Suggested Learning Resources
3) Online Reading: What is Normal Form? http://www.jaytomlin.com/music/settheory/help.html#normalform
- 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.
https://youtu.be/OWL6JDAPE8Q
Objective 48.1: Arrange pitch-class sets correctly (ascending order, clockwise, fewest
gaps) [Normal Order]