A direct correspondence is demonstrated between the phenomenon of "stochastic resonance" in static nonlinear systems and the dithering effect well known in the theory of digital waveform coding. It is argued that many static systems displaying stochastic resonance are forms of dithered quantizers, and that the existence or absence of stochastic resonance in such systems can be predicted from the effects of "dither averaging" upon their transfer characteristics. Also, results are introduced regarding stochastic resonance in certain nonlinear systems with memory (e.g., hysteretic systems).
Around 1970, an unexpected but enduring preoccupation with harmony emerged in the music of James Tenney. In his consequent body of work two structural archetypes appear: a “spectralist” one arising in the early 1970s and characterized by gradual processes and reference to the harmonic series, complemented (but not supplanted) a few years later by another invoking lattice (Tonnetz) models of harmonic proximity. These categories correlate with different concepts of “consonance” and “dissonance” as articulated in Tenney’s theoretical writings, and in part reflect his effort to decompose “harmonic perception” itself into distinct facets with correspondingly distinct qualitative referents, acoustical correlates, apposite models, and historical associations. This chapter examines Tenney’s harmonic theories and illustrates their compositional expression via analyses of his just-intoned Harmonium #1 (1976) and Harmonium #3 (1978).
It is shown that quantizing systems without feedback respond to the use of particular spectrally-shaped dither signals quite diffacntly h m those with feedback paths. For each type of system, conditions are given which ensure that the quantization mor will be wide.-sense stationary with no input dependence and with a predictable power spectral density function.
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