Carlton Gamer (born February 13, 1929 in Chicago, Illinois) is an American composer and music theorist. He has taught at Colorado College, Princeton University, and the University of Michigan. He studied at Northwestern University and Boston University and privately with Roger Sessions.
Gamer has composed more than seventy works in a variety of categories, including songs, music for dance, solo piano pieces, chamber music, choral works, orchestral works, and computer music.
His music has been featured in New York’s Carnegie Recital Hall (now Weill Recital Hall), the Kennedy Center in Washington, D.C., the Los Angeles County Museum of Art, and in some sixty other venues throughout the U.S. Among its presenters have been the International Society of Contemporary Music, the Society of Composers, Inc., the Current and Modern Consort of the University of Michigan School of Music, the College Music Society, and the John F. Kennedy Center for the Performing Arts—Rockefeller Foundation International Competition for Excellence in the Performance of American Music.
His works have been heard at conferences and festivals in the U.S., among them the WNYC American Music Festival, San Diego International Computer Music Conference, Southwestern Composers Conference, Grand Teton Music Festival, Colorado Contemporary Music Festival, Colorado College Summer Music Festival, and Colorado College New Music Symposium.
Gamer grew up in Champaign-Urbana, Illinois, where his father taught at the University of Illinois, and where at the age of eight he began to study piano with Tanya Kessler and composition with her husband Hubert Kessler, of the faculty of the University of Illinois School of Music, who had been a student of Heinrich Schenker.
From 1942 to 1946 he attended University High School, a laboratory school of Illinois State Normal University (now Illinois State University) in Bloomington-Normal, Illinois, during which time he continued his piano studies with two members of the faculty of Illinois Wesleyan University, first with Stefan Bardas and then with Chester Barris. In 1946 he graduated from University High School as valedictorian.
He went to Northwestern University (B.Mus., 1950), studying theory and composition with Frank Cookson and Anthony Donato and piano with Louis Crowder and Pauline Manchester Lindsey; and Boston University (M.Mus., 1951), studying composition with Gardner Read and musicology with Karl Geiringer. At Boston University he was a graduate assistant, teaching a course in orchestration, and served as research assistant for Read’s Thesaurus of Orchestral Devices.
In New York, 1951-3, he founded a workshop of composer-performers ("The Seven") who met regularly at his home to read through and critique each other’s music; they occasionally performed in public. The members were Sheldon Harnick, violin; Gerard Jaffe, viola; Juliette White, cello; Robert Dorough, recorder, flute, and piano; Eric Katz, recorder, Noel Stevens, clarinet, and himself, piano.
After studying composition privately with Roger Sessions in Princeton, N.J. in 1957, he was invited to be a fellow at the Princeton Seminars in Advanced Musical Studies in 1959 and 1960. His recollection of these seminars is found in his article, ”Milton at the Princeton Seminars.” (See Publications).
He taught at Princeton University as a Visiting Lecturer in Music in 1974, and as a Visiting Professor of Music in 1976 and again in 1981. In 1976 he was appointed a Senior Fellow of the Council of Humanities at Princeton. In the same year, he received a MacDowell Colony Fellowship.
In 1979 he taught at the Salzburg Global Seminar: “Musical Ideas and Musical Institutions” (Session 189) in Salzburg, Austria, with co-faculty Edward Cone, Ruth Katz, Gunther Schuller, Leo Treitler, and Peter Westergaard.
Glenn Giffin in the Denver Post describes Gamer as proposing in Arkhê “a grand program--creation and evolution...The composer uses various means to present this:...by bands of sound and much shifting back and forth between sections in orchestral drones with now one section and then another receiving prominence...[and] through musical cells that get manipulated and expanded to form a large structure.”  According to the American Record Guide "Carlton Gamer's Arkhê freely moves between the poles of tonality and atonality...[its] harmonies [are] often dense to the point of clusters."  Fanfare remarks that, "[This] work opens with a long crescendo on the note A (for Alpha, …) and soon erupts into a Big Bang of fascinating noises." The composer himself describes this piece as using "an externally imposed scheme to derive the duration of each section of the work, [based] upon the miniaturization of a geological time-scale formulated by recent scientific research." 
