# Music and Math

It has long been accepted that mathematics plays a major role in the work of composers going as far back as early music, and reaching its greatest flowering in the Baroque, and Bach. Western counterpoint can be reduced to a set of algorithms.

More recently, the parallel relationships of math Set Theory in music theory have been applied to discover fresh musical combinations and sounds that can be heard in the work of composers such as Arnold Schoenberg, Oliver Messiaen, Anton Webern, Alban Berg, Igor Stavinsky, Béla Bartók, Iannis Xenakis, Pierre Boulez, and Ryoji Ikeda. And there’s no need to stop with Western music; elements of set theory can be found in South Indian Carnatic music as well.

Musical Set Theory has been written about in books by these pioneers: Howard Hanson, Allen Forte, Joseph Schillinger, Nicolas Slonimsky, Milton Babbitt, John Rahn, George Perle, Elliot Carter, Robert Morris, and Joseph Straus.

Mathematical musical constructs have also been used and taught by jazz pedogosists such as Charlie Banacos, Jerry Bergonzi, George Garzone, Mick Goodrich, Jon Damian, Steve Coleman, Richie Beirach, Dave Liebman, John O’Gallagher and Dennis Sandole.

You will of course find a rich interchange of math and music once you enter computer the music field. Digital Signal Processing (DSP) and compositional algorithms –all are commonly used in Computer Music.  Curtis Roads’ “The Computer Music Tutorial” MIT Press 1996 is a good starting point for understanding some of these processes.

# Power Set in the Musical Context

Power Set Power set of a set A is the set whose members are all possible subsets of A. For example, the power set of {1, 2} is {{}, {1}, {2}, {1,2} } . A larger more complex example can be shown using the set {1, 2, 3, 4, 5, 6, 7}: Since the power[…]

# Cartesian Product in the Musical Context

Cartesian Product The Cartesian Product of A and B, denoted A × B, is the set whose members are all possible ordered pairs (a,b) where a is a member of A and b is a member of B. The cartesian product of {1, 2} and {red, white} is {(1, red), (1, white), (2, red), (2,[…]

# Symmetric Difference

Symmetric Difference in the Musical Context Symmetric Difference of sets A and B, denoted A △ B or A ? B, is the set of all objects that are a member of exactly one of A and B (elements which are in one of the sets, but not in both). For instance, for the sets[…]

# Set Difference

Set Difference in the Musical Context Set difference of U and A, denoted U \ A, is the set of all members of U that are not members of A. The set difference {1,2,3} \ {2,3,4} is {1}, while, conversely, the set difference {2,3,4} \ {1,2,3} is {4} . When A is a subset of[…]

# Fractions and the Musical Meter

Fractions and the Music Meter In western music, we use something all a meter to define a piece’s rhythmic structure. On staff paper, the meter is placed before the whole piece but after the clef (the clef is used for finding notes, to learn more about clefs click here). The music meter is essential for[…]

# Fractions

Fractions in the Rhythmical Musical Context Understanding fractions is an important conception to have when consulting music. In music fractions are mainly found in rhythm by way of meters, note division, note subdivision, tempo, and harmonic rhythm. Fractions are what allow musicians to simplify rhythm and help to explain why certain rhythmic patterns sound the[…]

# Amplitude in the Musical Context

Amplitude in the Musical Context At the very basic level, sounds of music are made up of primarily two different properties. Both properties are directly related to the vibration of soundwaves. These properties are Frequency and Amplitude. This article will focus on Amplitude. To learn more about Frequency click here. To understand Amplitude, one must[…]

# Frequency

Frequency in the Musical Context At the very basic level, sounds of music are made up of primarily two different properties. Both properties are directly related to the vibration of soundwaves. These properties are Frequency and Amplitude. This article will focus on Frequency. To learn more about Amplitude click here. To understand Frequency, one must[…]

# Union

“Union” in set theory is a very simple concept. If you had one set of items, let’s say a {cat, dog} and another set of items {fish, bird} the union of these two sets would be: {cat, dog, fish, bird} The symbol used for Union is “∪,” thus in set theory our example would be[…]

# Passing Diminished Scales

For those of you not familiar with Passing Diminished Scales here is a brief description. Passing Diminished Scales are used over Passing Diminished Chords. Passing Diminished Chords exist between the diatonic chords of a key center. So if we took the Diatonic Chords of C Major i.e. C Major 7, D minor 7, E minor[…]