A few basic things about music theory: Pitch-class set theory and its uses
Today, we’re going to discuss a few things about music theory. While most music theories revolve around scales and modes (which, of course, will cover at some point) I prefer another way of thinking.
Allen Forte was a musicologist that tried to analyze atonal music. He created a music theory revolving around pitch-class sets, which however, can be used to encompass not only atonal music, but tonal music as well.
Allen Forte
When we are referring to a pitch-class, we mean a note, not matter which octave it is in. So for example, the pitch-class C, contains all the Cs on a piano.
When we are referring to a pitch-class set, we mean a set that contains some (or all) pitch-classes.
A pitch-class set that contains the notes C, E and F. Instead of using musical notation, we could also just refer to our set as C, E, F, since the octave doesn’t matter.
This was a very useful invention for studying atonal music. Atonal music is not based on scales, but usually on things like certain series of notes, that don’t necessarily have any inner logic.
By defining the pitch-class set for a musical composition, the theorist can know upon which pitch-classes the musical piece is based and analyse them easier. However, what makes pitch-class set theory interesting for those who don’t write atonal music, is the fact that pitch-class sets provide a very easy way of encapsulating all other music theories.
One of the problems that people face when they start writing music, and they are not very accustomed with music theory, is this: If I want to play a solo, or an extra riff, or anything, over something else (melody or harmony), which notes should I play?
This problem is solved as follows. The notes of the first musical phrase that you’ll play over, constitute a pitch-class set. No matter the scale or the mode, a new musical phrase, always sounds in tune, as long as it shares the same pitch-class set as the original musical phrase.
So, let’s see the following example.
This meter is actually in C major. However, even if you don’t know scale theory, you can just consider all these notes a the following pitch-class set: C, D, E, F, G, A, B. Then you can play anything you like with these notes.
Of course, someone will wonder, why use this theory, while I know it is C major. Consider the following example now.
This example doesn’t clearly belong to any scale. However, pitch-class sets don’t possess such limitations. The pitch-class set for this example is: C, D, D# (or Eb), E, F, G, A, A#(or Bb) and B.
This can be applied to any example. So, pitch-class set theory makes it much easier to not only to analyze atonal music pieces, but also, to help you deal with musical phrases that don’t belong clearly to any scale.
Major scales, minor scales and modes can all be included in this system. We will cover these in future posts. For now, you just keep in mind, the above rule
No matter the scale or the mode, a new musical phrase, always sounds in tune, as long as it shares the same pitch-class set as the original musical phrase.
Since, scales and modes are so omnipresent, additional rules have been created for their use and analysis that we will cover in other articles. Until then, just keep playing and writing music 
