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Semitonal Key Pairings, Set-Class Pairings, and the Performance
of Schoenberg’s Atonal Keyboard Music
Benjamin Wadsworth
Kennesaw State University
email: [email protected]
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.
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