VIII. 20th- and 21st-Century Techniques
Collections
Mark Gotham; Megan Lavengood; Brian Moseley; and Kris Shaffer
Key Takeaways
This chapter introduces a number of pitch collections that appealed to many composers in the 20th century:
- diatonic collection, as separate from major/minor scales or diatonic modes
- pentatonic collection: a five-note collection that corresponds to the black keys of the piano; can also be generated as a stack of five perfect fifths or through the pitch interval pattern 2–2–3–2–3
- whole-tone collection: a six-note collection that is made up entirely of notes separated by whole steps
- octatonic collection: an eight-note collection that is formed by alternating whole- and half steps
- hexatonic collection: a six-note collection generated with the pitch interval pattern 1–3–1–3–1–3
- acoustic collection: a seven-note collection similar to the mixolydian mode but with a [latex]\uparrow\hat{4}[/latex]; corresponds roughly to the lowest partials of the harmonic series
Other pitch collections introduced include:
- Olivier Messiaen’s “modes of limited transposition”: a group of scales that cannot be transposed in 12 unique ways
- The “distance model” of generating collections with a repeating pattern of pitch intervals
Beyond the use of major/minor and the diatonic modes, there are four new(ish) collections that occupy a special place in the 20th century: the pentatonic, whole-tone, octatonic, and acoustic collections. This chapter discusses these collections along with some important questions of modal properties and extra-musical meaning.
Diatonic Collection and Pandiatonicism
You have probably encountered the concept of the diatonic collection many times already, especially in the chapters on modes in pop and in 20th-/21st-century music, or even when you first learned about major and minor keys. The diatonic collection is the basis of much Western music.
In the 20th and 21st centuries, composers sometimes used the diatonic collection, but without making any attempt to make a specific pitch sound like the the pitch center. Such examples are not tonal, nor are they modal; instead, they are considered pandiatonic. Igor Stravinsky often wrote pandiatonic passages; many can be heard throughout the opening of his ballet Petrushka.
Pentatonic Collection
The pentatonic collection is prevalent in music across the globe. It is a collection built with the interval pattern ma2–ma2–mi3–ma2–mi3. The pentatonic collection can be described with reference to the diatonic modes in multiple different ways ( ).
- Using the scale degrees of a major scale, a pentatonic scale can be formed with [latex]\hat{1}\text{, }\hat{2}\text{, }\hat{3}\text{, }\hat{5}\text{, and }\hat{6}[/latex].
- If you think of the diatonic collection as a stack of perfect fifths (F, C, G, D, A, E, B), then the pentatonic is a narrower form of the same collection: C, G, D, A, E.
- Finally, if you visualize the piano, note that the complement of C, D, E, F, G, A, B, C (t