An evolutionary idea also informs Gamer’s Choros, as described by Mark Arnest in the Colorado Springs Gazette Telegraph: In Part 1 of this work, Bios, the underlying program deals with the evolution of life; in Part 2, Choros, the evolution of humankind. Bios employs phonemic choral Sprechstimme; Choros instantiates stages in the evolution of vocal polyphony from the Mediaeval era to the present.
Nicholas Kenyon in The New Yorker characterizes “Quietly, with feeling” as “a diatonic piece of neo-Mendelssohnian rhapsody. It managed to sound fresh and new; an old language was used, for once, not with purely nostalgic intent.” 
Music critic Gilbert Johns, quoted in the Colorado Springs Gazette Telegraph, “lauds Gamer’s innovative approach to composition, which embraces atonalism and its 12-tone variation, known as serial music. ‘His technique is to rearrange ingeniously what he calls “little pitch cells” into melodic and harmonic entities. He thinks of himself as a composer who has internalized serial technique and given it his own voice...[Thus] he tries to create tonal-sounding music that is serially structured and that gives a richness to the listener’s experience.” 
Edward Rothstein in The New York Times finds in Gamer’s Piano Râga Music “wit merged with severity.”  Reviewing a later performance of the same work, Paul Griffiths in The New York Times describes Piano Râga Music as “hesitating between the worlds of its two dedicatees, Ravi Shankar and Milton Babbitt, before plunging into an immense, flamboyant mix.” 
Gamer himself, in his article “ET Setera” (p. 60), writes of his “interests as a composer of music in ETS 12”—i.e., the twelve-tone equal-tempered system: “In recent years these interests have centered more and more upon the attainment in the pitch domain of a sense of ‘less-than-twelveness’ embedded in ‘twelveness.’ I have become increasingly preoccupied with the properties of certain subcollections of pitches or pitch classes chosen from the universe of pitches within our system and the relationship of such subcollections to that system.” In his “Notes on the structure of Piano Râga Music” (p. 218), for example, Gamer shows how that work employs a 24-tone set generated from a single trichord. In “Lieder to texts by Rainer Maria Rilke” he employs all-trichord sets, each containing an all-interval tetrad, enabling him to embed quotations from tonal music into the serial texture. (Regarding all-interval tetrads, see his article “Microtones and projective planes,” p. 153.) (See Publications.)
Gamer has composed music in equal-tempered systems other than ETS 12. Robin Wilson, in his Gresham College lecture on “Music and mathematics,” discusses Gamer’s use of the 31-tone equal-tempered system in ORGANUM and of the seven-point projective plane in Fanovar.
Work in music theory
As a music theorist, Gamer has published articles in a number of journals or books on such topics as electronic music, microtonality, the properties of equal-tempered systems containing more or less than twelve tones per octave, and the definition and elaboration of the deep scale property as it applies to such equal-tempered systems (see “Electronic music” and “Some combinational resources of equal-tempered systems”); definitions of the concepts of difference set, block design, and projective plane and applications of these to such equal-tempered systems (see “Deep scales and difference sets,” “Musical block designs,” and “Microtones and projective planes”); the relationship between geometrical duality and musical inversion (see “Microtones and projective planes,” pp. 156–158); invariance matrices and their application to musical composition (see “Fanfares for the common tone”); and musical metatheory, with emphasis on the notion of syntactic models and the prescriptive and postdictive relevance of these to a “theory of composition” (see “The role of the composer as theorist,” “Sketch of a foundation for music theory today,” “Music worlds,” and “Busnois, Brahms, and the syntax of temporal proportions”).
