Anton Webern Op. 5, No. 4 Dr. Aleck Brinkman Esther Boyer College of Music Temple University.

Anton WebernAnton Webern Op. 5, No. 4 Op. 5, No. 4

Dr. Aleck BrinkmanDr. Aleck Brinkman

Esther Boyer College of MusicEsther Boyer College of Music

Temple UniversityTemple University

This presentation summarizes materialpresented in:

David Beach. “Pitch Structure and the AnalyticProcess in Atonal Music: An Interpretation of the

Theory of Sets,” Music Theory Spectrum 1 (1979):7-22.

IntroductionIntroductionmeasures 1-2measures 1-2

The main components are the two four-note The main components are the two four-note chords in measure 1 {045b} = 4-8(0156), and chords in measure 1 {045b} = 4-8(0156), and measure 2 {056b} = 4-9(0167)measure 2 {056b} = 4-9(0167)

4-9(0167)4-8(0156)

Voice leading between the two chords:Voice leading between the two chords: E moves to F# (top line)E moves to F# (top line) F remains fixedF remains fixed B and C participate in a Voice ExchangeB and C participate in a Voice Exchange

4-9(0167)4-8(0156)

The union of these two chords, {045b} U {056b} The union of these two chords, {045b} U {056b} = {0456b}, is set class (sc) 5-7(01267).= {0456b}, is set class (sc) 5-7(01267).

5-7(01267)

The addition of the Eb in the cello results in sc The addition of the Eb in the cello results in sc 6-5(012367)6-5(012367)

6-5(012367)

The intersection of the two chords, {045b} The intersection of the two chords, {045b} {056b} = {05b} = 3-5(016){056b} = {05b} = 3-5(016)

U

The remaining pitches {46} are subsequently The remaining pitches {46} are subsequently stated as a compositional unit by the violastated as a compositional unit by the viola

The pizzicato chord that ends the section The pizzicato chord that ends the section duplicates the pcs in the first chord in the piece duplicates the pcs in the first chord in the piece in the same register {045b} = 4-8(0156).in the same register {045b} = 4-8(0156).

4-8(0156)

4-8(0156)

Section ASection Ameasures 3-4measures 3-4

The SurfaceThe Surface

Sc 4-9, which appears in the Introduction as a vertical Sc 4-9, which appears in the Introduction as a vertical component, becomes the primary linear component in A. component, becomes the primary linear component in A. It is stated first at the original pitch level in violin 1, and It is stated first at the original pitch level in violin 1, and then at the fifth below in violin 2.then at the fifth below in violin 2.

Surface:4-9(0167) 4-9(0167)

4-9(0167)

The intersection of the pcs in these two statements {6b50) The intersection of the pcs in these two statements {6b50) {b4a5} = {b5} occurs as the internal elements of the {b4a5} = {b5} occurs as the internal elements of the former and terminal pitches of the latter. This transposition former and terminal pitches of the latter. This transposition also introduces the first statement of pc A (Bb).also introduces the first statement of pc A (Bb).

Surface:

U

4-9(0167)

4-9(0167)

The third statement of 4-9 (cello), returns to the The third statement of 4-9 (cello), returns to the original pitch level and is extended, resulting in original pitch level and is extended, resulting in another statement of sc 6-5(012367)another statement of sc 6-5(012367)

Surface:

4-9

4-9

6-5

6-5(012367)

4-9(0167)

Section ASection Ameasures 3-4measures 3-4

Deeper StructureDeeper Structure

The following slides illustrateThe following slides illustratethat the deeper structure isthat the deeper structure isalso related to these sets.also related to these sets.

The union of the linear statement of 4-9 in vln. 1 The union of the linear statement of 4-9 in vln. 1 and the E - F# gesture in the viola is another and the E - F# gesture in the viola is another statement of sc 5-7(01267).statement of sc 5-7(01267).

Section A Deeper Structure

5-7(01267)

5-7(01267)

In measures 3-4, new pitches in the cello {17} In measures 3-4, new pitches in the cello {17} combined with the sustained {06} result in combined with the sustained {06} result in another instance of 4-9(0167)another instance of 4-9(0167)

Section A Deeper Structure

4-9(0167)

This set combined with pc b (1st note in vln 2 This set combined with pc b (1st note in vln 2 statement of 4-9) results in yet another instance statement of 4-9) results in yet another instance of sc 5-7(01267)of sc 5-7(01267)

Section A Deeper Structure

5-7(01267)

5-7(01267)

5-7(01267)

The union of this instance of 5-7 and the previous one is The union of this instance of 5-7 and the previous one is sc 7-7(0123678), the complement of sc 5-7.sc 7-7(0123678), the complement of sc 5-7.

Section A Deeper Structure

5-7(01267)

5-7(01267)

7-7(0123678)

The intersection of these two instances of 5-7 is, The intersection of these two instances of 5-7 is, again, sc 3-5(016).again, sc 3-5(016).

Section A Deeper Structure

Other Complement relationships in this section:Other Complement relationships in this section:• M. 4: The union of two instances of sc 4-9 M. 4: The union of two instances of sc 4-9

results in sc 8-9(01236789).results in sc 8-9(01236789).

