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

2. This presentation summarizes material presented in: David Beach. “Pitch Structure and the Analytic Process in Atonal Music: An Interpretation of the Theory of Sets,” Music Theory Spectrum 1 (1979): 7-22.

3. Introduction measures 1-2

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

5. Voice leading between the two chords: E moves to F# (top line) E moves to F# (top line) F remains fixed F remains fixed B and C participate in a Voice Exchange B and C participate in a Voice Exchange 4-9(0167)4-8(0156)

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

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

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

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

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

11. Section A measures 3-4 The Surface

12. Sc 4-9, which appears in the Introduction as a vertical component, becomes the primary linear component in A. It is stated first at the original pitch level in violin 1, and then at the fifth below in violin 2. Sc 4-9, which appears in the Introduction as a vertical component, becomes the primary linear component in A. It is stated first at the original pitch level in violin 1, and then at the fifth below in violin 2. Surface: 4-9(0167)

13. The intersection of the pcs in these two statements {6b50) {b4a5} = {b5} occurs as the internal elements of the former and terminal pitches of the latter. This transposition also introduces the first statement of pc A (Bb). The intersection of the pcs in these two statements {6b50) {b4a5} = {b5} occurs as the internal elements of the former and terminal pitches of the latter. This transposition also introduces the first statement of pc A (Bb). Surface: U 4-9(0167)

14. The third statement of 4-9 (cello), returns to the original pitch level and is extended, resulting in another statement of sc 6-5(012367) The third statement of 4-9 (cello), returns to the original pitch level and is extended, resulting in another statement of sc 6-5(012367) Surface: 4-9 6-5 6-5(012367) 4-9(0167)

15. Section A measures 3-4 Deeper Structure The following slides illustrate that the deeper structure is also related to these sets.

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

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

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

19. The union of this instance of 5-7 and the previous one is sc 7-7(0123678), the complement of sc 5-7. The union of this instance of 5-7 and the previous one is sc 7-7(0123678), the complement of sc 5-7. Section A Deeper Structure 5-7(01267) 7-7(0123678)

20. The intersection of these two instances of 5-7 is, again, sc 3-5(016). The intersection of these two instances of 5-7 is, again, sc 3-5(016). Section A Deeper Structure

21. Other Complement relationships in this section: M. 4: The union of two instances of sc 4-9 results in sc 8-9(01236789). M. 4: The union of two instances of sc 4-9 results in sc 8-9(01236789). Section A Deeper Structure 4-9(0167) 8-9(01236789)

22. Other Complement relationships in this section: 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 point where all three sounding instruments have simultaneous attack points. 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 point where all three sounding instruments have simultaneous attack points. Section A Deeper Structure 5-7(01267) 7-7(0123678)

23. The A section contains 4 statements of 4-9, and five different statements of 5-7, no two of which are identical with regard to pitch content. The statements of the complements of these sets adds to coherence and homogeneity, since complementary sets have similar interval content. The A section contains 4 statements of 4-9, and five different statements of 5-7, no two of which are identical with regard to pitch content. The statements of the complements of these sets adds to coherence and homogeneity, since complementary sets have similar interval content. Section A Deeper Structure 4-9(0167) 5-7(01267) 4-9(0167)

24. Transition (end of measure 6)

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

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

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

28. Section B measure 7-10

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

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

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

32. The entire pitch content of the B section is sc 8-24 (0124568a); the first four pitches are its complement, The entire pitch content of the B section is sc 8-24 (0124568a); the first four pitches are its complement, 4-24(0248). 4-24(0248). 8-24(0124568a) 4-24(0248)

33. Transition (measure 10)

34. The transitional figure, {59b4604} = 7-17 (0123679), is a literal transposition of the first transition, at the fifth below. The same relationship was employed earlier between the first two linear statements of sc 4-9 in section A. The transitional figure, {59b4604} = 7-17 (0123679), is a literal transposition of the first transition, at the fifth below. The same relationship was employed earlier between the first two linear statements of sc 4-9 in section A. 7-19(0123679)

35. This particular transposition of 7-19 brings back the pitch content of mm. 1-2; the additional pc 9 is the final new pitch class to be introduced, i.e., it completes the aggregate. This particular transposition of 7-19 brings back the pitch content of mm. 1-2; the additional pc 9 is the final new pitch class to be introduced, i.e., it completes the aggregate. 7-19(0123679)

36. Section A’ measures 11-12

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

38. The first ideas restate material from measures 4- 5, with doubling at the octave. The total pitch collection is sc 5-7(01256). The first ideas restate material from measures 4- 5, with doubling at the octave. The total pitch collection is sc 5-7(01256). 5-7(01267)

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

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

41. This set, combined with the previous statement of the same set results in a final statement of sc 7-7(0123678) -- another instance of embedded complement relation. This set, combined with the previous statement of the same set results in a final statement of sc 7-7(0123678) -- another instance of embedded complement relation. 5-7(01267) 7-7(0123678)

42. CODA (measures 12-13)

43. The piece closes with a final statement of 7-19, again a literal transposition of the transition gesture. The piece closes with a final statement of 7-19, again a literal transposition of the transition gesture. 7-19(0123679)

44. This transpostion of the gesture results in another statement of 8-9(01236789) when it is combined with the previous instance of 4- 9). This is the only instance of literal comple- mentation in the piece, i.e., the union of this instance of 4-9 and 8-9 is a complete aggre- gate (all 12 pcs). This transpostion of the gesture results in another statement of 8-9(01236789) when it is combined with the previous instance of 4- 9). This is the only instance of literal comple- mentation in the piece, i.e., the union of this instance of 4-9 and 8-9 is a complete aggre- gate (all 12 pcs). 7-19(0123679) 4-9(0167) 8-9(01236789)