Polytempo Music
An Annotated Bibliography

by John Greschak
john@greschak.com
June 3, 2001 - May 23, 2003
 

Polytempo music: Music in which two or more tempi occur simultaneously.
(Also called: multi-tempo, multiple tempo, poly-tempo, polytempic or polytemporal.)

Introduction
Compositions
Articles
Books, Theses and Dissertations
Works Under Consideration
Update History
Acknowledgments
 

Introduction

This is a list of polytempo music compositions, and books or articles that discuss polytempo music. The list is limited to those pieces in which the composer has notated the music by using two or more different and simultaneous tempo markings, and consequently, the duration of a given type of note (e.g. a quarter note) is not the same in all parts at some point in time. Here, "tempo marking" means a metronome marking or a tempo term (e.g. allegro or accelerando).

Pieces for which more than one tempo might be perceived but for which all parts are written against a common tempo, no tempo markings are specified, or performers are instructed to deviate freely from specified tempi (e.g. as in rubato or senza tempo), have been excluded. More specifically:

Works such as Henry Brant's American Weather and Pierre Boulez's Rituel: In Memoriam Maderna in which the same tempo marking is specified for all parts, but the parts are to be performed in an uncoordinated manner (for example, by using independent conductors), have been included. Also, works such as Charles Ives' Three Harvest Home Chorales and Symphony No. 4 (specifically, the fourth movement) where at all points in time, one tempo marking is specified that applies to all parts, but the duration of a given type of note is not the same in all parts at some point in time, have been included.

The limitations or restrictions placed on the list given here are not intended to be taken as definitive properties of the class of music that is polytempo. Instead, the imposed limitations merely reflect the interests of the author and also serve to bound the size of the list.

For additional examples of pieces where more than one tempo might be perceived but that fall outside of the scope of this bibliography, see the books Modern Rhythmic Notation by Gardner Read and Music Notation in the Twentieth Century: A Practical Guidebook by Kurt Stone.

Detailed information regarding instances of simultaneous different tempi are described in the annotations. Also, the methods by which (and the degrees to which) performers are to be coordinated or synchronized are discussed.