Section A Deeper Structure

4-9(0167)8-9(01236789)

Other Complement relationships in this section:Other Complement relationships in this section:• M. 4 (last 8th note) through m. 6 (beat 2): again two M. 4 (last 8th note) through m. 6 (beat 2): again two

overlapping 5-7s result in 7-7. The overlap occurs at the only overlapping 5-7s result in 7-7. The overlap occurs at the only point where all three sounding instruments have point where all three sounding instruments have simultaneous attack points.simultaneous attack points.

Section A Deeper Structure

5-7(01267) 5-7(01267)

7-7(0123678)

The A section contains 4 statements of 4-9, and five different The A section contains 4 statements of 4-9, and five different statements of 5-7, no two of which are identical with regard statements of 5-7, no two of which are identical with regard to pitch content. The statements of the complements of to pitch content. The statements of the complements of these sets adds to coherence and homogeneity, since these sets adds to coherence and homogeneity, since complementary sets have similar interval content.complementary sets have similar interval content.

Section A Deeper Structure

4-9(0167)

5-7(01267)

5-7(01267)

4-9(0167)

TransitionTransition(end of measure 6)(end of measure 6)

The transition from section A to B is a seven-note The transition from section A to B is a seven-note ascending figure {046b17a] = 7-19 (0123679). ascending figure {046b17a] = 7-19 (0123679).

7-19(0123679)

The first four notes of this set {046b} are the same The first four notes of this set {046b} are the same pitches that were stated by the first violin in the pitches that were stated by the first violin in the Introduction.Introduction.

The other three pitches {17a} are the “new” The other three pitches {17a} are the “new” pitches that were first introduced in mm. 3-4.pitches that were first introduced in mm. 3-4.

Section BSection Bmeasure 7-10measure 7-10

Compositonal gestures and texture contrast with Compositonal gestures and texture contrast with the rest of the piece (triplets, pizz, pedal tones).the rest of the piece (triplets, pizz, pedal tones).

The main components are a melodic idea The main components are a melodic idea {b8030b80} = 4-17(0347) and its {b8030b80} = 4-17(0347) and its accompaniment {2a6+4b} = 5-30(01468). accompaniment {2a6+4b} = 5-30(01468).

4-17(0347)

5-30(01468))

The accompaniment is divided into the trichord The accompaniment is divided into the trichord 3-12 (014) and the dyad {4b}.3-12 (014) and the dyad {4b}.

The entire pitch content of the B section is sc 8-24 The entire pitch content of the B section is sc 8-24 (0124568a); the first four pitches are its complement,(0124568a); the first four pitches are its complement,

4-24(0248).4-24(0248).

8-24(0124568a)

4-24(0248)

TransitionTransition(measure 10)(measure 10)

The transitional figure, {59b4604} = 7-17 The transitional figure, {59b4604} = 7-17 (0123679), is a literal transposition of the first (0123679), is a literal transposition of the first transition, at the fifth below. The same relationship transition, at the fifth below. The same relationship was employed earlier between the first two linear was employed earlier between the first two linear statements of sc 4-9 in section A.statements of sc 4-9 in section A.

7-19(0123679)

This particular transposition of 7-19 brings back This particular transposition of 7-19 brings back the pitch content of mm. 1-2; the additional pc 9 the pitch content of mm. 1-2; the additional pc 9 is the final new pitch class to be introduced, i.e., is the final new pitch class to be introduced, i.e., it completes the aggregate.it completes the aggregate.

7-19(0123679)

Section A’Section A’measures 11-12measures 11-12

This section is a condensation of the main This section is a condensation of the main components of the first five measures.components of the first five measures.

The first ideas restate material from measures 4-The first ideas restate material from measures 4-5, with doubling at the octave. The total pitch 5, with doubling at the octave. The total pitch collection is sc 5-7(01256).collection is sc 5-7(01256).

5-7(01267)

The four-note chord that follows (pizz) recalls The four-note chord that follows (pizz) recalls the gesture at the end of the introduction, but the gesture at the end of the introduction, but restates sc 4-9(0167) from measure 2, trans-restates sc 4-9(0167) from measure 2, trans-posed literally a major third down. posed literally a major third down.

4-9(0167)

These pitches, combined with the sustained These pitches, combined with the sustained F# (6) above them result in an additional F# (6) above them result in an additional instance of sc 5-7(01267).instance of sc 5-7(01267).

5-7(01267)

This set, combined with the previous This set, combined with the previous statement of the same set results in a final statement of the same set results in a final statement of sc 7-7(0123678) -- another statement of sc 7-7(0123678) -- another instance of embedded complement relation.instance of embedded complement relation.

5-7(01267)5-7(01267)

7-7(0123678)

CODACODA(measures 12-13)(measures 12-13)

The piece closes with a final statement of The piece closes with a final statement of 7-19, again a literal transposition of the 7-19, again a literal transposition of the transition gesture.transition gesture.

7-19(0123679)

This transpostion of the gesture results in another This transpostion of the gesture results in another statement of 8-9(01236789) when it is combined statement of 8-9(01236789) when it is combined with the previous instance of 4-9). This is the only with the previous instance of 4-9). This is the only instance of literal comple-mentation in the piece, instance of literal comple-mentation in the piece, i.e., the union of this instance of 4-9 and 8-9 is a i.e., the union of this instance of 4-9 and 8-9 is a complete aggre-gate (all 12 pcs).complete aggre-gate (all 12 pcs).

7-19(0123679)

4-9(0167) 8-9(01236789)