Set Classes

A set class is a collection of all the sets with the same intervallic recipe, the intervals of which are realized either upward or downward.  A set type is also defined by an intervallic recipe, but the intervals are always realized upward from a “root.”  Given a set type of (037) we can realize a pitch class set of that type by specifying a root and then supplying the notes 0, 3, and 7 semitones above that note.  With a “root” of G, for instance, we get the set {G B-flat D}, or {7 t 2}, or a G minor triad.

Now compare the set class [037].  Now the intervals can be read as upward intervals +0, +3, and +7 semitones or as downward intervals -0, -3, and -7.  Let’s make G for the referential pitch class, the “zero” from which we build the interval pattern.  Going upward from G produces the set {G B-flat D}.  As noted above, this is a G minor triad.  Going downward produces another set–going 3 semitones below G and 7 semitones below G produces {G E C}.  This is a C major triad.  Major and minor triads, set types (047) and (037), belong to the same set class because they both can be described by the same intervallic recipe: [037].  Their intervallic content is the same.

 Introduction to Set Classes

 

Here are simple procedures for naming sets, including their set class.

How to Name Sets.v2

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