The two volumes of The Music of James Tenney provide comprehensive overviews of multiple elements of sound organisation that characterise Tenney’s music, matched by expertly crafted summaries of his theoretical writing. Engaging simultaneously with parallel threads of investigation, Tenney explored connections between acoustics, perception and music history. As author Robert Wannamaker (composer, musician, theorist and writer) points out in his preface, Tenney’s music emphasises the integration of theoretical investigation with the experience of sound.
Wannamaker’s first volume outlines periods of Tenney’s music under chapter headings such as ‘Computer Music and Ergodicity (1961–64)’, ‘Performance and the Social (1964–68)’ and ‘Spectra and Diaphony (1994–2006)’, each chapter examining elements of Tenney’s music during a time period identified by common factors. Parallel biographical summaries place the evolution of Tenney’s creative intentions in the context of his professional and social life. The second volume, conceived as a reference work, provides analyses of compositions not addressed in the first volume. Explanations of each composition place the music in historical context, illustrated by score excerpts and diagrams. Chapter headings are identical in both volumes, facilitating investigations into the music of specific time periods.
Tenney’s music frequently engages performers as participatory interpreters, asked to highlight changing elements heard within a composition. The skill and attention required of musicians can be challenging, as instructions to performers sometimes describe unusual methods of interpreting notation, specific ways of responding to sound, and unfamiliar instrumental techniques, each of which brings subtle details into the foreground of listeners’ experience. For musicians learning to perform Tenney’s music, Wannamaker’s explanations are invaluable. The abundant illustrations, which include score excerpts and diagrams, many of the latter created by Wannamaker, clarify structural foundations of the music and elements of pitch organisation. The combination of both volumes includes analyses of all Tenney’s mature compositions.
For two related compositions, In a Large, Open Space (1994) and In a Large, Reverberant Space (1995), both for 12 or more sustaining instruments, musicians are asked to perform overtones of a low-register pitch and to decide on the next pitch to be played without duplicating tones already sounding. Shimmering interconnecting textures of sound animate performances, subtly shifting as the performance progresses. Musicians add new pitches, enhancing harmonies perceived throughout the performance. The one-page scores, economical in design, introduce the complex experience of multidimensional pitch perception changing through time, bringing listeners’ attention to dissonant pitch relationships among higher harmonics. Wannamaker’s four pages of explanation outline perceptual elements that emerge throughout, pointing out that these pieces have been described as ‘performed sound installations’. Such detailed discussion provides contextual information helpful to musicians preparing future performances.
1. Honouring earlier composers
Tenney formally acknowledged composers whose innovative music most influenced his own, extending their musical concepts through his own compositions as forms of homage. Wannamaker’s discussion provides detailed perspectives on a multiplicity of musical influences including Webern, Ruggles, Ives, Cage and filmmaker Stan Brakhage. Pieces by Tenney that indicate a composer’s name in the title include Phases for Edgard Varèse (1963), Quiet Fan for Erik Satie (1970–71), Seegersong #1 and Seegersong #2 (1999), and Song ’n’ Dance for Harry Partch (1999). The chapter entitled ‘Canons and the Harmonic Series, 1972–1979’ describes a set of five pieces, each dedicated to other composers, including Recent Thoughts for Morton Feldman and CLOUDS for Iannis Xenakis. Additional compositions indicate dedications outside their titles, including Harmonium #1 (1976) for Lou Harrison and Chromatic Canon (1978) for Steve Reich.
2. Theoretical writing
Wannamaker’s articulate summaries of archival materials and publications clarify details of the many strands that integrate Tenney’s compositional practice with his writing on music history and theory. Key elements of his compositional innovations were developed through theoretical writing, often in response to questions that arose as new compositional directions took shape. Wannamaker’s overview demonstrates the diversity of theoretical and historical topics Tenney addressed and integrated with his music.
Tenney’s first book, META (+) HODOS began as a self-published typescript in 1961, republished in 1964 and again in 1986. Described as a phenomenology of twentieth-century musical materials and an approach to the study of form, it is available through Frog Peak Music. Tenney continued writing about musical form and perception as his explorations deepened, publishing A History of Consonance and Dissonance in 1988. His 1993 John Cage and the Theory of Harmony (both books available in PDF format through plainsound.org) connects Cage, whose music was seldom understood in the context of harmony, with a discussion that significantly broadens the meaning of the term. Tenney’s last book, From Scratch: Writings in Music Theory, edited by Larry Polansky, Lauren Pratt, Robert Wannamaker and Michael Winter, was published posthumously in 2015.
