Performing Arts Chapter 44 Name Pitchclass Sets Trichordsa Ion For What Pitchclass Set What Trichord

B. Normal Form | 627

NAME:

A. QUESTIONS FOR REVIEW

1. What is a pitch-class set? What is a trichord?

2. What is a normal form? How do you find it?

3. How do you transpose a set? How do you tell if two sets are related by transposi-

tion? How do you figure out the interval of transposition?

B. NORMAL FORM

• Write each trichord ascending within an octave, starting in turn on each of the

three notes.

• Above the staff write the number of semitones from the lowest to the highest

pitches.

chapter

44 Pitch-Class Sets: Trichords

628 | CHAPTER 44 | Pitch-Class Sets: Trichords

C. Transposition | 629

NAME:

C. TRANSPOSITION

1. Transpose these sets as indicated, writing your answer on the staff.

2. Transpose these sets as indicated, writing your answer on the staff and giving the

note names of the trichord below it.

630 | CHAPTER 44 | Pitch-Class Sets: Trichords

3. Identify these transpositions as follows:

• The following pairs of sets are related by transposition (Tn). Verify that by

writing the intervals.

• Then write the letter names of the pitch classes in normal form beneath the

staff and identify the interval of transposition.

D. INVERSION

1. Invert the trichords by T0I.

• In the first column, you will find trichords in normal form. Circle the notes of

the trichord on the left-hand clockface.

• Then, circle the notes of the inversion on the right-hand clockface.

• In the last column, write the notes of the inverted set in normal form.

Trichords Inversions

CC#

F#

B

GF

A#D

CC#

F#

B

GF

A#D

NAME:

CC#

F#

G#

D#

B

A

GF

E

A#D

CC#

F#

G#

D#

B

A

GF

E

A#D

CC#

F#

G#

D#

B

A

GF

E

A#D

CC#

F#

G#

D#

B

A

GF

E

A#D

F#

G#

D#

A

GF

E

F#

G#

D#

A

GF

E

CC#

F#

G#

D#

B

A

GF

E

A#D

CC#

F#

G#

D#

B

A

GF

E

A#D

2. Invert these sets as indicated. Write your answers both on the staff and in letter

names below the staff. Indicate intervals above the staff.

I

T5

D. Inversion | 633

NAME:

3. Identifying inversion

• The following pairs of sets are related by inversion (TnI). Verify by writing the

intervals over the staff.

• On the staff in the space between the two sets, write out the inversion of the

left-hand set, with the intervals indicated above the staff.

• Determine the transposition (Tn).

• Identify the inversion that connects the two sets.

634 | CHAPTER 44 | Pitch-Class Sets: Trichords

E. TRANSPOSITION AND INVERSION

Below are pairs of trichords written in normal form. Write the intervals over the

staff, then identify whether the sets are related by transposition, by inversion, by both

transposition and inversion, or by neither.

F. PRIME FORM

1. The following sets are in normal form. Put them into in prime form.

• Start by extracting the succession of intervals.

• Then, if necessary, rearrange the intervals so the smaller interval is on the left.

• Finally, replicate that interval succession starting on pitch-class 0.

F. PRIME FORM |635

NAME:

NORMAL

FORM

NORMAL

FORM WITH

INTERVALS

INTERVALS ARRANGED

WITH SMALLER ON

THEfiLEFT

INTERVAL SUCCESSION

STARTING ON PITCH-

CLASS 0

PRIME

FORM

a. [G, B, D] 4 3

[G, B, D]

3 4 3 4

0 3 7 (037)

b. [A, C, Eb] 3 3

[A, C, Eb]

3ff3 3ff3

0ff3ff6 (036)

c. [F#, B, C#] 5 2

[F#, B, C#]

2ff5 2ff5

0ff2ff7 (027)

1ff4 1ff4

2. Put the following sets into normal form and then into prime form.

NORMAL FORM PRIME FORM

a. C#–G–A [G, A, C#](026)

3

[A

A

b

CE

b

3

C

E

b

C

[A

,

C

,

E

b

]

3ff

3

3ff

0

0ff

3ff

6

3

36

3

36

3

(0

36

)

5

[F

#

F

#

BC

2

B

BC

B

[F

#

,

B,

C

#

]

2ff

5

2ff

0

0ff

2ff

7

27

5

2

27

2

(027)

4

1

1ff

4

1ff

4

conharm2_ch44_wkbk_inst_627-644.indd 635 21/08/19 3:38 PM

4

4ff

4

636 | CHAPTER 44 | Pitch-Class Sets: Trichords

G. COMPOSITION

1. Continue and complete a melody 8–12 measures in length in which most or all of

the three-note groups represent set-classes (014) or (015).

• Before you begin, think about the intervals that will be available to you within

these set classes.

