Music Theory
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[…]
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[…]
Using Algebra to Find an Octave’s Pitch
Finding an Octave’s Pitch Algebraically The one consistent interval used in music across all cultures is known as the octave. In music, the octave is known as the interval between one pitch and another that is either half or double its frequency (Hz). For example, if we were to take the pitch of middle C[…]