[2] Gamer studied at Northwestern University,[2] (achieving a bachelor of music in 1950), theory and composition with Frank Cookson and Anthony Donato, and piano with Louis Crowder and Pauline Manchester Lindsey.
[3] In New York City, from 1951 to 1953, Gamer founded a workshop of composer-performers ("The Seven")[2] who met regularly at his home to read through and critique each other's music; they occasionally performed in public.
[11] 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.
"[12] Fanfare remarked 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.
Bios employs phonemic choral Sprechstimme; Choros instantiates stages in the evolution of vocal polyphony from the Mediaeval era to the present.
[17] Reviewing a later performance of the same work, Paul Griffiths in The New York Times described it as "hesitating between the worlds of its two dedicatees, Ravi Shankar and Milton Babbitt, before plunging into an immense, flamboyant mix.
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.
Robin Wilson, in his Gresham College lecture on music and mathematics, discussed Gamer's use of the 31-tone equal-tempered system in ORGANUM and of the seven-point projective plane in Fanovar.
[26]Johnson termed 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...[27]Douthett, Martha M. Hyde, and Charles J. Smith, in their introduction to Music Theory and Mathematics, also observed 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.
Wilson Coker, in his review of the latter, wrote: "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.