# Mathematics

# 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

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[…]

# 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[…]