Octatonicism and Chromatic Harmony

Distorted Continuity : Chromatic Harmony , Uniform Sequences , and Quantized Voice

Uniform patterns are voice-leading patterns that are purely regular when represented with generic intervals which are related to real intervals through quantization. Various kinds of chromatic and diatonic sequences are uniform patterns. The generic intervals of uniform patterns provide a way of precisely and quantitatively comparing different kinds of chromatic patterns to diatonic ones by dra...

Chromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs

In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...

Helminths and harmony.

1995;36:539–43. 26 Verdu EF, Armstrong D, Idstrom J-P, et al. Effect of curing Helicobacter pylori infection on intragastric pH during treatment with omeprazole. Gut 1995;37:743–8. 27 Holtmann G, Cain C, Malfertheiner P. Gastric Helicobacter pylori infection accelerates healing of reflux esophagitis during treatment with the proton pump inhibitor pantoprazole. Gastroenterology 1999;117:11–16. 2...

Licensing and Consonantal Harmony

Chromatic Derivatives, Chromatic Expansions and Associated Spaces

This paper presents the basic properties of chromatic derivatives and chromatic expansions and provides an appropriate motivation for introducing these notions. Chromatic derivatives are special, numerically robust linear differential operators which correspond to certain families of orthogonal polynomials. Chromatic expansions are series of the corresponding special functions, which possess th...