Wannamaker draws connections between Tenney’s compositions, articles and books, outlining shared contexts and providing insights and observations about the music. He skilfully summarises Tenney’s observations of structural elements that emerged in music of the twentieth century and earlier, elucidating the implications of key innovations through a phenomenological perspective. Elements of form continued to influence Tenney’s composition as he described and demonstrated concepts of perceptual proximity, harmonic distance and audible degrees of similarity that formed the foundations of his music. Wannamaker outlines elements of Tenney’s theories in the context of his compositional decisions, clearly articulating links between the music and the theoretical writing.
3. Algorithmic music
Tenney’s first compositions using algorithmic procedures to control parameters of sound through digital technology (Five Stochastic Studies, 1962) were completed soon after he joined Max Mathews and John Pierce in their psychoacoustic research at Bell Labs. Through an early algorithmic control system made available by Mathews, Tenney created a continuum of gradual statistical transitions to generate systematic organisations of sound using automated compositional processes and synthetic waveforms. With these resources, Tenney generated music of increased density and complexity, developing his interest in sound structures featuring gradual and simultaneous shifts in parallel elements of sound. Wannamaker’s outline of technologies available at Bell Labs is followed by discussion of the potential to create waveforms integrating varying levels of noise with programmed compositional forms involving statistics and probability.
Twelve years later, Tenney employed an older automated technology, a player piano, for Spectral CANON for CONLON Nancarrow (1974). The piano was tuned to the first 24 harmonics of A-55, the music moving through parallel systematic pitch patterns within this overtone series. Wannamaker provides an evocative and detailed outline of changes in harmonic perception as the piece progresses. His eight pages of descriptive text, combined with detailed graphic illustrations from the score, demonstrate among other things the formal beauty of the composition. The illustration of pitch progressions can be followed in sound and imagined as an abstract work of visual art.
4. Harmonic Space
Tenney’s concept of harmonic space pervades his later compositions. Wannamaker outlines his approach to harmony prior to his use of the term ‘harmonic space’, describing examples in which formal resources of the harmonic series were integrated within compositional structures, and noting that Tenney prioritised perceptual responses of the human auditory system over the abstract arithmetical nature of the overtone series and its acoustical properties, choosing instead to emphasise the experience of listeners. Tenney based this position on the observation that compound frequency combinations can be perceived as single tones by the human auditory system.
In Chapter Seven, ‘Interlude: Harmonic Theory’, Wannamaker provides explanations of topics contextualising music described in the chapters that follow, including ‘The Meaning of Harmony’, ‘The Harmonic Series’, ‘Interval Tolerance and the Language of Ratios’ and ‘Toneness and Harmonicity.’ Chapter Eight, entitled ‘Canons and the Harmonic Series’, discusses five key works composed between 1972 and 1979. Chapter Nine, entitled ‘Harmonic Spaces’, discusses four key works completed between 1980 and 1985.
Tenney’s A History of Consonance and Dissonance, the manuscript dated 1980, outlines changing concepts of harmony in European music, identifying five historical periods characterised by evolving concepts of consonance and dissonance, each paradigm demonstrating subtly different aspects of harmonic perception. Tenney’s analyses led to his creation of graphic representations illustrating associations among pitch ratios, which, when applied to his compositions, evolved into visual representations of three-dimensional ‘harmonic space’.
5. Bridge (1984)
Tenney’s engagement with harmonic space emerged fully with Bridge, for two re-tuned pianos, eight hands, his first algorithmic composition since the music he had created using digital technologies at Bell Labs 20 years earlier. Wannamaker points out that the composition bridges two threads of Tenney’s previous compositional practice: algorithmic organisational structures were merged with tunings defined by frequency ratios. Does this explain the title? Wannamaker also speculates that the title could imply connections among contrasting compositional strategies, such as those heard in music by Cage and Partch.
