Harmonium #5


Harmonium #5 is a canon (at the fifth) in three voices. It has the rhythmic structure 5,3, 1 3/4, 1 1/4 (expressed in number of measures of 4/4), or 20, 12, 7, 5 (in quarter notes). This structure is expressed at the next higher level, as well, as 5, 3, 3 (11-bar segments). The rhythmic structure at the larger level is articulated as follows:  five 11-bar segments, during which the voices enter, one by one, the dynamic level increases from p to f, and the temporal density increases from very low through eighth-notes to groups of 2+3+4 per quarter-note; three 11-bar segments during which the dynamic levels and temporal density remain constant (the only changes in these parameters being in their distribution among the three voices); finally, three more 11-bar segments during which the dynamic levels and temporal density decrease again. This is subdivided into two "sub-sections" by changes of temporal density (more precipitously than such changes had occurred before). The harmonic progression — as in all the Harmonia — is a "circle of 5ths".  In this case, the "circle" is incomplete, dissolving into an arpeggiated chord of super-imposed fifths after ten of the twelve chromatic degrees in the cycle have been expressed (E-A-D-G-C-F-Bb-Eb-Ab-Db).

Harmonium #5 was commissioned by the Ontario Arts council for the Array Ensemble in Toronto.

James Tenney CA/US

James Tenney (1934–2006) was born in Silver City, New Mexico, and grew up in Arizona and Colorado, where he received his early training as a pianist and composer. He attended the University of Denver, the Juilliard School of Music, Bennington College, and the University of Illinois. His teachers and mentors have included Eduard Steuermann, Chou Wen-Chung, Lionel Nowak, Carl Ruggles, Lejaren Hiller, Kenneth Gaburo, Edgard Varèse, Harry Partch, and John Cage. A performer as well as a composer and theorist, he was co-founder and conductor of the Tone Roads Chamber Ensemble in New York City (1963–70). He was a pioneer in the field of electronic and computer music, working with Max Mathews and others at the Bell Telephone Laboratories in the early 1960s to develop programs for computer sound-generation and composition. He has written works for a variety of media, both instrumental and electronic, many of them using alternative tuning systems. He was the author of several articles on musical acoustics, computer music, and musical form and perception, as well as two books: META / HODOS: A Phenomenology of 20th-Century Musical Materials and an Approach to the Study of Form (1961; Frog Peak, 1988) and A History of ‘Consonance’ and ‘Dissonance’ (Excelsior, 1988). He received grants and awards from the National Science Foundation, the National Endowment for the Arts, the Ontario Arts Council, the Canada Council, the American Academy and Institute of Arts and Letters, the Fromm Foundation, the Deutscher Akademischer Austauschdienst, and the Jean A. Chalmers Foundation. He taught at the Polytechnic Institute of Brooklyn, the University of California, and at York University in Toronto, where he was named Distinguished Research Professor in 1994. His last position was the Roy E. Disney Family Chair in Musical Composition at the California Institute of the Arts. His music is published by Sonic Art Editions and the Canadian Music Centre, and is distributed by them and by Frog Peak. Recordings are available from Artifact, col legno, CRI, Hat[now]ART, Koch International, Mode, Musicworks, New World, Nexus, oodiscs, SYR and Toshiba EMI, among others.

James Tenney