Two-part Harmony


Book Description




The Harmony of the World


Book Description

The authors have presented and interpreted Johannes Kepler's Latin text to English readers by putting it into the kind of clear but earnest language they suppose Kepler would have used if he had been writing today.




Treatise on Harmony


Book Description

One of most important books in Western music. Detailed explanation of principles of diatonic harmonic theory. New 1971 translation by Philip Gossett of 1722 edition. Many musical examples.







Foundations of Modern Harmony


Book Description

Translated into English for the first time, Foundations of Modern Harmony, by composer and music theorist Karel Janec̆ek, addresses the analysis and composition of music not based on the tonal harmony that was common language until the early 20th century. Discussing this newer music requires a vocabulary in which all combinations of notes, or chords, can be named. Janec̆ek developed his theory of modern harmony over many years. In this book, he classifies chords according to their intervallic structure, their possible arrangements, and then based on their consonance and dissonance. His focus on what we hear leads to a discussion of “imaginary” pitches, those that are still heard after they are no longer sounding. Dealing with such issues as harmonizing a melody, resolving dissonant chords, and the formation and extinction of a sense of the tonic, Janeček’s work is an exciting complement to the theories of Schoenberg and Hindemith. His discussion of harmonic motion leads to the consideration of harmonic function, of establishing the tonic, of modulation, of atonal composition, and of static and kinetic conceptions of harmony. First published in 1965, Janeček’s concerns are of continuing importance to music theorists and composers.










The Missouri Harmony


Book Description




Music-Inspired Harmony Search Algorithm


Book Description

Calculus has been used in solving many scientific and engineering problems. For optimization problems, however, the differential calculus technique sometimes has a drawback when the objective function is step-wise, discontinuous, or multi-modal, or when decision variables are discrete rather than continuous. Thus, researchers have recently turned their interests into metaheuristic algorithms that have been inspired by natural phenomena such as evolution, animal behavior, or metallic annealing. This book especially focuses on a music-inspired metaheuristic algorithm, harmony search. Interestingly, there exists an analogy between music and optimization: each musical instrument corresponds to each decision variable; musical note corresponds to variable value; and harmony corresponds to solution vector. Just like musicians in Jazz improvisation play notes randomly or based on experiences in order to find fantastic harmony, variables in the harmony search algorithm have random values or previously-memorized good values in order to find optimal solution.




Vowel Harmony and Correspondence Theory


Book Description

Biographical note: Martin Krämer teaches at the University of Ulster, Ireland.