Tenney created his first harmonic space diagram for Bridge to illustrate relationships among intervals of the 22-tone just tuning. Pitch sequences of just-tuned ratios can extend throughout a theoretically infinite harmonic space, but for Bridge, Tenney mapped pitches only within the octave between 1/1 and 2/1. The organisation of pitch within harmonic space was generated digitally, then transcribed as traditional music notation. Definition of register was established by a separate element of the compositional algorithm.
Harmonic space diagrams indicate a tonic pitch with the ratio 1/1 as the central note. Frequency ratios are then added to themselves, creating horizontal and diagonal rows of same-sized intervals as points along a one-dimensional line, each sequence defining a dimension of harmonic space. The just-tuned frequency ratios for Bridge, using no prime numbers above five, are described as a five-limit tuning. Horizontally to the right of 1/1, the second ratio is the perfect fifth higher at 3/2. Each step further to the right adds the same ratio to itself, the third one being 9/8. The same process takes place in mirror image to the left, each step a fifth lower, showing ratios 4/3 and 16/9, together yielding a sequence of five perfect fifths. The second dimension is shown as an oblique line of ratios leading to the upper right, which for Bridge is the major third at 5/4, yielding the sequence 32/25, 8/5, 1/1, 5/4, 25/16. The third dimension, extending towards the upper left, is based on the just minor third at 6/5, yielding the sequence 25/18, 5/3, 1/1, 6/5, 36/25. The three pitch sequences intersect at 1/1, each indicating a different direction in harmonic space. To fill in the surrounding spaces, additional ratios are calculated by similar arithmetic processes by transposing pitch sets to begin at central ratios other than 1/1. The new ratios fill out the map, creating a two-dimensional matrix that identifies each of the 22 ratios within this three-dimensional harmonic space. For Bridge, Tenney repeated the pitch set of the central octave throughout the piano register rather than creating extended tunings for each octave.
6. Changes: 64 Studies for 6 Harps (1985)
Seventy-two equidistant pitches per octave are tuned on the harps, each harp tuned a sixth of a semitone apart. Many intervals within this tuning closely approximate frequency ratios based on prime numbers 3, 5, 7 and 11. Wannamaker provides 28 pages of explanation, outlining intricacies of pitch organisation and structural algorithms that control shifting processes that define vertical density, pitch range and other complex progressions, his explanations greatly assisting readers in conceptualising vectors of harmonic space. Changes is both Tenney’s longest composition and his most complex application of the harmonic space concept. Each study is approximately two minutes long, with a total duration of over two hours. Performances have been rare, but fortunately the two-CD recording available through New World Records (Tenney Reference Tenney2018) gives a sense of the magnitude and tone of the music.
7. Arbor Vitae (2006)
Wannamaker opens his discussion of Tenney’s last composition with these words: ‘In a stratospherically high register, faint sounds – almost as much bow noise as tone – emerge from silence like gleams of light in a vast dark space’, continuing his poetic description of the composition in palpable detail, setting the stage for his eight-page explanation illustrated by diagrams of compositional structures. Harmonic complexity is here, as in Changes, expanded to pitch classes linking frequency ratios based on 3, 5, 7 and 11. An elegant diagram demonstrates the gradual expansion as the pitch set takes the shape of a tree. The trunk, shown as 1/1 at the lower left, expands to four branches: the third, fifth, seventh and eleventh overtones. Each of these again branches three times, generating new pitch ratios, concluding with a diagonal row of 20 pitch ratios from the upper left to the lower right. As integers are multiplied, the connections among prime numbers are shown as arrow-like lines completing the branches of the tree. The symmetry and elegance of this pitch chart echo the clarity of the music.
8. Conclusions
Robert Wannamaker and his team deserve immense credit for creating this monumental integration of the many facets of Tenney’s music and writing, their daunting attention to detail lubricated by astute observation and insight. Thorough explanations of Tenney’s compositional practices provide context for deeper exploration of existing resources and enhance appreciation of Tenney’s legacy of music, books and articles. Extensive explanatory notes and references indicate the extent to which Tenney’s music and writing have stimulated discussion, and the 23 pages of references indicate the range of writers, colleagues and fellow composers who have had something to say about Tenney.