Gamer’s music-theoretical work has been cited in dictionaries and encyclopedias, including the Dictionary of Contemporary Music, Encyclopædia Britannica, Grove Music Online, and New Grove’s Dictionary of Music and Musicians. Further citations appear in Wikipedia articles on the Deep scale property, Triad (music), Trichord, Tetrad (music), Hexachord, 19 equal temperament, and Polite number.
His work has been cited in books and dissertations by Robert Morris, Andrew Mead, Timothy A. Johnson, Jack Douthett et al., and Robert Tyler Kelley, among others, and in numerous articles in a variety of journals, including Journal of Music Theory, Music Theory Spectrum, Perspectives of New Music, Music Analysis, Intégral, Music and Letters, Music Theory Online, Journal of the American Musicological Society, and College Music Symposium.
Gamer has been credited with early contributions to diatonic set theory. Morris, in his article on “Mathematics and the twelve-tone system,” writes: “While the twelve-tone system is no longer isolated from other aspects of music theory, there are many research projects that can be identified to carry on previous work. One obvious direction is to ask what happens when we change the ‘12’ in ‘twelve-tone system’? Carlton Gamer [in ‘Some combinational resources’ (1967) and ‘Deep scales and difference sets’ (1967)] was one of the first theorists to raise such issues. He showed that equal tempered systems of other moduli not only have different structures, they allow different types of combinatorial entities to be built within them.” 
Johnson terms Gamer a “precursor” in this area: “Students who wish to trace the historical development of diatonic set theory might begin with Milton Babbitt, an important american composer and theorist...Later, Carlton Gamer explored some fundamental aspects of the structure and nature of the diatonic collection--in particular, the notion of deep scales...” 
Douthett, Martha M. Hyde, and Charles J. Smith, in their “Introduction” to Music theory and mathematics, also observe that “Milton Babbitt and Carlton Gamer, among others, had noticed intriguing structural properties of the diatonic system when considered as a subset of the equal-tempered chromatic scale.” 
Gamer sometimes illustrates his theoretical ideas with short compositions, as in “Fanfare for the common tone” or “ET Setera.” Wilson Coker, in his review of the latter, writes: “Gamer’s article might almost a be a model for theorists in its subtle blend of the most abstract inquiry along with indications of useful application.” 
- Fifty pieces for solo piano, voice, chamber ensembles, or orchestra (1937-1947)
- Nocturne for cello and piano (1944, revised 1992)
- Wer nie sein brot mit Tränen ass (J. W. von Goethe,from Wilhelm Meister ) for soprano and baritone duet and piano (1945)
- "Go where glory waits thee" (Thomas Moore) for mezzo-soprano and piano (1945)
- "Reverie" (Langston Hughes) for mezzo-soprano or baritone and piano (1946)
- "Sea Charm" (Langston Hughes) for mezzo-soprano or baritone and piano (1946)
- Two songs from "A Shropshire Lad" (A. E. Housman)for tenor and piano: "Along the field as we came by" and "On your midnight pallet lying" (1946)
- "Drink in the beauty of this night" (Ream Lazaro) for baritone and piano (1946)
- Fragments for piano or harpsichord (1947, 1984)
- Barcarolle and Chaconne for piano (1947- 1949)
- Sonnet: "Oh, never say that I was false of heart" (William Shakespeare) for tenor and piano (1948, 1969)
- Two Songs to texts by Li Po for mezzo-soprano and flute: "On hearing the flute at Lo-Cheng one spring night” (1948, 1990) and "In the mountains" (1990)
- "After two years" (Richard Aldington) for tenor and piano (1949)
- Song: "A dream of death" (William Butler Yeats) for baritone or mezzo-soprano and piano (1949)
