VIII. 20th- and 21st-Century Techniques
This section introduces some common methodologies for the analysis of 20th- and 21st-century music, including set theory.
Prerequisites
This section assumes a familiarity with the topics covered in Fundamentals.
Organization
The first five chapters introduce students to the building blocks of set theory: integer notation, pitches vs. pitch classes, intervals and interval classes, sets and set classes, operations, and interval class vectors.
The chapter Analyzing with Set Theory (or not!) is an important conclusion to these earlier chapters: it discusses the philosophy of segmentation and also turns a critical eye to set theory as a methodology. What makes us group notes together and call them sets? What are we ignoring when we use set theory?
The final three chapters discuss collections, including modes, the octatonic collection, and others. Students are also taught here how tonic pitches can be heard within a composition using these collections.
A methodology for analyzing pitch in atonal music. Pitch classes are given an integer name (0–11, where C is 0, C♯ is 1, etc.). Groups of pitches are considered together as "sets." Sets may be related by inversion or transposition.
A system of naming pitch classes that treats C as 0, C♯ as 1, D as 2, etc.
