Dmitri Tymoczko's A Geometry of Music: Harmony and Counterpoint in the PDF

How is the Beatles' "Help!" just like Stravinsky's "Dance of the Adolescents?" How does Radiohead's "Just" relate to the improvisations of invoice Evans? and the way do Chopin's works take advantage of the non-Euclidean geometry of musical chords?

In this groundbreaking paintings, writer Dmitri Tymoczko describes a brand new framework for puzzling over track that emphasizes the commonalities between kinds from medieval polyphony to modern rock. Tymoczko identifies 5 uncomplicated musical beneficial properties that together give a contribution to the feel of tonality, and exhibits how those beneficial properties recur during the heritage of Western song. within the method he sheds new mild on an age-old query: what makes song sound good?

A Geometry of Music presents an available creation to Tymoczko's innovative geometrical method of song concept. The publication indicates easy methods to build uncomplicated diagrams representing relationships between universal chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing wonderful levels of constitution in another way hard-to-understand pieces.

Tymoczko makes use of this theoretical beginning to retell the historical past of Western song from the 11th century to the current day. Arguing that conventional histories concentration too narrowly at the "common perform" interval from 1680-1850, he proposes as a substitute that Western song contains a longer universal perform stretching from the overdue center a while to the current. He discusses a bunch of commonly used items by means of a variety of composers, from Bach to the Beatles, Mozart to Miles Davis, and plenty of in between.

A Geometry of Music is on the market to quite a number readers, from undergraduate song majors to scientists and mathematicians with an curiosity in song. Defining its phrases alongside the best way, it presupposes no specific mathematical heritage and just a simple familiarity with Western song concept. The publication additionally includes workouts designed to augment and expand readers' figuring out, besides a chain of appendices that discover the technical information of this intriguing new theory.