Skip to main content

Section 33.2 Normal Form

Normal form represents the notes of a pitch-class set (as they occur in the music) in their most compact form.
To determine normal form, follow these steps:
  1. Put the notes of a pitch-class set from a piece of music in ascending numeric order (like a scale). Eliminate any duplicate pitches.
  2. Examine every possible ascending “scale” ordering of the notes until you find the most compact form—that is, the one that spans the smallest interval from lowest to highest note.
  3. In the event that two orderings have the same interval span from lowest to highest note, choose the set that has the smaller interval between the first and penultimate notes. 1 
  4. In the event of an absolute tie, choose the set that begins on the smaller number. We will use a different set of pitches to demonstrate a complete tie. The normal form for the notes below is [2, 3, 8, 9].
  5. Normal form is written in square brackets with commas. The normal form found in step 3 above was [11, 2, 3, 7].
The Forte method for determining prime form would have measured from first to second note to break the tie instead of first to penultimate note, which is the method used in Rahn’s Basic Atonal Theory.