Compositions

Applebaum, Mark. 1995. Tlön for 3 Conductors and No Players. Arrigo, Girolamo 1963. Fluxus per Nove Strumenti. Firenze: Aldo Bruzzichelli. Arrigo-Nelson, John 2000. Temporal Quartets. Arrigo-Nelson, John 2002. Solo/Duo for Violin and Piano. Austin, Larry 1981. Canadian Coastlines: Canonic Fractals for Musicians and Computer Band. Berio, Luciano 1964. Folk Songs for Viola, Voice, Harp and Cello. London: Universal Edition. Boulez, Pierre 1974-5. Rituel: In Memoriam Maderna. London: Universal Edition. Brant, Henry 1953, revised 1968. Antiphony One for Symphony Orchestra Divided into 5 Separated Groups. New York: Carl Fischer. Brant, Henry 1954. Millenium 2. New York: Carl Fischer. Brant, Henry 1956. On the Nature of Things (after Lucretius): Spatial Tone Poem. New York: Carl Fischer. Brant, Henry 1969. Verticals Ascending: After the Rodia Towers: For Two Separated Instrumental Groups. New York: MCA Music. Brant, Henry 1973. Divinity: Dialogues in the Form of Secret Portraits for Harpsichord and Brass Quintet, Spatially Separated. New York: Carl Fischer. Brant, Henry 1974. Prevailing Winds for Invisible Woodwind Quintet, Spatially Separated. New York: Carl Fischer. Brant, Henry 1975/8. Curriculum: Spatial Tone Poem. New York: Carl Fischer. Brant, Henry 1976. American Weather: Antiphonal Motet for Two Widely Separated Choral Ensembles. New York: Carl Fischer. Brant, Henry 1976. Spatial Concerto: "Questions from Genesis" for Pianoforte Solo with Orchestra Divided into Widely Separated Groups, and Ensemble of Women's Voices (8 Sopranos, 8 Altos). New York: Carl Fischer. Brant, Henry 1977. Cerberus: after "A Report to an Academy" (Kafka) for Piccolo and Double Bass. New York: Carl Fischer. Brant, Henry 1977. American Debate: An Antiphonal Overture. New York: Carl Fischer. Brant, Henry 1978. Antiphonal Responses for 3 Bassoons, Orchestra, 8 Widely Separated Instruments and Piano Obbligato. New York: Carl Fischer. Brant, Henry 1978. Trinity of Spheres: 3 Orchestral Groups and 3 Conductors. New York: Carl Fischer. Brant, Henry 1981. Meteor Farm: A Spatial Concert of Ceremonies for Instrumental and Vocal Groups. New York: Carl Fischer. Brant, Henry 1982. Inside Track: Concerto for Solo Piano with Three Separated Instrumental Groups and Projected Images. New York: Carl Fischer. Brant, Henry 1983. Desert Forests: Spatial Panoramas for Separated Orchestral Groups. New York: Carl Fischer. Brant, Henry 1984. Orbits: Spatial Symphonic Ritual for 80 Trombones, Organ and Sopranino Voice. New York: Carl Fischer. Carter, Elliott 1951. String Quartet No. 1. New York: Associated Music Publishers. Carter, Elliott 1959. String Quartet No. 2. New York: Associated Music Publishers. Carter, Elliott 1971. String Quartet No. 3. New York: Associated Music Publishers. Colgrass, Michael 1976. Letter from Mozart for Orchestra. Carl Fischer. Constant, Marius 1968. Winds. Paris: Editions Salabert. Crumb, George 1977. Star-Child: A Parable for Soprano, Antiphonal Children's Voices, Male Speaking Choir and Bell Ringers, and Large Orchestra. New York: C. F. Peters. Ferneyhough, Brian 1969. Missa Brevis. London: Edition Peters. Ferneyhough, Brian 1969-71. Firecycle Beta: Symphonic Torso for Two Pianos and Orchestra with Five Conductors. Ricordi. Ghent, Emmanuel 1964. Triality: for Violin, Trumpet and Bassoon: in Conjunction with a Polynome: 2 Studies. Ghent, Emmanuel 1965. Dithyrambos for Brass Quintet. New York: Oxford University Press. Ghent, Emmanuel 1966. Hex: An Ellipsis for Trumpet, Instruments and Tape. Ghent, Emmanuel 1969. Helices for Violin, Piano and Tape. Greschak, John 2003. Platonic Dice: Dodecahedron: for 12 Woodwinds. Available: http://www.greschak.com/pdicedod.pdf. Henze, Hans Werner 1971. Compases para Preguntas Ensimismadas for Solo Viola and Orchestra. Mainz; New York: Schott. Hiller, Lejaren 1962. String Quartet No. 5 (in Quarter-tones). Bryn Mawr: T. Presser. Ives, Charles E. 1906. Central Park in the Dark. Hillsdale: Mobart. Ives, Charles E. 1908. The Unanswered Question for Chamber Orchestra or Chamber Ensemble. New York: Southern Music Publishing. Ives, Charles E. 1898-1912. Three Harvest Home Chorales. Ives, Charles E. 1909-16. Symphony No. 4. Ives, Charles E. 1903-14/1929. Three Places in New England (Orchestral Set No. 1). Bryn Mawr: T. Presser. Ives, Charles E. 1911-51. Universe Symphony. Ligeti, György 1962. Poème Symphonique for 100 Metronomes. Mainz: Schott. Ligeti, György 1969-70. Chamber Concerto for 13 Instrumentalists. Mainz: Schott. Ligeti, György 1983. Magyar Etüdök (Hungarian Studies) for Mixed A Cappella Choir (16 part). Mainz: Schott. Messiaen, Olivier 1987-91. Éclairs sur l'Au-Delà... (Illuminations of the Beyond) for Large Orchestra. Paris: Alphonse Leduc. Musgrave, Thea 1966. Chamber Concerto No. 2. London: Chester. Nancarrow, Conlon. Study No. 2 for Player Piano. Santa Fe: Soundings. Nancarrow, Conlon. Study No. 6 for Player Piano. Santa Fe: Soundings. Nancarrow, Conlon. Study No. 9 for Player Piano. Santa Fe: Soundings. Nancarrow, Conlon. Study No. 14 for Player Piano (Canon 4/5). Santa Fe: Soundings. Nancarrow, Conlon. Study No. 15 for Player Piano (Canon 3/4). Santa Fe: Soundings. Nancarrow, Conlon. Study No. 16 for Player Piano. Santa Fe: Soundings. Nancarrow, Conlon. Study No. 17 for Player Piano (Canon 12/15/20). Santa Fe: Soundings. Nancarrow, Conlon. Study No. 18 for Player Piano (Canon 3/4). Santa Fe: Soundings. Nancarrow, Conlon. Study No. 19 for Player Piano (Canon 12/15/20). Berkeley: Soundings. Nancarrow, Conlon. Study No. 24 for Player Piano (Canon 14/15/16). Santa Fe: Soundings. Nancarrow, Conlon. Study No. 27 for Player Piano (Canon 5% / 6% / 8% / 11%). Berkeley: Soundings. Nancarrow, Conlon. Study No. 31 for Player Piano (Canon 21/24/25). Berkeley: Soundings. Nancarrow, Conlon. Study No. 33 for Player Piano (Canon sqrt(2)/2). Santa Fe: Soundings. Nancarrow, Conlon. Study No. 35 for Player Piano. Berkeley: Soundings. Nancarrow, Conlon. Study No. 36 for Player Piano (Canon 17/18/19/20). Berkeley: Soundings. Nancarrow, Conlon. Study No. 37 for Player Piano (Canon 150 / 160-5/7 / 168-3/4 / 180 / 187-1/2 / 200 / 210 / 225 / 240 / 250 / 262-1/2 / 281-1/4). Santa Fe: Soundings. Nancarrow, Conlon. Study No. 40 for 2 Player Pianos (Canon e/pi). Berkeley: Soundings. Raxach, Enrique 1969, 1989. Inside Outside. Donemus. Reich, Steve 1967. Piano Phase for Two Pianos or Two Marimbas. London: Universal Edition. Reich, Steve 1967. Violin Phase for Violin and Pre-recorded Tape or Four Violins. London: Universal Edition. Reich, Steve 1970. Phase Patterns for Four Electric Organs. London: Universal Edition. Reich, Steve 1971. Drumming Part Two for Three Marimbas and Female Voices. Stockhausen, Karlheinz 1955-6. Zeitmasse (Time-measures) for Five Woodwinds. London: Universal Edition. Stockhausen, Karlheinz 1955-7. Gruppen (Groups) for 3 Orchestras. London: Universal Edition. Xenakis, Iannis 1969. Persephassa pour Six Percussionistes. Paris: Editions Salabert.

