Suggested Learning Resources


2) Video Lesson: Set Theory Video Part 1 David E Ferrell Channel

3) Online Reading: Pitch Class Set Definitions and other Terms

4) Interactive Lesson: 

Music Theory QuickThink:

- Pitch-class: Refers to a pitch regardless of octave (C4 and C5 are both considered C's... In integer notation, they are both considered 0 )

- Pitch-class-sets: A collection of pitches, usually written in integer notation.  They are UNORDERED, which means the order does not matter.  They are written in curly brackets.  Because order does not matter {0 2 5 7} is the same as {2 7 5 0} . However, even though the order does not mater in { } , we try to list them in ascending order , in a way that has the fewest gaps… (lowest number is not always first)  This is comparable to thinking of a triad in root position. 

- Ordered-pitch-intervals: These are the distance between two notes measured in half steps, using a plus or minus sign to show direction. Intervals can be larger than 12 and use a + or – to show direction (example +15 is fifteen half-steps up).  (The distance from D up to F# is +4.  In integer notation, the distance from 2 up to 6 is +4.)

- Unordered-pitch-intervals: These are the distance between two notes measured in half steps, but they do not specify direction up or down. This is often used when naming the interval size of two pitches that occur at the same time. Can be larger than 12.

- Ordered-pitch-class-intervals: This is the distance between two notes X and Y where the order (X before Y) matters, but the octave does not.  To find, subtract Y-X using mod 12 arithmetic. (Example: If you have the note A followed by the note D, you would translate the notes to the numbers 9 and 2, subtract 2-9.  Using mod12, you would change the 2 to a 14, resulting in 14-9 = 5.   5 is the ordered pitch-class-interval between A and D. The result will always be a number between 0 and 11.

- Unordered-pitch-class-interval: This is the distance between two pitch-classes using the shortest possible distance.  Order in which the notes occur does not matter.  The resulting number will be between 0 and 6. You can find the unordered-pitch-class-interval of notes X and Y by calculating X-Y and Y-X (using mod12) and taking the smaller of the two numbers.  (NOTE: This is a precursor to the concept of interval-classes and interval-class-vectors, to be studied later)

Objective 47.2: Examples in Music: YouTube

Objective 47.2: Distinguish between pitch-class, pitch-class-sets, ordered-pitch-intervals, unordered-pitch-intervals, ordered-pitch-class-intervals and unordered-pitch-class-intervals