A Geometry of Music: Harmony and Counterpoint in the by Dmitri Tymoczko

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 take advantage of 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 types from medieval polyphony to modern rock. Tymoczko identifies 5 uncomplicated musical positive aspects that together give a contribution to the feel of tonality, and exhibits how those beneficial properties recur in the course of the historical past of Western tune. within the approach he sheds new gentle on an age-old query: what makes track sound good?
A Geometry of song offers an available creation to Tymoczko's innovative geometrical method of song concept. The publication exhibits how you can build uncomplicated diagrams representing relationships between normal chords and scales, giving readers the instruments to translate among the musical and visible nation-states and revealing superb levels of constitution in in a different way hard-to-understand items.
Tymoczko makes use of this theoretical origin to retell the historical past of Western track 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 track contains a longer universal perform stretching from the overdue center a long time to the current. He discusses a number of everyday items by means of quite a lot of composers, from Bach to the Beatles, Mozart to Miles Davis, and plenty of in between.
A Geometry of song is obtainable to a number readers, from undergraduate track majors to scientists and mathematicians with an curiosity in tune. Defining its phrases alongside the best way, it presupposes no certain mathematical historical past and just a easy familiarity with Western song thought. The e-book additionally comprises workouts designed to enhance and expand readers' realizing, besides a sequence of appendices that discover the technical information of this intriguing new idea.

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Extra info for A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory)

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2 (a−b) Inversionally related passages in Bach’s A minor prelude, WTC II. (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.

Besides being well suited for contrapuntal music, these chords are all acoustically consonant, or restful and stable-sounding. 19 More generally, it would seem that composers who wish to combine harmonic consistency and conjunct melodic motion have relatively few options: they can either use familiar sonorities in more or less familiar ways, or they can use chromatic chords whose notes are clustered 18 This sort of texture was popularized during the 1960s by composers such as Ligeti and Lutosławski; precursors to the technique include Bartók’s Out of Doors (“Night Music”) and Ruth Crawford Seeger’s String Quartet.

22 As a result, tonal music is both self-similar and hierarchical, exploiting the same procedures at two different time scales. 10 shows the opening of the last movement of Clementi’s D major Piano Sonata, Op. 25 No. 6. The two parallel phrases present a series of three-voice chord progressions: I–V6–I followed by I–IV–I and then V7/V–V. The bottom staff shows that we can find a higher-level harmonic motion relating two diatonic collections: the first six measures limit themselves to the seven notes of D major, while the rest of the phrase abandons the Gn in favor of the Gs.

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