Suggested Learning Resources


2) Video Lesson: Normal Order, Davide E Farrell Channel

3) Online Reading: What is Normal Form?

4) Interactive Lesson: 

Music Theory QuickThink:

- Pitch-class-sets are a collection of unordered pitches in integer notation written in curly brackets.  Because they are unordered, their order does not technically matter. {0, 7, 1, 6} is the same collection as {6, 0, 1, 7} ... the curly brackets indicate that these are unordered pitches.  This is equivalent to talking about a triad; meaning [C, E, G]  and [E, G, C] are both describing a C Major triad even though the letters are mixed up.

- Even though the order of the integers does not matter in terms of the pitch collection, to make it easier for discussion and analysis, it is best to list the integers within the curly brackets in ascending order that contains the fewest gaps possible.  (this does not mean it will always start with the lowest number)

- An effective way of doing this, is visualizing a clockface, and finding the order around the clockface (moving clockwise) that produces the fewest gaps.

- Example {0,10,9,1} in ascending order is {0,1,9,10} , and the ascending order with the fewest gaps is {9,10,0,1} . This would be equivalent to listing the C Triad in root position.

Objective 48.1: Examples in Music: YouTube

Objective 48.1: Arrange pitch-class sets correctly (ascending order, clockwise, fewest gaps) [Normal Order]