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Tuesday, August 10, 2010. Two C Major Preludes. In an earlier post. I briefly described a computational method that can be used to classify and visualize perceived tonality in a piece of music. I'm interested in using techniques like this to extract mathematical information from musical compositions. Separated by two hundred years, it is easy to discern that these two pieces are harmonically very different from one another. I am curious to quantify that difference in some way. Monday, August 9, 2010.

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SoundMath | soundmath.blogspot.com Reviews

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Tuesday, August 10, 2010. Two C Major Preludes. In an earlier post. I briefly described a computational method that can be used to classify and visualize perceived tonality in a piece of music. I'm interested in using techniques like this to extract mathematical information from musical compositions. Separated by two hundred years, it is easy to discern that these two pieces are harmonically very different from one another. I am curious to quantify that difference in some way. Monday, August 9, 2010.

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SoundMath | soundmath.blogspot.com Reviews

https://soundmath.blogspot.com

Tuesday, August 10, 2010. Two C Major Preludes. In an earlier post. I briefly described a computational method that can be used to classify and visualize perceived tonality in a piece of music. I'm interested in using techniques like this to extract mathematical information from musical compositions. Separated by two hundred years, it is easy to discern that these two pieces are harmonically very different from one another. I am curious to quantify that difference in some way. Monday, August 9, 2010.

INTERNAL PAGES

soundmath.blogspot.com

1

SoundMath: Harmonics

http://soundmath.blogspot.com/2010/05/harmonics.html

Monday, May 31, 2010. A version of the following will appear in the 2011 volume "Encyclopedia of Mathematics in Society". Harmonics are components of a musical sound with well-defined frequency relationships to one another. For a pitch of frequency f. Typically measured in units of cycles per second or Hertz (Hz), the n. Th harmonic has frequency n. In this context the frequency f. Is referred to as the fundamental frequency. Harmonics are closely related to overtones. Is referred to as the 1. Harmonic, ...

2

SoundMath: May 2010

http://soundmath.blogspot.com/2010_05_01_archive.html

Monday, May 31, 2010. A version of the following will appear in the 2011 volume "Encyclopedia of Mathematics in Society". Geometry is the study of shapes. Musical information can often be represented naturally by shapes, allowing insights to be gained from geometric techniques. One indication of the close connection between music and geometry comes from the fact that Euclid, whose Elements of Geometry. Century mathematician Leonhard Euler also developed geometric tools for music analysis. In the equally ...

3

SoundMath: Wind Instruments

http://soundmath.blogspot.com/2010/08/wind-instruments.html

Monday, August 9, 2010. A version of the following will appear in the 2011 volume "Encyclopedia of Mathematics in Society". The sources of vibrations. The rapid open-close vibration of the vocal cords is present in many wind instruments. In brass instruments such as the trumpet, trombone, French horn and tuba, the lips of the performer form a small aperture that opens and closes in response to air pressure. These are sometimes called lip-reed. Tube resonators and overtones. San Diego: Academic Press, 1991.

4

SoundMath: Simple Linear Transformations of the Octave

http://soundmath.blogspot.com/2010/05/simple-linear-transformations-of-octave.html

Sunday, May 9, 2010. Simple Linear Transformations of the Octave. A few weeks ago, a colleague in the music department sent me a page he had written describing some remarkable counting properties of the twelve pitches of the musical octave, with the circle of fourths and circle of fifths most remarkable. Here is a generalization of his ideas. There is some cool group theory on Z. C C# D D# E F F# G G# A A# B C. 0 1 2 3 4 5 6 7 8 9 10 11 0. F(x)= x 1 (mod 12). F (f (.f (x) )= x n for n =1, 2, 3,. Because ...

5

SoundMath: Geometry of Music

http://soundmath.blogspot.com/2010/05/geometry-in-music.html

Monday, May 31, 2010. A version of the following will appear in the 2011 volume "Encyclopedia of Mathematics in Society". Geometry is the study of shapes. Musical information can often be represented naturally by shapes, allowing insights to be gained from geometric techniques. One indication of the close connection between music and geometry comes from the fact that Euclid, whose Elements of Geometry. Century mathematician Leonhard Euler also developed geometric tools for music analysis. In the equally ...

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Tuesday, August 10, 2010. Two C Major Preludes. In an earlier post. I briefly described a computational method that can be used to classify and visualize perceived tonality in a piece of music. I'm interested in using techniques like this to extract mathematical information from musical compositions. Separated by two hundred years, it is easy to discern that these two pieces are harmonically very different from one another. I am curious to quantify that difference in some way. Monday, August 9, 2010.

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