Graphic notation

Abstract: There are many books on counterpoint and harmony, but few indeed on the theory of rhythm. Those few approach it through its graphic notation, or in terms of metrical feet, as if it were poetry. Maury Yeston treats rhythm instead in the context of sounded music, with a view to clarifying its ambiguous and little studied, but crucial, relationship with pitch. Although his work is strongly influenced by the methods of the German theorist Heinrich Schenker, it is a strikingly original contribution to musical theory in its own right. Maury Yeston begins by developing analytic procedures for understanding the rhythm of tonal music in terms of pitch levels. He then focuses on certain structures that arise from the interaction of these levels, thereby discovering some fundamental aspects of logical form in the system of musical rhythm. In the course of the inquiry, Mr. Yeston redefines traditional notions of meter, syncopation, and accent. In addition, his study provides a basis for understanding the relationships by which unique rhythmic designs are integrated aesthetically in a cohesive musical composition.

Abstract: John Cage (1912–1992) was without doubt one of the most important and influential figures in twentieth-century music. Pupil of Schoenberg, Henry Cowell, Marcel Duchamp, and Daisetz Teitaro Suzuki, among others, he spent much of his career in pursuit of an unusual goal: ‘giving up control so that sounds can be sounds’, as he put it. This book celebrates the richness and diversity of Cage’s achievements - the development of the prepared piano and of the percussion orchestra, the adoption of chance and of indeterminacy, the employment of electronic resources and of graphic notation, and the questioning of the most fundamental tenets of Western art music. Besides composing around 300 works, he was also a prolific performer, writer, poet, and visual artist. Written by a team of experts, this Companion discusses Cage’s background, his work, and its performance and reception, providing in sum a fully rounded portrait of a fascinating figure. Contents List of illustrations; Notes on contributors; Preface; Acknowledgements; Chronology; Part I. Aesthetic Contexts: 1. Cage and America David Nicholls; 2. Cage and Europe Christopher Shultis; 3. Cage and Asia: history and sources David W. Patterson; Part II. Sounds, Words, Images: 4. Music I: to the late 1940s David W. Bernstein; 5. Words and writings David W. Patterson; 6. Towards infinity: Cage in the 1950s and 1960s David Nicholls; 7. Visual art Kathan Brown; 8. Music II: from the late 1960s William Brooks; Part III. Interaction and Influence: 9. Cage's collaborations Leta E. Miller; 10. Cage and Tudor John Holzaepfel; 11. Cage and high modernism David W. Bernstein; 12. Music and society William Brooks; 13. Cage and postmodernism Alastair Williams; 14. No escape from heaven: John Cage as father figure Kyle Gann; Endnotes; Bibliography; Index.

Abstract: We have developed a simple algebraic approach to music description and composition called Haskore. In this framework, musical objects consist of primitive notions such as notes and rests, operations to transform musical objects such as transpose and tempo-scaling, and operations to combine musical objects to form more complex ones, such as concurrent and sequential composition. When these simple notions are embedded into a functional language such as Haskell, rather complex musical relationships can be expressed clearly and succinctly. Exploiting the algebraic properties of Haskore, we have further defined a notion of literal performance (devoid of articulation) through which observationally equivalent musical objects can be determined. With this basis many useful properties can be proved, such as commutative, associative, and distributive properties of various operators. An algebra of music thus surfaces.