How do I calculate the Forte number from the Prime form?

Question

How do I calculate the Forte number from the prime form of a set? For Example: I have the prime form (0,1,5,8)... How would I determine the Forte number from this set? Or would I use a different form of the pitch class set to figure this out? I have been trying to figure this out for weeks but can't seem to know how to figure this out myself without using a calculator.

Answer 1

In most instances, it's a logical progression of increasing the outer integers. When it comes to trichords, for example, (012) is Forte label 3–1, (013) is 3–2, (014) is 3–3, and so on.

But that's not very helpful with something like (0158); you don't want to walk through all tetrachords to try to determine which one it is, and with tetrachords the algorithm becomes a bit more complex. Really, your best bet is to just have a chart nearby with all of the Forte numbers on them. I know of several music theorists and analysts of twentieth-century music that have such a chart just taped on the wall for easy reference.

And if you'll be spending a lot of time with these, I recommend keeping track of the six set classes that are different based on the Forte and Rahn labeling systems; see more in the table here.