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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 wondering song that emphasizes the commonalities between types from medieval polyphony to modern rock. Tymoczko identifies 5 simple musical good points that together give a contribution to the experience of tonality, and indicates how those positive aspects recur in the course of the historical past of Western song. within the procedure he sheds new gentle on an age-old query: what makes tune sound good?
A Geometry of track offers an obtainable creation to Tymoczko's innovative geometrical method of song idea. The e-book exhibits how you can build basic diagrams representing relationships between wide-spread chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing astonishing levels of constitution in differently hard-to-understand items.
Tymoczko makes use of this theoretical origin to retell the heritage 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 tune contains a longer universal perform stretching from the overdue center a long time to the current. He discusses a bunch of commonplace items by way of a variety of composers, from Bach to the Beatles, Mozart to Miles Davis, and plenty of in between.
A Geometry of tune is on the market to quite a number readers, from undergraduate song majors to scientists and mathematicians with an curiosity in tune. Defining its phrases alongside the way in which, it presupposes no distinct mathematical heritage and just a simple familiarity with Western track concept. The e-book additionally includes routines designed to augment and expand readers' figuring out, besides a chain of appendices that discover the technical information of this fascinating new idea.

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

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Suppose, by way of illustration, that our friend Lyrico decides to write music using only the seven triads in the C diatonic collection. 12). 13), where each chord can be connected to its neighbors by a single-step motion. 12 Voice leading between diatonic triads. 13 Single-step voiceleading between diatonic triads can be modeled with a circle. theory to which C major and A minor are one step apart (since they are adjacent on the circle) while C major and D minor are three steps apart (since there are two chords between them).

Where the left hand of (a) begins with an ascending octave leap, followed by a series of descending semitones, the left hand of (b) begins with a descending octave leap followed by a series of ascending semitones. In other words, the direction of motion has changed while the distances remain the same. 1 Transposition moves every point in the same direction by the same amount. Here, the arrows indicate ascending transposition by two semitones. 1). 7 Registral inversion changes the octave in which notes appear (for instance, transforming a root position chord C4-E4-G4 into a first-inversion E4-G4-C5).

This means that the music exhibits two sorts of efficient voice leading: on the level of the half measure, there is a sequence of eight efficient voice leadings between triads; while on a larger temporal level there is a 22 This is not all that modulation does, of course, but it is typically part of it. 10 Two levels of voice leading in Clementi’s Op. 25 No. 6. single efficient voice leading between D major and A major scales, occurring somewhere near the seventh measure of the example. 11 shows that similar processes occur in twentieth-century music.

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