math
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[…]
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[…]