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| Author | : Dmitri Tymoczko |
| Publisher | : OUP USA |
| Total Pages | : 469 |
| Release | : 2011-03-21 |
| Genre | : Mathematics |
| ISBN | : 0195336674 |
In this groundbreaking book, Tymoczko uses contemporary geometry to provide a new framework for thinking about music, one that emphasizes the commonalities among styles from Medieval polyphony to contemporary jazz.
| Author | : Godfried T. Toussaint |
| Publisher | : CRC Press |
| Total Pages | : 371 |
| Release | : 2019-11-25 |
| Genre | : Mathematics |
| ISBN | : 135124776X |
The original edition of The Geometry of Musical Rhythm was the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explained how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly disparate fields. The book also introduced the distance approach to phylogenetic analysis and illustrated its application to the study of musical rhythm. The new edition retains all of this, while also adding 100 pages, 93 figures, 225 new references, and six new chapters covering topics such as meter and metric complexity, rhythmic grouping, expressive timbre and timing in rhythmic performance, and evolution phylogenetic analysis of ancient Greek paeonic rhythms. In addition, further context is provided to give the reader a fuller and richer insight into the historical connections between music and mathematics.
| Author | : Godfried T. Toussaint |
| Publisher | : CRC Press |
| Total Pages | : 357 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 1466512032 |
The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explains how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly dispara
| Author | : Miguel Gutierrez; Makoto Taniguchi |
| Publisher | : iUniverse |
| Total Pages | : 124 |
| Release | : 2010-07-07 |
| Genre | : Mathematics |
| ISBN | : 1450227988 |
This monograph covers a fresh and original look at musical chords. The idea emanates from the fact that an intervallic representation of the chord leads naturally to a discrete barycentric condition. This condition itself leads to a convenient geometric representation of the chordal space as a simplicial grid. Chords appear as points in this grid and musical inversions of the chord would generate beautiful polyhedra inscribed in concentric spheres centered at the barycenter. The radii of these spheres would effectively quantify the evenness and thus the consonance of the chord. Internal symmetries would collapse these chordal structures into polar or equatorial displays, creating a platform for a thorough degeneracy study. Appropiate morphisms would allow us to navigate through different chordal cardinalities and ultimately to characterise complementary chords.
| Author | : John Martineau |
| Publisher | : eBook Partnership |
| Total Pages | : 416 |
| Release | : 2020-08-08 |
| Genre | : Mathematics |
| ISBN | : 1912706245 |
The Quadrivium consists of the four Liberal Arts of Number, Geometry, Music, and Cosmology, studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. They synthesize number, space, and time. Geometry is number in space, music is number in time, and the cosmos expresses number in space and time. Number, music, and geometry are metaphysical truths, good and beautiful everywhere at all times. Life across the universe investigates them. They foreshadow the physical sciences. This is the first volume to bring together the Quadrivium for many hundreds of years
| Author | : Anthony Ashton |
| Publisher | : Bloomsbury Publishing USA |
| Total Pages | : 68 |
| Release | : 2003-04-01 |
| Genre | : Science |
| ISBN | : 0802714099 |
Ashton presents a short, illustrated introduction to the evolution of simple harmonic theory. Illustrations.
| Author | : Richard Cohn |
| Publisher | : OUP USA |
| Total Pages | : 256 |
| Release | : 2012-01-23 |
| Genre | : Music |
| ISBN | : 019977269X |
Reconstructing historical conceptions of harmonic distance, Audacious Euphony advances a geometric model appropriate to understanding triadic progressions characteristic of 19th-century music. Author Rick Cohn uncovers the source of the indeterminacy and uncanniness of romantic music, as he focuses on the slippage between chromatic and diatonic progressions and the systematic principles under which each operate.
| Author | : Guerino Mazzola |
| Publisher | : Birkhäuser |
| Total Pages | : 1310 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 303488141X |
With contributions by numerous experts
| Author | : John Martineau |
| Publisher | : |
| Total Pages | : 409 |
| Release | : 2010 |
| Genre | : Cosmology |
| ISBN | : 9781907155048 |
Composed of six previously published works.
| Author | : David Lewin |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 291 |
| Release | : 2011 |
| Genre | : Music |
| ISBN | : 0199759944 |
Generalized Musical Intervals and Transformations is by far the most significant contribution to the field of systematic music theory in the last half-century, generating the framework for the "transformational theory" movement.
