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| PITCH CLASS SETS | |
| NORMAL ORDER AND TRANSPOSITIONAL EQUIVALENCE | |
| BEST NORMAL ORDER, PRIME FORMS AND INVERSIONAL EQUIVALENCE | |
| SET TYPES | |
| INTERVAL VECTOR | |
| AGGREGATES | |
| SEGMENTATION | |
| EMPTY AT PRESENT |
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Definition. A pitch-class set (PCset) is an unordered collection of pitch classes.
See your textbook starting at page 178 for a discussion.
How to indentify a pitch-class set:
Since a pitch-class set can be construed from any grouping of pitches your job is to find what you think are the most important groups of pitches. Some suggestions would be the following.
Sondheim, "Sunday In The Park With George"
From our work in class we were able to locate 10 different pitch-class sets on the first page of the score. It is the rhythmic organization that makes these pitch-class sets very clear. These PCsets are (G, F, Bb, Eb); (G, Bb, Ab, Eb); (G, C, Ab, Eb, Bb); and (G, D, Ab, Eb, Bb).
These are simply "raw" pitch-class sets. In order to study how they are used in this piece, and to generalize that use to the compositonal styles of other composers we must place them in some universally understood format. Otherwise, it would be impossible to draw any important conclusions about Sondheim's musical style.
After we have located the pitch-class sets we wish to study they need to be placed in Normal Order. Continue scrolling to review how to establish Normal Order for any Pitch Class Set.
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Definition. The normal order of a pitch-class set is that ordering of the pitches that spans the smallest possible interval.
See your textbook starting at page 179 for a discussion.
Two pitch-class sets are said to demonstrate "transpositional equivalence" when the notes of the second pitch-class set can be demonstrated to be a particular transposition interval above or below the first pitch-class set. For example: Pitch-class A contains pitches 3 7 6 9. When A is compared to pitch-class B (pitches 6 10 9 0) we find that each pitch class number in B is a minor third above A. 6-3 = (3); 10-3 = (7); 9-3 = (6); 0(12)-3 = (9)
Normal Order may not be the most bsic order for the pitches of a given pitch-class set. Continue scrolling to review how to establish the Best Normal Order for any Pitch Class Set.
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Definition. The best normal order of a pitch-class set is that ordering (when comparing both normal order and its inversional equivalent) of the pitches that spans the smallest possible interval.
See your textbook starting at page 182 for a discussion.
The normal order of a major triad is 0 4 7. However, we know that the minor triad uses the same intervals as the major triad (minor thirds, major thirds and perfect fifths). In short, the minor triad is the inversional equivalent of the major triad (CEG=major third, minor third outlining a perfect fifth, where as C Ab F= major third, minor third outling a perfect fifth by inversion). Since the minor triad's interval order up from the root is 0 3 7 this version of the two triads is the best normal order since the intervals are "most packed to the left."
Another name for best normal order is Prime Form. This opens the concept of Set Type and Interval Vector. Continue scrolling to review Set Types and Interval Vector.
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Definition. The set type (set class) is the complete collection of a pitch class set. This collection includes the set, its 12 transpositions, its inversion and the 12 transpositions of its inversion. All members of the set type are represented by the Prime Form.
See your textbook starting at page 185 for a discussion.
For convienence a set type is named by using the numbers of its prime form. Thus, the numbers (0 3 7) represent the name of the major/minor triad set type. A second name is also given the set types. These are numbers that the Yale music theorist, Alan Forte assigned each set type in his early attempt to organize the field of Atonal music. The meaning of the numbers will be discussed in class. These numbers include a cardinal number (for the total number of pitches in the set) and a position number (a set's position on Forte's listing of sets).
The total name of a set type would be, in order, the Forte number followed by the prime form numbers in parenthesis. Thus, the major/minor triad set type would be 3-11(0 3 7). A complete listing of the prime forms using the set type organization found on page 185 in your textbook will be found on Information Sheet No 4. You will be referriing to this chart many times during this semester.
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