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....
Continuous calibration of a vacuum ultraviolet system from 65 to 125 nm by a cascade arc and comparison with the calibrated line radiation of a hollow cathode.
A high-power stationary helium cascade arc has been developed as a standard source for continuum radiation in the VUV spectral range from 65 to 125 nm. The calibration of the VUV system response was based on the calculated and measured continuum radiation of a 2-mmphi pure He arc. Diagnostics of the arc plasma in partial thermal equilibrium yielded the electron density and the temperature that were inserted in the calculations of the continuous radiation. The results were compared with the helium, argon, and krypton radiation lines of a high-current hollow cathode lamp. This lamp was built according to the construction drawings of a hollow cathode, which was calibrated by means of the electron synchrotron radiation at the Physikalisch Technische Bundesanstalt Berlin.