Bach – The Art of Fugue, BWV 1080 [just audio complete on Organ]

The Art of Fugue or The Art of the Fugue (original German: Die Kunst der Fuge), BWV 1080, is an incomplete masterpiece by Johann Sebastian Bach (1685–1750). The work was most likely started at the beginning of the 1740s, if not earlier. The first known surviving version, which contained 12 fugues and 2 canons, was copied by the composer in 1745. This manuscript has a slightly different title, added afterwards by his son-in-law Johann Christoph Altnickol: Die Kunst der Fuga. Bach’s second version was published in 1751 after his death. It contains 14 fugues and 4 canons. “The governing idea of the work”, as the eminent Bach specialist Christoph Wolff put it, is “an exploration in depth of the contrapuntal possibilities inherent in a single musical subject.”

Philip Glass – Sesame Street – Geometry of Circles

Read This for more information — Philip Glass composed this music for Sesame Street in 1979. It is not sampled from his other works. It has aired on Sesame Street as recently as 1994 and probably later. For the full details, see these articles on Muppet Wiki: The four known pieces have been edited together here for convenience. Since this was uploaded, Sesame Workshop has uploaded one of the four cartoons to their official channel on YouTube. You can find it here: Additionally, another short has been released on the vintage DVD collection Sesame Street: 40 Years of Sunny Days:

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