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Thursday, November 10, 2011

Wednesday, September 28, 2011

Monday, April 25, 2011

Der Zermesser

"Der Zermesser" is an autonomous, room-filing object whose end in itself is to feel its way around and to articulate the connection between its own form and its surroundings. The basic shape is a regular tetrahedron, capable of changing its propagation in the room by means of attached motors. It can also move freely by tilting and therefore capture space.




http://www.leo.ok.ag/index.php/der-zermesser.html

Chiplotle: an HPGL (Hewlett-Packard Graphics Language) Python API

http://music.columbia.edu/cmc/chiplotle/

Composing With Hyperscore: An Intuitive Interface For Visualizing Musical Structure


http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.120.6536&rep=rep1&type=pdf

Sunday, April 24, 2011

Music - original and synthetic

around_the_world-atc-midi.wav

One `holy grail' of automatic sound analysis is music transcription, which could be defined as trying to convert a real recording of music into an equivalent MIDI representation.

Notes on sources

The track selection and MIDI file processing was done by Rob Turetsky. The manual transcriptions were created by Angel Umpierre during an internship in Summer 2003. Thanks to them both.

Acknowledgment

This material is based in part upon work supported by the National Science Foundation under Grant No. IIS-0238301. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

http://www.ee.columbia.edu/~dpwe/sounds/music/

A Regression Approach to Music Emotion Recognition

http://mpac.ee.ntu.edu.tw/~yihsuan/pub/TASLP08.pdf

Music and Computers (A Theoretical and Historical Approach)






Phil Burk, SoftSynth.com
Larry Polansky, Department of Music, Dartmouth College
Douglas Repetto, Computer Music Center, Columbia University
Mary Roberts
Dan Rockmore, Department of Mathematics, Dartmouth College



Contents

Preface to the Archival Version (Spring, 2011)
Preface and Acknowledgments
How to Use the Web Site
The Vision of Mathematics Across the Curriculum
Scanned copy of the Teaching Guide (8.4MB pdf file)

Introduction
 
Chapter 1 The Digital Representation of Sound, Part One:
Sound and Timbre
1.1What is Sound?
1.2Amplitude
1.3Frequency, Pitch and Intervals
1.4Timbre
 
Chapter 2 The Digital Representation of Sound, Part Two:
Playing by the Numbers
2.1The Digital Representation of Sound
2.2Analog v. Digital
2.3Sampling Theory
2.4Binary Numbers
2.5Bit Width
2.6Digital Copying
2.7Storage Concerns
2.8Compression
 
Chapter 3 The Frequency Domain
3.1The Frequency Domain
3.2Phasors
3.3Fourier and the Sum of Sines
3.4The DFT, FFT and IFFT
3.5Problems with the FFT/IFFT
3.6Some Alternatives to the FFT
 
Chapter 4 The Synthesis of Sound by Computer
4.1Introduction to Synthesis
4.2Additive Synthesis
4.3Filters
4.4Formant Synthesis
4.5Introduction to Modulation
4.6Waveshaping
4.7Frequency Modulation
4.8Granular Synthesis
4.9Physical Modeling
 
Chapter 5 The Transformation of Sound by Computer
5.1Sampling
5.2Reverb
5.3Localization/Spatialization
5.4The Phase Vocoder
5.5Convolution
5.6Morphing
5.7Graphical Manipulation


Computer Music Center


Studio 317, one of four composition studios at the C-PEMC, circa 1970. Clockwise from the center front, Vladimir Ussachevsky (seated), Milton Babbitt, Bülent Arel, Pril Smiley, Mario Davidovsky, Alice Shields, Otto Luening.


http://music.columbia.edu/cmc/about/

Lifting operators for 0-1 integer programming (Daniel Bienstock)

This research extends the work of Lovasz and Schrijver, Sherali-Adams, and Lasserre, on the idea of lifting an n-dimensional polyhedron to a space whose coordinates are indexed by members of a subset-lattice of an n-element set. 
Instead, in work to appear in the PhD dissertation of Mark Zuckerberg, we have devised operators that lift to a space whose coordinates are indexed by the much larger subset algebra of an n-element set. 
This leads to provably stronger operators. As an example of our results, we have obtained a polynomial-time algorithm that solves a relaxation of set-covering problems that is stronger than that provided by the set of all valid inequalities with coefficients 0,1,2, ..., k (for any fixed k). 
Our current research centers on extending these operators with the goal of making them computationally practicable. 



http://www.corc.ieor.columbia.edu/projects/algebra/algebra.html