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 beneficial properties that together give a contribution to the experience of tonality, and indicates how those gains recur during the historical past of Western track. within the approach he sheds new gentle on an age-old query: what makes song sound good?
A Geometry of song presents an available advent to Tymoczko's progressive geometrical method of tune concept. The e-book exhibits the right way to build basic diagrams representing relationships between favourite chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing excellent 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 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 track includes a longer universal perform stretching from the past due heart a long time to the current. He discusses a number of typical items by means of quite a lot of composers, from Bach to the Beatles, Mozart to Miles Davis, and lots of in between.
A Geometry of song is available to a variety of 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 distinctive mathematical history and just a uncomplicated familiarity with Western song thought. The publication additionally comprises routines designed to enhance and expand readers' figuring out, in addition to a sequence of appendices that discover the technical information of this intriguing new concept.
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Additional resources for A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory)
The equation in the preceding paragraph has two constants, c1 and c2, the ﬁrst of which determines the number corresponding to the frequency A440, and the second of which determines the size of the octave. In this book, I will always choose c1 = 69 and c2 = 12. This creates a linear pitch space in which the unit of distance is the semitone and middle C is (arbitrarily) assigned the number 60. 2, labels for familiar equal-tempered pitches 1 Transposition preserves these distances, since f/g = cf/cg.
20 These same notes are one step apart relative to the pentatonic scale C-D-E-G-A and three steps apart relative to the chromatic scale. Similarly, C and E are two steps apart relative to the diatonic and pentatonic scales, and four apart relative to the chromatic scale. The three scales therefore give us three different ways of measuring musical distance, and three different estimates of the relative sizes of the intervals C-E and E-G. ” As we will see, the richness of tonal music lies partly in the way it exploits these various conceptions of musical distance.
1). 1 Circular pitch class space. 5 refers to the pitch class Dμ, or D quartertone sharp, halfway between D and Ef. 2 Octave equivalence seems to be nearly universal in human cultures (Dowling and Harwood 1986), and there is some evidence for it in nonhuman animals (Wright et al. 2000). 3 Alternatively, we can take points on the circle to represent categories of notes all sharing the same chroma. 4 As a result, many properties of linear pitch space are transferred to circular pitch-class space.