Articles

Austin, Larry 1985. “Charles Ives's Life Pulse Prelude for Percussion Orchestra: A Realization for Modern Performance from Sketches for his Universe Symphony.” Percussive Notes: Research Edition 23(6): 58-84. Cowell, Henry 1927. “The Impasse of Modern Music.” The Century Magazine 114(6): 671-7. Ghent, Emmanuel 1967. “Programmed Signals to Performers: A New Compositional Resource.” Perspectives of New Music 6(1): 96-106. Reprinted in Boretz, Benjamin and Edward T. Cone (Eds.) 1976. Perspectives on Notation and Performance. New York: Norton. Ghent, Emmanuel 1967. “The Coordinome in Relation to Electronic Music.” Electronic Music Review 1(1): 33-43. Greschak, John 2000. “Viewing a Finale Document on a Wearable Computer for Performance Purposes.” Finale: IWBNI Suggestion No. 644. Available: http://www.greschak.com/notation/finale/iwbni/fs644.htm. Greschak, John 2001. “The Word ‘Polytempo’.” Polytempo Music Articles. Available: http://www.greschak.com/polytempo/ptword.htm. Greschak, John 2001. “Facilitating the Performance of Polytempo Music: An Overview.” Polytempo Music Articles. Available: http://www.greschak.com/polytempo/ptperf.htm. Greschak, John 2001. “Technology-Assisted Conducting of Polytempo Music: Some Possibilities.” Polytempo Music Articles. Available: http://www.greschak.com/polytempo/pttac.htm. Greschak, John 2001. “Tempo Scales in Polytempo Music: A Survey.” Polytempo Music Articles. Available: http://www.greschak.com/polytempo/ptts.htm. Ligeti, Lukas 2000. “Beta Foly: Experiments with Tradition and Technology in West Africa.” Leonardo Music Journal 10: 41-47. Available: http://muse.jhu.edu/demo/lmj/10.1ligeti.html. Stockhausen, Karlheinz 1959. "How Time Passes." die Reihe 3 (Musical Craftsmanship): 10-40. Bryn Mawr: T. Presser. English translation of the original German version by Cornelius Cardew. Sullivan, Timothy 1997. “Multiple Tempi: A Survey and Method.” Conference of the Canadian University Music Society. Willey, Robert 2003. “An Analysis and Realization of Conlon Nancarrow's Study No. 37 for Player Piano.” Available: http://www.willshare.com/willeyrk/creative/papers/study37.

