Forte Numbers: A Very Short Primer

In my own practice I've been making less use of scale and arpeggio language lately and looking at more neutral, atonal terminology instead. There's a good chance this will show up in some upcoming posts so here's a primer.

In 12-tone music we're interested in working with collections of notes that can be used to give a specific "flavour" to a melodic line or harmony. In fact, as with scales and arpeggios, the notes aren't the important part: it's the intervallic structure they define that matters.

Look at a major triad: it's 1-3-5, meaning the first, third and fifth notes of the major scale in the appropriate key. But if we're not thinking tonally, this is less helpful. We'd prefer to say something like the following. Start on any note. Go up 4 semitones and you get the next note. Go up another 3 semitones and you get the third note. That's a major triad.

The problem is that you can voice the major triad in different ways, leading to different recipes. For example: start on any note, go up 7 semitones, then go up another 9. That produces the "same" major triad. Of course it's not the same, but it does contain notes with the same names (C, E and G) and we consider it to be the same type of thing.

So we need a way to gather up all the many ways to make a "major triad" into one box. We can do this by minimizing the intervals involved, following a standard recipe. The exact recipe isn't important for us: what matters is that it can be done. The resulting notes are said to be in "normal form".

In fact you can take any collection of the 12 notes of the chromatic scale and once you put them into normal form there aren't actually that many possibilities. They were (AFAIK) first listed by Allen Forte in his important 1973 book The Structure of Atonal Music.

Forte identifies each possibility by a pair of numbers like 3-11. The first number says how many notes are in it. The second it just its position in his list. It so happens that 3-11 is the major triad. Although they're a bit arbitrary, Forte's numbers have become a universal way to talk about collections of notes -- "pitch class sets", in the jargon -- without leaning on older tonal language that isn't always appropriate.

Here is Wikipedia's version of Forte's list. It's a bit nicer than the one in the original book. Wiki can be awful for music theory but in this case they did a good job. If you sometimes want to look up the Forte number of a bunch of notes of interest, along with a lot of other information, this calculator is worth bookmarking.

Here's a bit more about how this stuff works in case you're curious, but I'm unlikely to get deep into this stuff in posts here simply because it's not very accessible to casual readers. For the purposes of this blog we'll mostly use Forte's names for things that don't have good names already.