VIII. 20th- and 21st-Century Techniques
Set Class and Prime Form
Brian Moseley and Megan Lavengood
Key Takeaways
- A set class is a group of pitch-class sets related by transposition or inversion.
- Set classes are named by their prime form: the version of the set that is transposed to zero and is most compact to the left (compared with its inversion).
- You can find prime form mathematically or by using the clock face.
- All possible set classes are summarized in the set class table, and are available on Wikipedia and many other websites.
The simplest way to define set class is “a group of pitch-class sets related by transposition or inversion.” This may initially seem confusing, but it’s just another kind of class. As you have learned in other chapters, “class” is another name for “group.” Recall the other kinds of classes you have already learned about.
- Pitch vs. pitch class: A pitch occurs at a specific octave, and often we conceive of it with a specific spelling. A pitch class is a group of pitches that is related by transposition or inversion.
- Interval vs. interval class: An interval has a specific distance in semitones, while an interval class is a group of intervals that are inversions of each other or related by octaves.
Introduction
Pitch-class set vs. set class (pitch-class set class) is the topic of this chapter. The reason the definition of “set class” may seem more confusing is that it involves two kinds of groups: classes and sets.
- A class is a group that is related in some way.
- A set is a group that is not necessarily related in any specific way.
As an analogy, consider biology and the way different living things are categorized. Plants in the same class are are all biologically related in a specific way: Angiospermae is a class of plants that produce flowers. But we can group together plants for other reasons: the group of plants in someone’s front yard, for example. That would be a set of plants, but not a class of plants.
So a pitch-class set is a group of pitches that the analyst decides to put together for some reason. The pitch-class set class—a term that is very unwieldy, so theorists have agreed to shorten it to the last two words, set class—is the group of groups of pitches that are all related by transposition or inversion.
Why transposition and inversion?
One way of analyzing a lot of post-tonal music is by studying the transpositional and inversional relationships between pitch-class sets. Take the short example below: two passages from Béla Bartók’s “Subject and Reflection” ( ). Comparing across the two passages, the two sets that comprise the right hand, [10, 0, 2, 3, 5] and [3, 5, 7, 8, 10], are related by T5. The two left-hand sets are also related in the same way..Now looking within each passage, the right and left hands are related to each other by inversion. In the first passage, they are related by I8; in the second, by I6.
To quickly explain why these snippets of notes all sound the same, we can say th