Books, Theses and Dissertations

Cole, Hugo 1974. Sounds and Signs: Aspects of Musical Notation. London: Oxford University Press. Cowell, Henry 1930. New Musical Resources. New York: Alfred A. Knopf. Epstein, David 1995. Shaping Time: Music, the Brain, and Performance. New York: Schirmir. Gann, Kyle 1995. The Music of Conlon Nancarrow. Cambridge UK: Cambridge University Press. Read, Gardner 1978. Modern Rhythmic Notation. Bloomington: Indiana University Press (1978); London: Victor Gollancz (1980). Saunders, James E. 1996. “The Final Frontier: The Development of Polytempo in the Music of Conlon Nancarrow.” Masters dissertation, Royal Northern College of Music. Stauffer, George B. 1997. The Mass in B Minor: The Great Catholic Mass. New York: Schirmer; London: Prentice Hall. Stone, Kurt 1980. Music Notation in the Twentieth Century: A Practical Guidebook. New York; London: Norton. Thomas, Margaret Elida 1996. “Conlon Nancarrow's 'Temporal dissonance': Rhythmic and Textural Stratification in the Studies for Player Piano.” Ph.D. dissertation, Yale University, UMI No. DA9632450.

Works Under Consideration

This is a list of works that are known or suspected to be suitable for inclusion in the bibliography of polytempo music given here. They are being researched.

Update History

June 3, 2001: Completed the first version of this page. Frequent updates shall be posted as works under consideration are processed and as new candidates are discovered or suggested. A backlog of such items already exists thanks to the help of Bob Kosovsky (a librarian in the Music Division of The New York Public Library) and many others on the Society for Music Theory List who have responded to a query that he posted there.

June 8, 2001: Added several works under consideration.

June 10, 2001: Added the article “Beta Foly: Experiments with Tradition and Technology in West Africa” by Lukas Ligeti and more works under consideration. Excluded mensuration canons, augmentation and diminution.

June 22, 2001: Added over a dozen entries including works by Austin (article), Berio, Boulez, Brant, Carter, Colgrass, Epstein (book), Ferneyhough, Ives, Ligeti, Musgrave, Stockhausen and Xenakis. Excluded rubato and senza tempo passages.

July 1, 2001: Added an Acknowledgments section and some works under consideration.

July 11, 2001: Added ten works by Henry Brant.

July 15, 2001: Added the article “The Word ‘Polytempo’” by John Greschak.

August 2, 2001: Added two works by Charles Ives (Three Harvest Home Chorales and Symphony No. 4), four works by Henry Brant (Verticals Ascending, Spatial Concerto, Trinity of Spheres and Orbits), Brian Ferneyhough's Missa Brevis, and Steve Reich's Violin Phase. Added Henry Cowell's article “The Impasse of Modern Music” and book New Musical Resources.

August 5, 2001: Added the article “Facilitating the Performance of Polytempo Music: An Overview” by John Greschak.

August 22, 2001: Added seventeen works by Conlon Nancarrow.

August 30, 2001: Added the article “Technology-Assisted Conducting of Polytempo Music: Some Possibilities” by John Greschak.

September 1, 2001: Added the article “Multiple Tempi: A Survey and Method” by Timothy Sullivan.

September 8, 2001: Added two works by Henry Brant (Desert Forests and Millenium 2), George Crumb's Star-Child, and Steve Reich's Drumming.

September 13, 2001: Added the article “How Time Passes” by Karlheinz Stockhausen.

September 20, 2001: Added the article “Tempo Scales in Polytempo Music: A Survey” by John Greschak.

December 17, 2001: Added György Ligeti's Poème Symphonique, Steve Reich's Piano Phase, Karlheinz Stockhausen's Zeitmasse, and Olivier Messiaen's Éclairs sur l'Au-Delà.

April 20, 2003: Added John Greschak's Platonic Dice: Dodecahedron.

April 23, 2003: Added the article “An Analysis and Realization of Conlon Nancarrow's Study No. 37 for Player Piano” by Robert Willey.

May 23, 2003: Added John Arrigo-Nelson's Temporal Quartets and Solo/Duo.

Acknowledgments

I thank the following composers for responding to my inquiries regarding their polytempo works: Emmanuel Ghent, Henry Brant, Timothy Sullivan and Evgeni Kostitsyn. Also, I thank the following individuals who have suggested works to be included in this bibliography: Bob Kosovsky, John Snyder, Stephen Taylor, Mike Baker, Zac Cairns, Robert Coburn, Mark Williams, Michael D. Golden, Eliot Handelman, Timothy Sullivan, Joseph Harris, Joshua Cohen, Emmanuel Ghent, Jonathan Dawe and John Arrigo-Nelson.