33.2: Normal Form
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:
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Put the notes of a pitch-class set from a piece of music in ascending numeric order (like a scale). Eliminate any duplicate pitches.
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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.
- 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
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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].
- Normal form is written in square brackets with commas. The normal form found in step 3 above was [11, 2, 3, 7].