Semitonal Key Pairings, Set-Class Pairings, and the Performance

of Schoenberg’s Atonal Keyboard Music

Benjamin Wadsworth

Kennesaw State University

email: bwadswo2@kennesaw.edu

SMT Annual Meeting

Indianapolis, Indiana

November 4, 2010

Example 1. Leichtentritt’s dialectical observation in mm. 1-3 of Op. 11/2.

Figure 1. Model of Set-Class Pairings (SCPs).

Aesthetic Orientation of superset

Superset combinations of subset layers

Performance strategies

Atonal, blurred tonality; dissonant

2+ instances of ic 1 between layers

“Kaleidoscopic”

Significant tonal deformation; locally dissonant against consonant backdrop

1 instance of ic 1 between layers

“Estranged”

Extended tonality, clarity; consonant

0 instances of ic 1 between layers

“Unitary”

Figure 2. Possible subset layers in a Set-Class Pairing (SCP).

Subset layer type Available set-classes

I: tonal chords [03], [04], [05], [037], [0258], [0358]

II: ic 2/4/6 symmetrical

chords

[02], [04], [06], [024], [026], [048], [0246], [0248], [0268],

[02468], [02468t]

III: ic 3/6 symmetrical

chords

[03], [06], [036], [0369]

IV: ic 5 symmetrical chords [02], [03], [05], [024], [025], [027], [0247], [0257], [0358]

[02479]

V: chords including ic 1

(trichords)

[012], [013], [014], [015], [016]

Figure 3. Types of Set-Class Pairings, Dissonant Supersets, and Examples.

Type of Pairing Opposed Elements Common Dissonant, ic 1-rich Syntheses

Examples

1. Tonal chords [03], [04], [05], [037], [0258], [0358], often related by ic 1

Octatonic and subsets: [0134], [0147], etc.; hexatonic and subsets: [0145], etc.

Op. 11/1: mm. 4-8 Op. 19/2: m. 3, 5 Op. 19/5: mm. 12-13

2. Whole-tone/[02468t]

C WT and C# WT; or subsets of these

Total chromatic; hexatonic; subsets

Op. 11/1: m. 58 Op. 19/2: m. 9

3. Diminished seventh/[0369]

[0369]s related by ic 1 C/C# OCT, C#/D OCT, D/D# OCT and subsets

Op. 11/3: m. 4 Op. 19/4: m. 6

4. Quartal/pentatonic/ [024579]

[025], [027], [0257], etc. related by T1, by ic 1 wedge, or by another Tn

Variable: chromatic, diatonic, gapped chromatic common

Op. 11/3: m. 20 Op. 19/1: m. 3 Op. 19/4: m. 11

5. Interval classes including ic 1

ic 3/1, 1/4, 1/1 Variable (except 1/1 case)

Op. 11/1: mm. 42-44 Op. 11/3: m. 0 Op. 23/1: mm. 13-16 Op. 19/3: m. 7

6. Trichords with semitone

2 instances of [016], [014], [012], [013], [015] related by ic 1 or another ic

Chromatic, octatonic, hexatonic, subsets of them

Op. 11/3: m. 32 Op. 11/1: m. 3

7. Tonal/ Symmetrical

[03] or [05] against WT subsets

Variable Op. 11/2: m. 2

8. Different symmetrical collections

Any two cyclic collections with ic 1 relationships

Variable Op. 11/3: m. 18 Op. 19/1: m. 14

Example 2. Semitonal Pairings of G/G# and F/E in Op. 11/1, mm. 1-11.

Example 3. A SKP of D/C# in mm. 1-9 from Schoenberg’s Op. 11/2.

Example 4a. An Intervallic Pairing in mm. 0-1 from Schoenberg’s Op. 11/3.

Example 4b. An instance of quick layer changes in Schoenberg’s Op. 11/3.

Example 4c. An instance of constant layers in Schoenberg’s Op. 11/3.

Example 5. An SKP and SCP analysis of Op. 19/5 by Schoenberg.

Bibliography Bailey, Robert. 1985. “An Analytical Study of the Sketches and Drafts.” In Wagner: Prelude and ‘Transfiguration’ from Tristan und Isolde. New York: Norton: 113- 146. Brinkmann, Reinhold. [1969] 2000. Arnold Schönberg, drei Klavierstücke Op. 11: Studien zur frühen Atonalität bei Schönberg. Wiesbaden: F. Steiner. Cherlin, Michael. 2007. Schoenberg’s Musical Imagination. Cambridge: Cambridge

University Press. Carpenter, Patricia. 1983. “’Grundgestalt’ as Tonal Function.” Music Theory Spectrum 5: 15-38. Cinnamon, Howard. 1993. “Tonal Elements and Unfolding Nontriadic Harmonies in the Second of Schoenberg’s Drei Klavierstucke, Op. 11.” Theory and Practice 18: 127-170. Cramer, Alfred. 2002. “Schoenberg’s Klangfarbenmelodie: A Principle of Early Atonal

Harmony.” Music Theory Spectrum 24.1: 1-34. Dineen, Murray. 2005. The Tonal Problem as a Method of Analysis: In Memoriam Patricia Carpenter.” Theory and Practice 30: 69-96. Leichtentritt, Hugo. 1959. Musical Form. Cambridge: Harvard University Press. Lewin, David. 1968. “Inversional Balance as an Organizing Force in Schoenberg’s Music and Thought.” Perspectives of New Music 6.2: 1-21. Ogdon, Will. 1981. “How Tonality Functions in Schoenberg’s Opus 11, no. 1.” Journal

of the Arnold Schoenberg Institute 5.2: 169-181.

Perle, George. [1962] 1991. Serial Composition and Atonality. Berkeley: University of California Press. Reti, Rudolf. [1958] 1960. Tonality, Atonality, Pantonality. London: Barrie & Rockcliff. Schoenberg, Arnold. [1954] 1969. Structural Functions of Harmony, ed. L. Stein. New York: Norton. -----. 1978. Theory of Harmony. Translated by Roy E. Carter. Berkeley: University of California Press. ----. [1995] 2006. The Musical Idea and the Logic, Technique, and Art of its

Presentation. Edited, Translated, and with a Commentary by Patricia Carpenter and Severine Neff. New York: Columbia University Press. Simms, Bryan. 2000. The Atonal Music of Arnold Schoenberg: 1908-1923. Oxford: Oxford University Press. Straus, Joseph. 2003. “Uniformity, Balance, and Smoothness in Atonal Voice Leading.” Music Theory Spectrum 25.2: 305-352. Travis, Roy. 1966. “Directed Motion in Schoenberg and Webern.” Perspectives of New Music 4.2: 85-89. Vaisala, Olli. 1999. “Concepts of Harmony and Prolongation in Schoenberg’s Op. 19/2.” Music Theory Spectrum 21.2: 230-259. Von der Nüll, Edwin. 1932. Moderne Harmonik. Leipzig: Fr. Kistner & C. F. W. Siegel.

Wittlich, Gary. 1974. “Interval Set Structure in Schoenberg’s Op. 11, No. 1.” Perspectives of New Music 13.1: 41-55.