- String Quartet (1950, revised and re-entitled Between Heaven and Earth, 2012)
- Pastorale for flute, clarinet, and strings (1950-51)
- Fantasy for Orchestra (1951, revised and re-entitled Generation, 2012-13)
- Conversation for flute (or recorder) and piano' (1952)
- Serenade for flute, violin, and clarinet (1952, revised 1964)
- Theme and Variations for Clarinet and Piano (1953)
- Fantasy for Flute, Clarinet, and Piano (1953)
- Aria da Capo (composition for dance with narrator) (text by Ilka Suarez and Carlton Gamer, after Edna St. Vincent Millay’s play) (1953, revised 1986)
- The Block Dwellers for piano (composition for dance) (1954)
- Dance for Three Couples--for Violin, Clarinet, and Piano (composition for dance) (1954)
- Two Things (Neo-Platonic Soliloquy) (Donald Babcock) (a cappella choir) (1957, revised 1988)
- Three Haiku by Bashô (a cappella choir). The Colorado College Music Press (1958)
- Rhyme from Grandma Goose (Annamarie Ewing) for tenor and piano (1958)
- Three songs for soprano and piano (1958):
- Each more melodious note I hear (H. D. Thoreau)
- o sweet spontaneous earth (e. e. cummings)
- Passing” (Lillian de la Torre, from Guillaume Apollinaire)
- Carol: Lo, in the silent night (Angelus Silesius) (two-voice a cappella) (1959)
- Duetude for flute and clarinet (1959, revised 1998)
- Sonata for Violin and Piano (1959-1960)
- Octet for String Quartet and Wind Quartet (1960)
- Sonata Breve for piano (1961)
- Canonettes for keyboard, or clarinet (or viola) and cello (or bassoon) (1962, revised 1992)
- Piano Râga Music (for Milton Babbitt and Ravi Shankar) (1962, 1967,1970).
- Laudate Dominum: Psalm 116, Vulgate (a cappella choir). The Colorado College Music Press (1963)
- Arkhê for orchestra (1968 / 1993)
- War is the enemy (Carlton Gamer) (rock refrain) (1968)
- Mid-century Love Letter (Phyllis McGinley) for soprano and piano (1969)
- There is a Spirit-- in memoriam A. J. Muste (James Nayler) (a cappella choir) (1970)
- Lieder for baritone voice, oboe, cello, and horn to texts by Rainer Maria Rilke:
- Liebeslied: (voice, oboe, cello) (1971)
- Herbsttag (voice, oboe, cello, horn) (1983)
- Dear Friend (Carlton Gamer) for soprano and piano (1972)
- Variation on a Thing by JKR for digital synthesis in 7-tone equal temperament (1974).
- Three Pieces From the Gardens of the West for piano:'
- Of Time Past (1978)
- Our Second Music (1978)
- Quietly, with Feeling (after Mendelssohn) (1976)
- Fanfare for the Common Tone (x3) for two trumpets (1976).
- Mondi for piano (1983)
- I’ll Remember April (after Raye, DePaul, and Johnston) for piano (April, 1987)
- New Beginnings (1987)
- Part I: ORGANUM from Canto LXXXI (Ezra Pound) for digitally synthesized voice in 31-tone equal temperament (1976)
- Part II: New Beginnings for piano and percussion (Cameo (for S. G.) for piano (1991))
- Gahu on J, K, R (for James K. Randall) for speaking chorus and African percussion ensemble (1991)
- Star in Clay (Katharine Lee Bates) for choir, brass, and timpani (1993)
- Fanovar for flute, oboe, clarinet, trumpet, trombone, violin and cello--or for digital synthesis in 7-tone equal temperament (1994) 
- For Elaine for piano (1999, 2004)
- Choros for chamber chorus, string quartet, early instruments, piano, organ, and percussion, with incidental vocal solos and speaker:(1999)
- Part I: Bios (Carlton Gamer)
- Part II: Choros (James Nayler, Anaximander Gospel of John, St. Augustine, Heloise, Dante, San Juan de la Cruz. Rainer Maria Rilke, and Anna Akhmatova) (1999)
- Quattro Voci (per Quattro Mani) (for Susan Grace and Alice Rybak) for two pianos (2009)
- Mountains and Skies (Montes et caeli): a CC fanfare for concert band (2016)
- "The New Fact and the Creative Life" (essay), The Colorado Quarterly, University of Colorado, Boulder (1961).
