A Geometry of Music

A Geometry of Music
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.

The Geometry of Musical Rhythm

The Geometry of Musical Rhythm
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

The Geometry of Musical Rhythm

The Geometry of Musical Rhythm
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.

Cymatics

Cymatics
Author: Hans Jenny
Publisher: Macromedia
Total Pages: 0
Release: 2001
Genre: Cycles
ISBN: 9781888138078

An overview of the pioneering work done by Dr. Hans Jenny with audible vibration on various substances. His research had led to speculation about the origin of matter and its relation to vibration and sound.

Harmonograph

Harmonograph
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.

Sacred Geometry: Language of the Angels

Sacred Geometry: Language of the Angels
Author: Richard Heath
Publisher: Simon and Schuster
Total Pages: 465
Release: 2020-10-20
Genre: Body, Mind & Spirit
ISBN: 1644111195

Reveals how the number science found in ancient sacred monuments reflects wisdom transmitted from the angelic orders • Explains how the angels transmitted megalithic science to early humans to further our conscious development • Decodes the angelic science hidden in a wide range of monuments, including Carnac in Brittany, the Great Pyramid in Egypt, early Christian pavements, the Hagia Sophia in Istanbul, Stonehenge in England, and the Kaaba in Mecca • Explores how the number science behind ancient monuments gave rise to religions and spiritual practices The angelic mind is founded on a deep understanding of number and the patterns they produce. These patterns provided a constructive framework for all manifested life on Earth. The beauty and elegance we see in sacred geometry and in structures built according to those proportions are the language of the angels still speaking to us. Examining the angelic science of number first manifested on Earth in the Stone Age, Richard Heath reveals how the resulting development of human consciousness was no accident: just as the angels helped create the Earth’s environment, humans were then evolved to make the planet self-aware. To develop human minds, the angels transmitted their own wisdom to humanity through a numerical astronomy that counted planetary and lunar time periods. Heath explores how this early humanity developed an expert understanding of sacred number through astronomical geometries, leading to the unified range of measures employed in their observatories and later in cosmological monuments such as the Giza Pyramids and Stonehenge. The ancient Near East transformed megalithic science into our own mathematics of notational arithmetic and trigonometry, further developing the human mind within the early civilizations. Heath decodes the angelic science hidden within a wide range of monuments and sites, including Carnac in Brittany, the Great Pyramid in Egypt, Teotihuacan in Mexico, early Christian pavements, the Hagia Sophia in Istanbul, and the Kaaba in Mecca. Exploring the techniques used to design these monuments, he explains how the number science behind them gave rise to ancient religions and spiritual practices. He also explores the importance of lunar astronomy, first in defining a world suitable for life and then in providing a subject accessible to pre-arithmetic humans, for whom the Moon was a constant companion.

Sacred Geometry for Artists, Dreamers, and Philosophers

Sacred Geometry for Artists, Dreamers, and Philosophers
Author: John Oscar Lieben
Publisher: Simon and Schuster
Total Pages: 538
Release: 2018-08-28
Genre: Body, Mind & Spirit
ISBN: 1620557029

An illustrated guide to harmonics--the sacred geometry principles that underlie the natural world--and its practical applications • Demonstrates how the vesica piscis is a matrix from which ideas and forms emanate, connecting cosmic time cycles, measures of space, and musical tones • Provides harmonic analyses of ancient sculpture, architecture, the solar system, the Earth-Moon relationship, and the structure of water and waves • Explains how to apply sacred geometry to create building floor plans, pottery figures, gardens, and sacred ceremonial spaces We are in the midst of a revival of an ancient way of looking at the world--an approach that enabled great civilizations of the past to bring forth inventions of great beauty and power. This school of thought--harmonics--envisioned the natural world and the solar system as an interlocking matrix of harmonious numbers, perfectly woven into the creative fabric of life and the surrounding universe. Exploring the art and science of harmonics, John Oscar Lieben shows how to create harmonious forms using the ancient tools of number, geometry, and musical tone--an approach that resonates with nature’s own ways of creation. He demonstrates many practical applications that result from the study of harmonics, providing analyses of ancient sculpture and architecture, as well as original examples of building floor plans, pottery figures based on planetary proportions, gardens based on harmonic principles, and ceremonial spaces that honor cosmic harmonies and sacred geometric relationships. Showing how harmonics can also be applied to the mysteries of time and space, the author demonstrates how the vesica piscis and many other variations of the vesica shape reveal numerical synchronicities and correspondences that connect cosmic time cycles, measures of space, and musical tones. The author applies harmonics and the “vesica construction” matrix to illustrate many of nature’s wonders, including the Earth-Moon relationship, the interactions of the Golden Number and the musical scale, and how the Flower of Life symbol connects the universal field with the pattern of raindrops falling on a pond. Offering an approach to sacred geometry that pairs the mystical with the practical, the cosmic with the earthly, the author reveals how the art and science of harmonics should be required study for both the artist and the seeker of eternal truths as well as the scientist who seeks an entrance into the sacred foundations of nature.

The Geometry Code

The Geometry Code
Author: Bruce Rawles
Publisher: Elysian Publishing
Total Pages: 218
Release: 2012-04
Genre: Geometry
ISBN: 9780965640572

Integrate practical insights from modern physics, ancient Hermetic Laws, non-dual meta-physics, transpersonal psychology, and humor, as tools for undoing conflicting beliefs we've dreamed ourselves into. The seven Hermetic laws are explored in depth and demonstrate how a mindfulness that embraces 'other' as 'self' can reverse the typical misapplication of these inescapable laws of Mentalism, Correspondence, Vibration, Polarity, Rhythm, Cause & Effect and Generation. Ubiquitous geometric symbols, paired to each of these laws - the circle, vesica piscis, sine wave, line, spiral, fractal and yin-yang - and their countless commonplace variations, seen from the vantage point of shared interests, reflect these ideas. The inspired use of natural law restores attributes of life, love, strength, purity, beauty, perfection and gratitude to our awareness.

Quadrivium

Quadrivium
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

Quadrivium

Quadrivium
Author: John Martineau
Publisher:
Total Pages: 409
Release: 2010
Genre: Cosmology
ISBN: 9781907155048

Composed of six previously published works.