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Collections and Scales |
As composers sought new sounds, many of them turned to novel scales as replacements for the hegemonic major/minor system that characterizes most functional tonal music. To be sure, major and minor scales maintained currency in the twentieth century, but they were but one variety of scale amongst many.
When characterizing many of these new musical resources, the word “collection” is often more appropriate than "scale." A collection is a group of notes—usually five or more. Imagine a collection as a source from which a composer can draw musical material—a kind of “soup” within which pitch-classes float freely. Collections by themselves do not imply a tonal center. But in a composition a composer may establish a tonal center by privileging one note of the collection, which we then call a scale.
##Diatonic Collection##
The diatonic collection is any transposition of the 7 white keys on the piano. Refer to these collections by the number of sharps and flats they contain: the “0-sharp” collection, the “1-sharp” collection, and so on. The “2-flat” collection, for example, contains the pitch classes {F, G, A, B-flat, C, D, E-flat}.
When these collections gain a tonic note, they morph into scales, which by tradition we name according to the “modal” system established in centuries ago. Seven unique scales can be formed from a single diatonic collection by taking each note of the collection and treating it as a tonic. Imagine the “0-sharp collection” which contains {C, D, E, F, G, A, B}: Ionian treats C as tonic, Dorian treats D as tonic, Phrygian treats E as tonic, Lydian treats F as tonic, Mixolydian treats G as tonic, Aeolian treats A as tonic, and Locrian treats B as tonic.
##Pentatonic Collection##
Pentatonic collections are five-note subsets of the diatonic collection. Here’s a quick way to create a pentatonic collection: (1) List the notes of a major scale. (2) Remove scale degress 4 and 7. (E.g., the pentatonic collection {C,D,E,G,A} corresponds to scale degrees 1,2,3,5,6 of the C major scale.)
Removing scale degrees 4 and 7 results in a collection with no half steps. As a result of its "halfsteplessness", any member of the collection easily functions as a tonal center.For example, given the 0-sharp pentatonic collection, there are five unique scales formed when each of the collection's pitch classes become a 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.
##Whole Tone Collection#
This is a group of notes generated entirely by whole tones: {0,2,4,6,8,10}, for example.
There are only two unique whole-tone collections. WT0 contains the pitch classes {0,2,4,6,8,10} and WT1 contains the pitch classes {1,3,5,7,9,11}. We often refer to these as the “even” and “odd” whole-tone collections in reference to the parity (even or odd) of the integers in the collection.
##Octatonic Collection##
Called octatonic because it has eight pitch classes, the octatonic collection is full of compositional potential and has been used by many composers to a variety of ends. An octatonic collection is easily generated by alternating half steps and whole steps. Using pitch class numbers, one example is {0,1,3,4,6,7,9,10}.
The interval content of this collection is very homogenous, and this intervallic consistency leads to one of its most interesting properties. When we transpose the above collection by 3—adding 3 to each of the integers in the collection—{0,1,3,4,6,7,9,10} becomes {3,4,6,7,9,10,0,1}. Comparing the two shows that these collections are exactly the same! In fact, you would come up with the same collection if you transposed it by 6 or 9 as well.
Olivier Messiaen called such collections “modes of limited transposition." (The whole-tone scale is also a mode of limited transposition.) And as a result of the property, there are only three unique octatonic collections. We name these arbitrarily as OCT(0,1) , OCT(1,2) , and OCT(2,3). The numbers to the right of “OCT” are pitch classes within that scale. (E.g., the {0,1,3,4,6,7,9,10} collection I discussed above is OCT(1,2).)
##Other Collections and Scales##
There are many, many other collections and scales used by composers and musicians in the twentieth- and twenty-first centuries. Messiaen, for example, described five more modes of limited transposition, and there are other smaller collections that have the same property. Acoustic scales, formed from the first seven unique partials of the overtone series, are common in the music of Debussy, Bartok, and Crumb—ocassionally as a representation of nature. Jazz musicians have an entire set of scales used for improvisation. Non-Western musics often have unique systems of scales and collections, such as the rāgas used in Indian classical music.
More generally, any large set of pitch classes that form the basis for a passage may function as a collection, even if it has no familiar name. Most often, music theorists refer to these collections with pitch-class set notation.