- "Some Combinational Resources of Equal-Tempered Systems", Journal of Music Theory, Vol. 11, No. 1 (Spring, 1967), pp. 32–59.
- "Electronic music," The Encyclopædia Britannica (1968 edition).
- "Flawed words and stubborn sounds: a conversation with Elliott Carter," (review essay), Perspectives of New Music, Vol. 11, No. 2 (Spring-Summer, 1973)
- "Notes on the structure of Piano Râga Music," Perspectives of New Music, Vol. 12, No. 2 (Spring-Summer, 1974).
- "Fanfares for the common tone" (with Paul Lansky), Perspectives of New Music, Vol. 14-15, No. 1-2 (1976), pp. 228–35.
- "Sketch of a foundation for music theory today." College Music Symposium, Vol. XVII/1 (spring 1977) 153-56.
- "Et setera: some temperamental speculations," Music Theory: Special Topics, ed. Richmond Browne, Academic Press (1981), pp. 59–81. ISBN 0-12-138080-7.
- "Music Worlds," Semiotic Investigations: Proceedings of a Mellon Faculty Seminar, The Colorado College Studies 18 (1982), pp. 83–98.
- "Busnois, Brahms, and the Syntax of Temporal Proportions" (essay), A Festschrift for Albert Seay, ed. Michael Grace, Colorado College, Colorado Springs, CO (1982), pp. 201–215.
- "Musical Block Designs" (with Robin J. Wilson), Ars Combinatoria, Vol. 16-A (December, 1983), pp. 217–225.
- "Trapezoidal Numbers" (with David W. Roeder and John J. Watkins), Mathematics Magazine, Vol. 58, No. 2 (Mar., 1985), pp. 108–110.
- "Composers of the Nazi Era: Eight Portraits" (book review), Shofar: An Interdisciplinary Journal of Jewish Studies, Vol. 20, No. 3 (Spring, 2002), pp. 123–125.
- "Microtones and Projective Planes" (with Robin Wilson), Music and Mathematics, ed. John Fauvel, Raymond Flood, Robin J. Wilson, Oxford University Press (2003).
- "Milton at the Princeton Seminars" in Milton Babbitt: A Composers' Memorial; Scores and Texts in Memoriam, Perspectives of New Music Special Supplement to Vol. 49/2, and The Open Space Magazine Special Issue 14 (Spring, 2012), pp. 361–364.
- "Deep scales and difference sets in equal-tempered systems". American Society of University Composers. Proceedings, Vol. 2 (1967), pp. 113–122.
- "The role of the composer as theorist: Some introductory remarks." American Society of University Composers. Proceedings, Vol. 7 (1972), pp. 12–14.
- "Displacement as matrix and matter of twentieth century arts," in Frank Brinkhaus and Sascha Talmor, ed’s.: Memory, History and Critique. European Identity at the Millennium. Proceedings of the 6th International Society for the Study of European Ideas (ISSEI) Conference at the University for Humanist Studies, Utrecht, The Netherlands, MIT Press (August. 1996).
- Janáček, Bloch, Gamer: Violin & Piano Sonatas; Crystal Records; ASIN: B000003J5E
- MMC New Century, Vol. 13; Master Musicians Col; ASIN: B00003L9JB
- Society of Composers, Inc: View from the Keyboard; Capstone; ASIN: B00005YCDV
- Harmony for a New World; Innova; ASIN: B0002L56MO
- Gamer, Carlton. "Curriculum vitae of Carlton Gamer" (PDF). Alliance Digital Repository (ADR) of Colorado Alliance of Research Libraries. Retrieved 27 March 2014.[permanent dead link]
- "Carlton E. Gamer--Distinguished Alumni, Class of 1946". University High School. 2006. Archived from the original on 2016-03-03. Retrieved 27 March 2014.
