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# Pitch class

In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class.

In musical set theory it is more accurate to say that a pitch class is an equivalence class of all pitches that are octaves apart, which would be labeled by an integer, not a traditional letter name. In both cases, when "pitch class" is used, the use of "pitch" indicates a specific frequency or note and does not include its octaves.

Using integer notation and mod 12, two pitches, x and y, are in the same pitch class only if for some integer n:

x = 12n + y

If one only knows the pitch interval, ip, between two pitches, one may use this definition: A pitch class is the set of all pitches such that for any two members of the set x and y:

$\operatorname{ip}(x,y) = 12n$

for some non-negative integer n.