Theory Orals: Post-Tonal

Question 1

What is the interval vector?

Answer 1

A systematic listing of all intervals within a given set. Displayed with Interval Classes.

Question 2

What is the interval vector used for?

Answer 2

To determine how many common tones are preserved during transposition or whether a set can map onto itself during transposition.

Question 3

What is the index vector? How is it useful?

Answer 3

o Tallies the number of common tones found in the summation square, but in an easy to read row format.

Question 4

What is the summation square?

Answer 4

Determines the number of common tones under Inversion. Determines if a Set is Inversionally related.

Question 5

What is invariance?

Answer 5

The preservation of some aspect of a row under transposition or inversion.

Question 6

With which composer is Invariance associated?

Answer 6

Anton Webern

Question 7

In a given row, how do you preserve an adjacent segment of, say, three notes in a second row?

Answer 7

This is determined by finding the prime form of a set and seeing if any other sets within the row match. If so, is it by transposition or inversion? From there, transpose or invert the row to keep that particular set invariant.

Question 8

How do you determine inversional symmetry?

Answer 8

One must look at the AIS of two given sets and determine if each AIS can be positioned as mirror images of one another. If so, then the sets are inversionally symmetrical.

Question 9

Why is Inversional Symmetry significant?

Answer 9

All sets are transpositionally related, even if just by the trivial case of T¬0, but not all sets are inversionally related. So, the ones that are inversionally symmetrical are far more interesting and significant.

Question 10

Name a piece that includes the technique of hexachordal combinatoriality.

Answer 10

Schoenberg: String Quartet No. 4 or Klavierstücke, op. 33a

Question 11

Define Hexachordal combinatoriality?

Answer 11

Combinatorial rows are those that can produce a transposition, inversion, retrograde, and/or retrograde inversion in which the first six pitches, or hexachord, or the new row will be completely different than the first hexachord of the former. In other words, the first hexachord of both the old and the new rows will create an aggregate.

Question 12

Name the 6 all-combinatorial hexachords.

Answer 12

(012345), (02468T), (014589), (012678), (023457), (024579)

Question 13

How many Major triads are in an octatonic collection?

Answer 13

FOUR - As well as 4 minor and diminished triads, as well as 4 Mm 7ths, mm 7ths, and fully diminished 7ths.

Question 14

What is the relationship between (0146) and (0137)?

Answer 14

• -They have the same interval-class vector: [1,1,1,1,1,1]
• -They are “All Interval-Class” Tetrachords
• -They are also Z-related, meaning that they have different prime forms, but the same interval vector.

Question 15

What is the relationship between set classes that have the same interval vector?

Answer 15

They are “Z-Related,” meaning that they have different prime forms, but the same interval vector.

Question 16

What is significant about the list of hexachord set classes?

Answer 16

• -The large number of Z-Related Sets.

- -Most are complements of themselves, rather than having separate complements.

Question 17

What is special about the interval vector for the diatonic collection?

Answer 17

• -7-35: [2,5,3,4,6,1]
• -It is the only set with a CLEAR hierarchy of intervals, in that the Interval Vector shows a different number for each interval class.
• -This is prevalent when understanding key relations, as it is interesting to note that there are 6 out of 7 common tones at the level of the Subdominant and Dominant, while 5 out of 7 being at the level of the Sub-tonic and Super-tonic, and 4 out of 7 at the level of the mediant and Sub-mediant. This is parallel to our understanding of closely related keys in tonal theory, which does have some influence in post-tonal theory.

Question 18

Give several examples of “complementarity” as used in set theory (e.g., pitch-classes, interval classes, on the set-class list, in terms of T/I, etc.).

Answer 18

• -Pitch class and Interval Class: 1 & 11, 2 & 10, 3 & 9, 4 & 8, 5 & 7, and 6 on its own.
• -Set List: Organized by Abstract Complements
• -Take the pair of complementary sets, such as a tetrachord and an octachord, which are listed next to each other on the Forte Set List. Looking at the interval vector of the smaller cardinality, in this case 4 the tetrachord, and add to each number in the interval vector (except interval class 6), the difference between the cardinalities, in this case 4, then one will have the interval vector of the larger cardinality, in this case the octachord. The exception is that one must take HALF of the difference, in this case 2, to add to interval class 6.

Question 19

What is a derived row?

Answer 19

A row in which all of the discreet trichords or discreet tetrachords have the same prime form.

Question 20

With whom is the concept of derived row most associated?

Answer 20

Anton Webern

Question 21

How many Trichords exist? Can you name them?

Answer 21

• -12

- -(012), (013), (014), (015), (016), (024), (025), (026), (027), (036), (037), (048)

Question 22

How many common tones are kept between two diatonic collections under T5 or T7? Under T1?

Answer 22

Interval Class Vector: [2,5,3,4,6,1]

Question 23

How many row forms are there if the row is symmetrical?

Answer 23

24 row forms: because in a non-symmetrical row, there are 48.

Question 24

What are the interval preferences of Schoenberg, Berg, and Webern?

Answer 24

• -Schoenberg and Webern: Preference for interval-classes 1, 2, & 6 (Viennese Trichord)
• -Berg: Preference for interval-classes 3, 4, and 5.

Question 25

What are the row styles of Schoenberg, Berg, and Webern? Name a piece as an example.

Answer 25

• -Schoenberg: Combinatorial Row - Klavierstücke, Op. 31a
• -Berg: All-Interval Row - Lyric Suite
• -Webern: Symmetrical Row - Variations for Orchestra
• -Webern: Derived Row - Concerto, Op. 24

Question 26

What are the main differences between Forte’s The Structure of Atonal Music and Straus’s Introduction to Post-Tonal Theory?

Answer 26

Forte: Emphasis on Similarity Relationships

• -How a set is similar to another.
• -Nexus Set/Pair - one set and its complement.
• -Similarity Relationships between complements and cardinalities (subsets and supersets)

Strauss: No Emphasis on Similarity Relationships

• -Only 1st Half of Straus’ book is on Pitch-Class Theory
• -After the set theory chapters, the books becomes much more comprehensive, in that he discusses triadic transformations, serialism, and voice leading, rather than just abstract sets.

Question 27

What are some musical styles in the 20th century (name composers and stylistic trends)?

Answer 27

Neo-Classicism

• -Stravinsky and Hindemith
• -Evokes the past in the use of forms, Use of Diatonic harmonies, pitch centricity, modal

Pre WW2 Serialism

• -2nd Viennese School
• Liberate the dissonance, expansion of compositional palette of sounds, 12-tone, the full chromatic, atonality

Integral (Post WW2) Serialism

• -Boulez, Stockhausen, Berio, Babbitt
• -Serialism determined not only pitch, but attack, duration, and dynamics

Minimalism

• -Glass, Reich, Adams
• -Constant pulse, minimal harmonic motion, minimal texture, very repetitive

Quotation and Collage

• -Berio, Rochberg, Zimmermann
• -Reaction to intense integral serialism in the mid 20th century. Bringing back aspects that were recognizable.

Question 28

What set class has this interval vector: ?

Answer 28

(025)

Question 29

How do you determine if a hexachord can produce each type of combinatoriality?

Answer 29

Consult the list in UPTM. There are only 6.

Question 30

Create a row that will have exactly 11 other row forms that preserve its first trichord.

Answer 30

As long as it starts with 048. 048…

Question 31

Discuss Stravinsky’s serial technique

Answer 31

• -Segments used, rather than full rows, like Memoriam Dylan Thomas.
• -Rotational Arrays

Question 32

Which hexachord can is only combinatorial at T6?

Answer 32

(013458)