The Geometry of Music

To read along with this blog go here April 23, 2008 – One of my favorite phrases I have quoted from people’s reviews of my book is from K. Flekkoy, who had this to say at “an imaginative and strangely ‘musical’ way of imagining superimposed dimensions”.

Dr. Dmitri Tymoczko – The geometry of music

In my talk, I will explain how to translate basic concepts of music theory into the language of contemporary geometry. I will show that musicians commonly abstract away from five types of musical transformations, the “OPTIC transformations,” to form equivalence classes of musical objects. Examples include “chord,” “chord type,” “chord progression,” “voice leading,” and “pitch class.” These equivalence classes can be represented as points in a family of singular quotient spaces, or orbifolds: for example, two-note chords live on a Mobius strip whose boundary acts like a mirror, while four-note chord-types live on a cone over the real projective plane. Understanding the structure of these spaces can help us to understand general constraints on musical style, as well as specific pieces. The talk will be accessible to non-musicians, and will exploit interactive 3D computer models that allow us to see and hear music simultaneously. Dr. Dmitri Tymoczko is from Princeton University. Note: Original video was 320×240.

SIAM AN10: Geometry in Music; Dmitri Tymoczko

What could be a better medium to communicate math to the public than the universal language of music? Ever since Pythagoras used numerical terms to express intervals between notes and derived musical tones from geometrical patterns, mathematicians have linked music to numbers. At the SIAM Annual Meeting in Pittsburgh in July, Dr. Dmitri Tymoczko made the connection with help from multimedia graphics and compositions by Chopin, Mozart and Schubert. Created by Adam Bauser of Bauser Media Group

TEDxAmericasFinestCity – Bill Wesley – Geometry of Music

Geometry of emotion through array orchestra. Bill Wesley Inventor / Musician — Array Orchestra Bill Wesley was born into a family of scientists, artists, and writers. In this lively intellectual atmosphere, he began to produce shows featuring live musical composition and live visual animation. To facilitate better sound and light in these shows he designed various new types of instrumentation. In this spirit the Array System of note arrangement was conceived. Because of this unique musical arrangement, the experience of playing an Array instrument is that less shifting around of movement is required for playing all chord progressions. With multiple duplications of all notes available, complex voicing of notes are also within reach — allowing the player to access the same notes with each hand in different locations similar to four hands on two pianos. Bill Wesley has invented and manufactured with Patrick Hadley, a wide variety of Array instruments right here in San Diego. These include the Array Mbira, two types of Array MIDI Controllers, the Array Nail Violin, the Array Rasp, the Array Drum, the Array Rhythm Machine, the Array Guitar, the Array Psaltry, and the Array Vina. TED was founded in 1984. The annual TED conference brings together the world’s leading thinkers and doers to share ideas that matter in a variety of disciplines — technology, entertainment, science, humanities, business, art, design. Short talks, demonstrations and performances are given by hand

Sri Yantra ~ Wealth Meditation *Bhajan Music*

Sri Yantra represents the Supreme Goddess, Srimati Radharani, Sri Mahalaxmi , “The Goddess of Fortune!” It is one the most auspicious, important and powerful Yantras, which not only gives the maximum benefit, but also proves beneficial for almost everybody. It is the source of attaining all worldly desires & fulfilling all wishes through inner cosmic power & mental strength. accompanying Music ~ Shri Radhe Sharanam Mamah by JT Jasraj. Sri Yantra bhija Mantra. Om Shreem Hreem Shreem Kamle Kamalalaye Praseed, Praseed, Shreem Hreem Shreem Om Mahalaxmaye Namah. Om Shareeng Hareeng Kaleeng Hareeng Shrimahalakshmiaye Namah. Yantra is a Sanskrit word that is derived from the root yam meaning to control or subdue [1] or “to restrain, curb, check” [2]. Meanings for the noun derived from this root include:[3][4] “any instrument or machine” (ie that which is controlled or controls. For instance the body is said to be a yantra[5]) “any instrument for holding, restraining, or fastening” (for instance a symbol which ‘holds’ the essence of a concept, or helps the mind to ‘fasten’ on a particular idea) “a mystical or astronomical diagram” (usually a symbol, often inscribed on an amulet) sometimes said to possess mystical or magical powers. -tra is an indoeuropean suffix meaning ‘ instrument’, found in Latin ‘ aratrum’ and in tantra and mantra. A yantra depicts both macrocosmic and microcosmic forces acting together – the movement towards and away from the centre – “control” and

Bridging Heaven & Earth Show # 69 with Jonathan Quintin and the Music of Christa Ray

Jonathan, an internationally recognized teacher, healer, and artist, was born and raised in the rural and rugged landscape of New Zealand. In his extensive travels around the world, he was fascinated by the various teachings that strove for higher consciousness. A universal theme he encountered was the presence of Sacred Geometry. He was so inspired by the beauty, love, and power of Sacred Geometry that he chose to devote the rest of his life to the pursuit of the subject that combined art, science, and mystery. Jonathan has spent the last twelve years dedicated to the study and artistic expression of Sacred Geometry, focusing upon its therapeutic qualities and employing it as a tool for deeper understanding of the majesty of Life. Christa, who also appeared on Show #29 with Oceanna, has an angelic presence and is a powerful healer using sound technology for awakening and healing. She has a beautiful voice and her sacred toning exercises balance and nurture the soul and heart. Christa teaches many workshops around the country using sound to heal. Bridging’s website is: Bridging’s International Healing Art Project website is