By Dmitri Tymoczko
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 make the most the non-Euclidean geometry of musical chords?
during this groundbreaking paintings, writer Dmitri Tymoczko describes a brand new framework for pondering tune that emphasizes the commonalities between kinds from medieval polyphony to modern rock. Tymoczko identifies 5 simple musical beneficial properties that together give a contribution to the experience of tonality, and indicates how those good points recur through the heritage of Western song. within the approach he sheds new mild on an age-old query: what makes song sound good?
A Geometry of tune presents an available advent to Tymoczko's innovative geometrical method of song thought. The e-book indicates easy methods to build uncomplicated diagrams representing relationships between time-honored chords and scales, giving readers the instruments to translate among the musical and visible nation-states and revealing outstanding levels of constitution in differently hard-to-understand items.
Tymoczko makes use of this theoretical starting place to retell the heritage of Western song from the 11th century to the current day. Arguing that conventional histories concentration too narrowly at the "common practice" interval from 1680-1850, he proposes as an alternative that Western tune contains a longer universal perform stretching from the overdue heart a long time to the current. He discusses a bunch of widespread items through a variety of composers, from Bach to the Beatles, Mozart to Miles Davis, and plenty of in between.
A Geometry of song is out there to a number readers, from undergraduate song majors to scientists and mathematicians with an curiosity in tune. Defining its phrases alongside the best way, it presupposes no designated mathematical heritage and just a simple familiarity with Western track thought. The ebook additionally comprises workouts designed to augment and expand readers' figuring out, besides a chain of appendices that discover the technical information of this intriguing new conception.
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Additional resources for A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory)
Because measure are inversionally related, they are direction reversing, inversions change the and sound more similar to each other than to either of the chords character of musical passages more dramatically in the other measure. than transpositions: nobody would ever mistake the inverted form of Bach’s theme for the original. ”8 For this reason, many twentieth-century composers consider inversionally related chords to be similar. 2c, then every pitch would be sent to the place where its reﬂection 8 Major and minor triads are of course importantly different, even though they are related by inversion; nevertheless, they are more similar to one another than to three-note chromatic clusters.
C) Inversion as reﬂection in pitch space. Here, the note A3 is unaltered by the inversion, so the inversion can be written I A3 A3. All other notes move by twice their distance from A3. ) Because measure are inversionally related, they are direction reversing, inversions change the and sound more similar to each other than to either of the chords character of musical passages more dramatically in the other measure. than transpositions: nobody would ever mistake the inverted form of Bach’s theme for the original.
Chapter 6 proposes that there is an “extended common practice” stretching from the beginning of Western counterpoint to the tonal music of the twentieth century. What links these different styles is the combination of harmonic consistency and conjunct melodic motion: the idea that music should have a two-dimensional coherence, both harmonic (or vertical) and melodic (or horizontal). Chapter 7 uses geometrical models to investigate the functional harmony of the classical period, brieﬂy considering the relation between traditional harmonic theory and the views of Heinrich Schenker.