2:3:4 Harmony within the tritave
In the Pythagorean tuning system, the fifth is used to generate a scale of 12 notes per octave. In this paper, we use the octave to generate a scale of 19 notes per tritave; one can play this scale on a traditional piano. In this system, the octave becomes a proper interval and the 2:3:4 chord a proper chord. We study harmonic properties obtained from the 2:3:4 chord, in particular composition elements using dominants, inversions, major and minor chords, and diminished chords. The Tonnetz (array notation) turns out to be an effective tool to visualize the harmonic development in a composition based on these elements. 2:3:4 harmony may sound pure, yet sparse, as we illustrate in a short piece.
Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective
The papers collected in this issue represent an emerging species of transformational theory drawn together under the Neo-Riemannian designation. This introductory essay sketches the origins and recent development of neo-Riemannian theory, and positions it with respect to several other genera of music theory, as well as to an evolving post-structuralist critical practice. Along the way, it seeks to situate Hugo Riemann amidst the flurry of activity occuring beneath the banner bearing his name, and to provide comfort to the perplexed observer who, innocently prying apart these covers and peering within, spies the theoretical tradition of A. B. Marx and Oettingen romping merrily with that of Babbitt, Forte, and Morris. Strange fellows indeed! ... or perhaps, upon reflection, not so strange....
The Rāgs of North Indian Music: Their Structure and Evolution
more significant than those of the previous IFMC Journal. The Council, the editor, and the publisher are to be congratulated on an important contribution to ethnomusicology. Although space does not permit a total listing of the contents, some of the most valuable papers in the 1969 volume, in this writer's opinion, include a concise and informative history of the IFMC by Maud Karpeles, the Council's guiding spirit for a quarter of a century; "The Value of Music in Human Experience," a "think-piece" by John Blacking; "The Russian Protiazhnaia," a posthumously published paper by the late Viktor M. Beliaev, pioneer scholar in Russian folk music; and detailed studies of scale structure in Maori music by Mervyn McLean and in South and Central American Indian music by Luis Felipe Ramon y Rivera. Different aspects of folk music's role in contemporary society are investigated in several articles. The 1970 volume contains more papers of shorter length, most of which center upon the understanding of cultural change through music and the interrelationship between various music repertories and strata of music cultures in Western and non-Western societies. Of special interest are Balint Sarosi's "Gypsy Musicians and Hungarian Peasant Music," Archie Green's "Hear These Beautiful Sacred Selections," and Akin Euba's "New Idioms of Music-Drama among the Yoruba." Indeed, the 1970 volume could well serve as a textbook for a study of recent change and adaptation in the traditional music cultures of the world. In this respect, a comparison with the early issues of the IFMC Journal is appropriate: The folk music scholar of the past lamented the demise of traditions that he regarded as stable until "contaminated" by Western and other outside forces; now, he recognizes that change has always been present, though often unrecorded, and tries to understand the nature of folk tradition through the transformations it undergoes today.-Bruno Nettl, Chairman of the Division of Musicology, Professor of Music and Anthropology, University of Illinois, Urbana.