- "The Kennedy Center".
- Howard, Malcolm (July 27, 2000). "CC's New Music Symposium highlights contemporary composers". Colorado Springs Independent.
- Calcutta School of Music (March 4, 2005). "Winter Concert Programme: Jazz and the blues in the Classical style". Missing or empty
- >. "About our history". University of Illinois School of Music.[permanent dead link]
- Read, Gardner (1953). Thesaurus of Orchestral Devices. New York, Toronto, London: Pitman Publishing Corporation.
- "American Music Festival". Archive for February 1952--WNYC. 1952. Archived from the original on 2014-03-27.
- Gitelman, Claudia (2001). Dancing with Principle: Hanya Holm in Colorado, 1941-1983. Boulder, Colorado: University Press of Colorado. pp. 53, 61. ISBN 0-87081-651-9.
- Lang, Paul Henry (1962). Problems of Modern Music: The Princeton Seminars in Advanced Musical Studies. W.W. Norton.
- > "Musical ideas and musical institutions". Session 189. Salzburg Global Seminar. April 22 – May 5, 1979. Retrieved 27 March 2014.[permanent dead link]
- Giffin, Glenn (November 20, 1972). "Review of Colorado Springs Symphony concert of November 16 and 17, 1972". Denver Post.
- Hicken, Stephen D (Jul–Aug 2000). "Review of Arkhé in The Newest Music I.". American Record Guide. 63 (4): 274. ISSN 0003-0716.
- "Review of Arkhé in review of MMC New Century". Fanfare. 23 (5): 265. May–June 2000.
- Arnest, Mark (April 23, 1999). "Preview of Colorado College Chamber Chorus premiere of Choros". Colorado Springs Gazette.
- Kenyon, Nicholas (December 3, 1979). "Review of Rebecca La Brecque's piano recital, Carnegie Recital Hall, November 9, 1979". The New Yorker.
- Johns, Gilbert (October 4, 1991). "Quoted in preview of Carlton Gamer's Music for Piano (1991)". Colorado Springs Gazette Telegraph.
- Rothstein, Edward (March 18, 1984). "Music: Debuts In Review". The New York Times. Retrieved 27 March 2014.
- Griffiths, Paul (April 29, 1997). "Review of Henry Martin's piano recital, Mannes College, April 25, 1997". The New York Times.
- Gamer, Carlton (July 20, 2002). "Introductory remarks to performance of "Two Lieder to texts of Rainer Maria Rilke" by Herbert Beattie". Sixth Annual New Music Symposium. Colorado College. Missing or empty
- Wilson, Robin (2006). "Yea, Why Try Her Raw Wet Hat?". The Royal Institution of Great Britain. Retrieved 27 March 2014.
- See Forte 1974.
- See Gamer and Moog n.d.
- See Higgins n.d.
- See Griffiths et al 1980
- Morris 1987: 62, 71, 329. 350-51
- Mead 1994
- Johnson 2003: 152, 162.
- Douthett et al 2008: 1, 3.
- Kelley 2005.
- Search on JSTOR
- Morris 2007: 97-98.
- Jphnson 2003: 152.
- Douthett et al 2008: 1.
- Coker (1982): 126.
- Perspectives of New Music, Vol. 49, No. 2
- OPEN SPACE Magazine, Special Issue 14, Spring 2012
- Perspectives of New Music, Vol. 12, No. 2 Spring-Summer, 1974; in American Society of University Composers Journal of Scores, Vol. 15, 1968; and by the Association for the Promotion of New Music.
- In Carlton Gamer: “ET Setera: Some temperamental speculations,” in Music Theory: Special Topics, ed. Richmond Browne, Academic Press, 1981.
- from Moments Musicaux for Roger Sessions Perspectives of New Music Vol.16, No.2, Spring-Summer, 1978)
- Perspectives of New Music, Vol. 14, No.2 / Vol. 15, No.1, Spring-Summer / Fall-Winter, 1976.
