# Scales

# 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[…]

# 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[…]