Note: Normal form, prime form, and packing

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Guides to pc set analysis, including this one, usually say that the normal forms of sets are "packed to the left." Though a convenient expression, it is not quite true. When we learned the steps for determining normal form (see page 4 of this guide), we learned that when two or more set forms are tied for overall size, we seek the smallest interval from first pc to second-last, then from first to third-last, and so on, working in from the end until the tie is broken. In fact, then, we are not really looking for the form most packed to the left, but for the one most packed from the right!

This "packed from the right" convention is the one found in several guides to pc set analysis, including John Rahn's Basic Atonal Theory and Joseph N. Straus's Introduction to Post-Tonal Theory. Allen Forte's The Structure of Atonal Music, however, favours a true "packed from the left" approach: in the case of overall ties, one looks for the smallest interval between first and second pc, then first and third, and so on, working out to the end.

The conflict is usually discounted as a minor one, since the two approaches mostly produce the same results. For some sets, however, the results differ. Morever, 6 out of the 208 prime forms are affected by these differences. Below is a list of the set classes in question, with their prime forms cited "packed from the right" and "packed to the left."

Forte    
name:		 Prime form
packed from the right    		 Prime form
packed to the left    
5-20 (01568) (01378)
6-Z29 (023679) (013689)
6-31 (014579) (013589)
7-z18 (0145679) (0234589)
7-20 (0125679) (0124789)
8-26 (0134578T) (0124579T)


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