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 considering tune that emphasizes the commonalities between kinds from medieval polyphony to modern rock. Tymoczko identifies 5 simple musical gains that together give a contribution to the experience of tonality, and indicates how those good points recur in the course of the heritage of Western song. within the method he sheds new gentle on an age-old query: what makes track sound good?
A Geometry of tune offers an obtainable creation to Tymoczko's innovative geometrical method of song concept. The publication indicates tips on how to build easy diagrams representing relationships between universal chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing incredible levels of constitution in another way hard-to-understand items.
Tymoczko makes use of this theoretical starting place to retell the heritage of Western tune 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 a substitute that Western track contains a longer universal perform stretching from the overdue heart a while to the current. He discusses a bunch of everyday items through a variety of composers, from Bach to the Beatles, Mozart to Miles Davis, and lots of in between.
A Geometry of tune is available to quite a number readers, from undergraduate track majors to scientists and mathematicians with an curiosity in track. Defining its phrases alongside the way in which, it presupposes no designated mathematical historical past and just a uncomplicated familiarity with Western song idea. The booklet additionally comprises workouts designed to augment and expand readers' realizing, in addition to a sequence of appendices that discover the technical information of this interesting new concept.
Read Online or Download A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) PDF
Best geometry books
This specified reference, geared toward learn topologists, supplies an exposition of the 'pseudo-Anosov' idea of foliations of 3-manifolds. This concept generalizes Thurston's conception of floor automorphisms and divulges an intimate connection among dynamics, geometry and topology in three dimensions. major issues again to in the course of the textual content comprise the significance of geometry, specially the hyperbolic geometry of surfaces, the significance of monotonicity, specifically in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, utilizing finite combinatorical items reminiscent of train-tracks, branched surfaces and hierarchies to hold extra advanced non-stop gadgets.
In lots of difficulties of utilized arithmetic, technological know-how, engineering or economics, an strength expenditure or its analogue may be approximated via top and reduce bounds. This e-book presents a unified account of the idea required to set up such bounds, through expressing the governing stipulations of the matter, and the boundaries, when it comes to a saddle practical and its gradients.
- The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge
- Geometria 2
- Basic Geometry, Third Edition
- Riemanian geometry of contact and symplectic manifolds
Additional resources for A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory)
Let us further imagine that Lyrico chooses to use a C major chord as his drone. 1a). This is because its notes are all reasonably far apart. To obtain conjunct melodic motion, Lyrico can therefore introduce “passing tones” that connect the chord tones by short melodic steps. ” Lyrico can now write melodies that move freely along this scale, alternating between stable and unstable notes. 1 (a) Conﬁning a melody to the notes one day in a more ornery mood of the C major chord produces large leaps, so it is and decides to use the dissonant necessary to add “passing tones” (b).
Some of these (such as the familiar “circle of ﬁfths”) are relatively simple, but others (such as the Möbius strip containing two-note chords) are considerably more complex. One goal of the book is to provide a user-friendly introduction to these musico-geometrical spaces, explaining how they work, and showing how they allow us to visualize a wealth of musical possibilities at a glance. Suppose, by way of illustration, that our friend Lyrico decides to write music using only the seven triads in the C diatonic collection.
Can be determined by counting keys on an ordinary piano, so that the Cs above middle C is 61, the D above that is 62, and so on. 17. In principle, we could eschew letter-names for the remainder of this book, conducting the discussion entirely in numerical terms. For clarity, however, I will use familiar letter names whenever possible. These should be taken as shorthand for numerical pitch labels: “Cs4” and “61,” like “Bob Dylan” and “Robert Zimmerman,” are different ways of referring to the same thing.
A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) by Dmitri Tymoczko