- Excerpt and analysis in Carlton Gamer and Robin Wilson: Microtones and projective planes in Music and Mathematics from Pythagoras to Fractals, Oxford University Press, 2003. (See Publications.)
American Music Festival (1952). Archive for February 1952—WNYC. 
Arnest, Mark (1999). Preview of Colorado College Chamber Chorus premiere of Choros, Packard Hall, Colorado College, April 23, 1999. Colorado Springs Gazette Telegraph, April 23. 1999.
Calcutta School of Music (2005). Winter Concert Programme: “Jazz and blues in the Classical style,” March 4, 2005.
Coker, Wilson (1982). Review of Richmond Browne, ed.: Music Theory: Special Topics (1981) in Music Theory Spectrum, Vol. 4.
Douthett, Jack; Martha M. Hyde; and Charles J. Smith, ed.’s (2008) Music Theory and Mathematics: Chords, Collections, and Transformations. Rochester, New York: University of Rochester Press. ISBN 978-1-58046-266-2.
Gamer, Carlton (2002), Introductory remarks to performance of “Two Lieder to texts of Rainer Maria Rilke” by Herbert Beattie, ’bass-baritone, et al., Sixth Annual New Music Symposium, Packard Hall, Colorado College, July 20, 2002.
Gamer, Carlton and Robert A. Moog (n.d.): “Electronic instrument,” in Encyclopædia Britannica.. <https://web.archive.org/web/20110524000948/http://www/. britannica.,com/EBchecked/topic/183802/electronic-instrument>
Giffin, Glenn (1972). Review of Colorado Springs Symphony concert of November 16 and 17, 1972. Denver Post, November 20, 1972.
Griffiths, Paul; Mark Lindley; and Ioannis Zannos (1980). “Microtone,” in Stanley Sadie, ed.: New Grove’s Dictionary of Music and Musicians, 2d edition.
Griffiths, Paul (1997). Review of Henry Martin’s piano recital, Mannes College, April 25, 1997. The New York Times, April 29, 1997.
Higgins, Paula (n.d.). “Busnoys, Antoine,” in Grove Music Online. 
Howard, Malcolm (2000). “CC’s New Music Symposium highlights contemporary composers,” Colorado Springs Independent, July 27, 2000
Johns, Gilbert (1991). Quoted in preview of Carlton Gamer’s Music for Piano (1991), Packard Hall, Colorado College, October 6, 1991. Colorado Springs Gazette Telegraph, October 4, 1991.
Kelley, Robert Tyler (2005): "Mod-7 transformations in Post-Functional Music" (dissertation). Florida State University.
“The Kennedy Center” (n.d.). <http://www.kennedy-center.org/about>
Kenyon, Nicholas (1979). Review of Rebecca La Brecque’s piano recital, Carnegie Recital Hall, November 9, 1979. The New Yorker, December 3, 1979.
Lang, Paul Henry, ed. (1962). Problems of Modern Music: The Princeton Seminars in Advanced Musical Studies, W.W. Norton.
Morris, Robert (2007). “Mathematics and the Twelve-Tone System,” Perspectives of New Music, Vol. 45, No. 2, Summer 2007, pp. 97–98.
Read, Gardner  . Thesaurus of Orchestral Devices, New York, Toronto, London: Pitman Publishing Corporation.
Review of Arkhé (2000a), in review of MMC New Century, Vol. 13 (see Discography). American Record Guide, July–August. 
Review of Arkhé (2000b), in review of MMC New Century, Vol. 13 (see Discography). Fanfare, May–June.
Rothstein, Edward (1984). “Debuts in review,” on Robert Shannon’s League-ISCM piano recital, Carnegie Recital Hall, March 15, 1984. The New York Times, March 18, 1984.
University of Illinois School of Music (n.d.). “About our history.” .
Wilson, Robin (2005). “Music and mathematics,” Gresham College Lecture, The Royal Institution of Great Britain, March 18, 2005.