Register in the Music of Edgard Varese Music Theory Spectrum 3 Spring 1 25 Bernard Jonathan W 1986 On Density 21 5 A Response to Nattiez Music Analysis 5 nos 2 3 July October 207 231 Brouwer Candace 1997 98 Pathway Blockage and Containment in Density 21 5 Theory and Practice 22 23 35 54 Guck Marion 1984 A Flow of Energy Density 21 5 Perspectives of New Music 23 no 1 Autumn Winter 334 347 Kresky Geoffrey 1984 A Path Through Density Perspectives of New Music 23 no 1 Autumn Winter 318 333 Marvin Elizabeth West 1991 The Perception of Rhythm in Non Tonal Music Rhythmic Contours in the Music of Edgard Varese Music Theory Spectrum 13 no 1 Spring 61 78 Nattiez Jean Jacques 1982 Varese s Density 21 5 A Study in Semiological Analysis translated by Anna Barry Music Analysis 1 no 3 October 243 340 Siddons James 1984 On the Nature of Melody in Varese s Density 21 5 Perspectives of New Music 23 no 1 Autumn Winter 298 316 Tenney James and Larry Polansky 1980 Temporal Gestalt Perception in Music A Metric Space Model Journal of Music Theory 24 205 241 External links EditPerformance of Density 21 5 John McMurtery flute Portal Classical music Retrieved from https en wikipedia org w index php title Density 21 5 amp oldid 1115421805, wikipedia, wiki, book, books, library,

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