• When you are done, analyze your melody by identifying the normal and prime

forms of the sets you have used.

2. Write a six-measure progression and melody.

• Continue and complete a progression of six chords for the left-hand part.

• All chords should contain three different notes and lie within an octave, and all

should be members of set-class (025).

• Then add a melody in the right hand that either arpeggiates the chords or elab-

orates them with passing or neighboring notes.

NAME:

H. ANALYSIS

1. Anton Webern, Pieces for String Quartet, Op. 5, No. 2

• Determine the normal form for each circled set and write it in the blank

provided.

• Label the arrows with the appropriate Tn and TnI between sets.

T4

T6I

T0I

[G, B, C#]

• The circled sets all belong to the same set class. What is its prime form?

(026)

• Do all five circled sets share a note in common? If so, what note? Yes, G.

• Looking at the transpositions, what tone(s) does each transposition in the

• Is there a larger collection that these sets combine to form? If so, what?

2. Arnold Schoenberg, Piano Pieces, Op. 11, No. 1

• Determine the normal form for each set, and write it in the blank provided.

• Label the arrows with the appropriate Tn and TnI between sets.

T0I

T0

T10

T2

T6I

T6

[G, G#, B ][ G, G#, B ][

Db, E, F ]

[G, Bb, B ]

The circled sets all belong to the same set class. What is its prime form? (014)

What is the common-tone relationship between the sets in m. 3? They share a Db.

H. Analysis | 639

NAME:

3. Anton Webern, Movements for String Quartet, Op. 5, No. 3

• Determine the normal form for each circled set, and write it in lettered blank

provided.

• Label the arrows with the appropriate Tn and TnI between sets.

[B, D, Eb][

G, Bb, B ]

[C, Eb, E ]

[G, Bb, B ][

C, Eb, E ][ B, D, Eb][

G#, A, C ]

[E, G, G#][

D#, F#, G ][D#, F#, G ][

G#, B, C ]

[E, G, G#][A, C, Db]

T8T8T0I

T4T3T1

T11 T11

(a)

(g)

(g) (h) (i) (j) (k) (l) (m)

(h) (i) (j) (k) (l) (m)

(a) (b) (c) (d) (e) (f )

(b) (c) (d) (e) (f )

• The circled sets all belong to the same set class. What is its prime form?

• Discuss intervals of transposition and common tones for the pairs of chords in

mm. 1–5 and 8, as well as for the three chords in m. 6. What might have moti-

vated the choice of intervals of transposition between the chords?

4. Anton Webern, Concerto for Nine Instruments, ii

• The melody of this example (in the treble staff ) can be segmented into trichords,

each consisting of three consecutive notes. The first note of each trichord is

labeled with a letter.

T1I

HEXDEbHEXCDbHEXD#EHEXC#D

T1I T11I T11I

• The circled sets all belong to the same set class. What is its prime form?

(014)

H. Analysis | 641

NAME:

5. Sofia Gubaidulina, Refiections on the Theme B-A-C-H

• Determine the normal form for each circled set, and write it in the lettered

blank provided.

• Label the arrows with the appropriate Tn and TnI between sets.

T5T5T5T5T5

(a)

(b)

(d)

• The circled sets all belong to the same set class. What is its prime form?

• How do the circled sets relate to one another through the excerpt?

642 | CHAPTER 44 | Pitch-Class Sets: Trichords

6. Sofia Gubaidulina, String Trio, ii

• Determine the normal form for each circled set, and write it in the lettered

blank provided.

• Label the arrows with the appropriate Tn and TnI between sets.

• Identify the larger collection formed by the first three sets, and label it under

the bracket.

T9I

T9IT3IT8

(a)

(b)

(c) (d)

(e)

(f )

• What is the role of common tones in the first three sets? Compare the progres-

sion of the last three sets to the first three.

NAME:

7. Milton Babbitt, String Quartet No. 2

• Determine the normal form for each circled set, and write it in the lettered

blank provided.

• Label the arrows with the appropriate Tn or TnI between sets.

(b)

[C#, E, F ][ Ab, A, C ]

T1I

(a)

(b)

• The circled sets all belong to the same set class. What is its prime form?

• Within each instrumental part, what Tn or TnI connects the two sets?

• What is the relationship between the collection in first violin and viola

644 | CHAPTER 44 | Pitch-Class Sets: Trichords

8. Tan Dun, Intercourse of Fire and Water (for solo cello)

• Determine the normal form for each trichord consisting of three consecutive

notes and write it in the blank provided.

• Label the arrows with the appropriate Tn or TnI between sets.

T5T5

(a)

(b)

(c)

(d) (e)

• The circled sets all belong to the same set class. What is its prime form?

• What larger collection is formed collectively by all of these sets? PENTC:

• Describe the network of common tones that connects these sets.