: Rahn Atonal Prime Form Confusion A review via the mark I eyeball of the prime form tables in "Basic Atonal Theory" (Rahn, 1980) versus modern software calculations of the prime form yields some differences; are these errors

Vote Up Vote Down   0 Reactions

Login to give Reaction!

They are both right and here's why.

There are two different algorithms for determining the prime form which are Forte's and Rahn's. In most cases they are the same, however there are a handful that are not the same. The one's you've noted are not the same with both algorithms. The breakdown of them are as follows:

Pitch Class Set Forte Prime Rahn Prime
7-Z18 (0,1,2,3,5,8,9) (0,1,4,5,6,7,9)
7-20 (0,1,2,4,7,8,9) (0,1,2,5,6,7,9)
8-26 (0,1,2,4,5,7,9,10) (0,1,3,4,5,7,8,10)

You can even try it out yourself on this calculator.

Here's a more in depth explanation of why this is and what the actual difference is bewteen the two from the What is this? button next to the two algorithms.

There are two algorithms for computing the prime form of a Pitch Class
Set. The first was introduced by Allen Forte in The Structure of
Atonal Music and the second is used by John Rahn in his book Basic
Atonal Theory and is also used by Joseph N. Straus in his Introduction
to Post-Tonal Theory.

The difference between the two algorithms is apparent when examining
Pitch Class Set 6-31. The Prime Form using the Forte algorithm is
(0,1,3,5,8,9), and the prime form using the Rahn algorithm is
(0,1,4,5,7,9). As you can see, the Forte algorithm puts a priority on
making the small numbers smaller (i.e. 3 instead of 4), whereas the
Rahn algorithm wants the larger numbers to be smaller (i.e. 7 instead
of 8).

Which is better? Well, it depends on who you ask. Computer programmers
and computer music people will typically prefer the Rahn algorithm
because it is computationally more elegant. However, the Forte
algorithm has the more established pedigree, and so it tends to be
preferred by academics.