Suggested Learning Resources

1) YFIO

2) Video Lesson:

3) Online Reading: More Properties of Pitch Class Sets and Interval Vectors http://composertools.com/Theory/PCSets/PCSets8.htm

4) Interactive Lesson: 

Music Theory QuickThink:

COMMON TONE THEOREM – If you look at the Interval-class-vector , the # in each labeled position tells you how many common tones will appear between the original set and the resulting set when transposed by the labeled position # and the original set. For IC VECTOR 060603  ,if you transposed the set by 2, you would have 6 common tones between the original set and the resulting set.  (for spot 6, you have to double the number to get the number of common tones)

Transpositions number larger than 6 simplify to the number that adds to 12. (Example, 9 simplifies to 3. 8 simplifies to 4)

Objective 55.1: Examples in Music: YouTube

https://youtu.be/DaFSKiKNF08

Objective 55.1: Use the Common-Tone-Theorem and Interval-class-vectors to calculate number of common tones between two pitch-class-sets