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VIII. 20th- and 21st-Century Techniques
Collections

### Core Idea

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](https://viva.pressbooks.pub/openmusictheory/chapter/major-scales/) or [diatonic modes](https://viva.pressbooks.pub/openmusictheory/chapter/diatonic-modes/)

### Explanation

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 \uparrow\hat{4}; 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

Chapter Playlist

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 (Example 1).

Using the scale degrees of a major scale, a pentatonic scale can be formed with \hat{1}\text{, }\hat{2}\text{, }\hat{3}\text{, }\hat{5}\text{, and }\hat{6}.

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 (the white notes) is G♭, A♭, B♭, D♭, E♭ (the black notes). The black-note collection is, once again, the pentatonic.

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Example 1. (a–c) Three ways of generating a pentatonic collection, and (d) a rotation of the pentatonic collection.

What the pentatonic collection removes from the diatonic is the two notes that create half steps (\hat{4} and \hat{7}, if you are thinking in terms of major scale degrees). The absence of semitones arguably makes the pentatonic more readily rotatable and considered as a collection, without a strong emphasis on a particular note as tonic. Any member of the collection easily functions as a tonal center. For example, there are five unique modes of the collection given in (a) of Example 1, formed by rotating the collection so that each pitch class becomes tonic: C pentatonic (C, D, E, G, A), D pentatonic (D, E, G, A, C), E pentatonic (E, G, A, C, D), and so on. Letter (d) of Example 1 gives an especially common rotation of the pentatonic collection that is referred to as the minor pentatonic.

The pentatonic scale is especially common as a basis for melodic composition. One example can be heard during the first movement of Chen Yi's percussion concerto, at the entrance of the strings at 2:13. Notice that the pentatonic melody is sometimes accompanied by atonal-sounding chords in the brass. Pentatonic melodies don't need to be harmonized within the pentatonic collection, and in fact often aren't; after all, there are only two possible triads in the pentatonic collection (C major and A minor, for example, in the collection C–D–E–G–A).

Whole-Tone Collection

The whole-tone collection is exactly what it sounds like: a scale made up entirely of six whole steps. Similar to the pentatonic scale, the whole-tone scale is rotationally ambiguous, since there is only one size of step. Composers often exploit this ambiguity by using the whole-tone collection to produce an unsettled feeling in the listener (in film and TV, one famous trope is to use the whole-tone scale to accompany a dream sequence).

There are only two unique whole-tone collections: one that contains the even-numbered pitch classes [0, 2, 4, 6, 8, 10] and one that contains the odd-numbered pitch classes [1, 3, 5, 7, 9, 11]. If you need to distinguish between these two collections in an analysis, you can use the abbreviations WT0 an

### Key Quote

Such examples are not tonal, nor are they modal; instead, they are considered pandiatonic.

### Application Scenarios

You have probably encountered the concept of the diatonic collection many times already, especially in the chapters on [modes in pop](https://viva.pressbooks.pub/openmusictheory/chapter/modal-schemas/) and in [20th-/21st-century music](https://viva.pressbooks.pub/openmusictheory/chapter/diatonic-modes/), or even when you first learned about [major](https://viva.pressbooks.pub/openmusictheory/chapter/major-scales) and [minor](https://viva.pressbooks.pub/openmusictheory/chapter/minor-scales) 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.](https://open.spotify.com/track/691BiD2G6asBcKOooxqTTu?si=cbFPXmyXRi6C9c0i0gx1Ww)

The pentatonic collection is prevalent in music across the globe. It is a collection built with the [interval](https://viva.pressbooks.pub/openmusictheory/chapter/intervals-and-dyads/) pattern ma2–ma2–mi3–ma2–mi3. The pentatonic collection can be described with reference to the diatonic modes in multiple different ways (Example 1).

Example 1. (a–c) Three ways of generating a pentatonic collection, and (d) a rotation of the pentatonic collection.

### Key Terminology

whole-tone collection pentatonic collection octatonic collection acoustic collection harmonic series pitch interval transposition pandiatonic collection mixolydian interval diatonic

### Related Links

major/minor scales diatonic modes Chapter Playlist modes in pop 20th-/21st-century music major minor throughout the opening of his ballet Petrushka.interval the first movement of Chen Yi's percussion concerto
Source: https://viva.pressbooks.pub/openmusictheory/chapter/collections/
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