Knowing the math of 12-tone rows will expand your understanding of the spirit of experimentation in classical music.
National Standards: 1-11
Prepare: Have the class read The Power of 12 (page 24 of the student edition). The article explains the concepts behind 12-tone music.
Listen to a playlist of audio samples illustrating the examples from the article:
Click here to download the files for audio playback on the Notion app.
Key points in the article:
- A 12-tone row is a series of notes that are similar to a scale. 12-tone music gives even emphasis to every note in the 12-tone row it employs.
- 12-tone rows can be varied for further experimentation. The original row, called the prime form, is called a retrograde form when reversed.
- If in the prime row the distance between the first two notes is one half step up, an inversion form of the prime row would find the distance between the first two notes to be two half step down.
- Just like scales, 12-tone rows can be transposed if each note in the row is raised or lowered by an equal amount throughout the row.
- Beginning with the work of Arnold Schoenberg, a pioneer of 12-tone music, 12-tone rows have been used frequently in classical music as well as in jazz.
Begin: Try some of the techniques with the class, noting the tips described in each example. Lessons might include:
- Asking students to play through examples 1-3 to become familiar with the sound of a 12-tone row and its variations.
- Separating students into groups to play example 6, and for an added challenge, 7.
- Reading through examples 5-7 on the piano for the class.
Develop: Play the following video of the music used in example 5, the Präludium to Arnold Schoenberg’s Suite for Piano, Op. 25, the first piece to include a 12-tone row in every movement.
What does this music sound like to you? How would you describe it?
What effect does the use of 12-tone rows have on the music?
(The music sounds less organized, though through his conscious use of 12-tone rows, Schoenberg applied a thoughtful order.)
If you could pick one style of music that this most closely resembles, what would it be?
Expand: Now play the following video of the music used in example 7, “T.T.T. (Twelve Tone Tune)” by Bill Evans:
What similarities does this piece of music share with Schoenberg’s composition?
(Use of a 12-tone row.)
What makes it different from Schoenberg’s composition?
(Rhythm and instrumentation.)
Schoenberg’s Suite for Piano, Op. 25 was written in the early 1920s. Evans’ composition was written in the early 1970s. How might the experimental nature of 12-tone music have influenced the evolution of jazz?
Apply (Optional): Using classroom pianos or available instruments and blank notation paper or notation software on classroom computers, have students each select a 12-tone row from the matrix in example 4 and write a short composition based on the row. Then have them write a second composition on the inversion of that row. Once they’re done, go around the room and have each student play their composition for the class.