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 Atonal, blurred tonality; dissonant Significant tonal deformation; locally dissonant against consonant backdrop Extended tonality, clarity; consonant Superset combinations of subset layers 2+ instances of ic 1 between layers 1 instance of ic 1 between layers 0 instances of ic 1 between layers Performance strategies Kaleidoscopic Estranged 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 III: ic 3/6 symmetrical [02], [04], [06], [024], [026], [048], [0246], [0248], [0268], [02468], [02468t] [03], [06], [036], [0369] chords IV: ic 5 symmetrical chords [02], [03], [05], [024], [025], [027], [0247], [0257], [0358] [02479] V: chords including ic 1 [012], [013], [014], [015], [016] (trichords)
Figure 3. Types of Set-Class Pairings, Dissonant Supersets, and Examples. Type of Pairing Opposed Elements Common Dissonant, ic 1-rich Syntheses 1. Tonal chords [03], [04], [05], [037], Octatonic and subsets: [0258], [0358], often [0134], [0147], etc.; related by ic 1 hexatonic and subsets: [0145], etc. 2. Whole- C WT and C# WT; or Total chromatic; tone/[02468t] 3. Diminished seventh/[0369] 4. Quartal/pentatonic/ [024579] 5. Interval classes including ic 1 subsets of these [0369]s related by ic 1 [025], [027], [0257], etc. related by T 1, by ic 1 wedge, or by another T n hexatonic; subsets C/C# OCT, C#/D OCT, D/D# OCT and subsets Variable: chromatic, diatonic, gapped chromatic common ic 3/1, 1/4, 1/1 Variable (except 1/1 case) Examples Op. 11/1: mm. 4-8 Op. 19/2: m. 3, 5 Op. 19/5: mm. 12-13 Op. 11/1: m. 58 Op. 19/2: m. 9 Op. 11/3: m. 4 Op. 19/4: m. 6 Op. 11/3: m. 20 Op. 19/1: m. 3 Op. 19/4: m. 11 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 7. Tonal/ Symmetrical 8. Different symmetrical collections 2 instances of [016], [014], [012], [013], [015] related by ic 1 or another ic [03] or [05] against WT subsets Any two cyclic collections with ic 1 relationships Chromatic, octatonic, hexatonic, subsets of them Op. 11/3: m. 32 Op. 11/1: m. 3 Variable Op. 11/2: m. 2 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.
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