Review: Functions, Scales, Abstract Systems and Contextual Hierarchies in the Music of Bartók

Bibliographic Information and Research Context

• Original Publication Date: August 1994, published in Music & Letters, Vol. $75$, No. $3$.

• Source Title: "Functions, Scales, Abstract Systems and Contextual Hierarchies in the Music of Bartók".

• Author of Review: Michael Russ.

• Reviewed Work: The Music of Béla Bartók by Paul Wilson ($1992$, Yale University Press).

• Academic Landscape: The study of Bartók is characterized by "never-ending supply of divergent analytical texts" from "fine theoretical minds." Wilson’s work joins a field populated by:

  • Ernõ Lendvai: Known for the axis system and Golden Section proportions.

  • Elliot Antokoletz: Known for his $1984$ study on tonality and progression based on interval cycles.

  • Malcolm Gillies: Researcher focused on notation and tonal structure ($1989$).

  • Richard Cohn: Known for work on inversional symmetry ($IS$) and transpositional combination ($TC$).

• Theoretical Tensions: There is a noted degree of antipathy between theorists. Wilson described Antokoletz's $1984$ book as a "failure," while both Wilson and Antokoletz distrust the theoretical soundness of Lendvai's work.

Paul Wilson's Theoretical Scope and Argument

• Chronological Focus: Wilson's book specifically examines music composed between the Piano Sonata ($1926$) and the Concerto for Orchestra ($1943$).

• Core Thesis: Bartók moved toward atonality in the early $1920s$, but later resumed interest in tonal conventions. Wilson argues that while Bartók's musical language changed over time, certain "structural overlays" (characteristics of underlying organization) remained constant.

• Selected Repertoire for Analysis:

  • Piano Sonata ($1926$) - full analysis.

  • Third String Quartet ($1927$) - full analysis.

  • Fifth String Quartet ($1934$) - specific movements.

  • Sonata for Two Pianos and Percussion ($1937$) - specific movements.

  • Concerto for Orchestra ($1943$) - specific movements.

Methodological Stance: Contextualism vs. Precompositional Systems

• Detached Analytical Position: Wilson posits that any theory of Bartók is an "outsider's view," not necessarily a reproduction of the composer's mental process. Structure is inferred from "performances" of the music and interpretive skill.

• Rejection of Precompositional Pitch Systems: Wilson argues against systems like Lendvai's axes or Antokoletz's inversionally related interval cycles if they exist prior to the specific composition. He believes functions only have meaning if validated contextually.

• Babbitt’s 1949 Perspective: Milton Babbitt noted the tension in Bartók’s music between "generalized functional tonal relationships" (external/semantic) and "unique, internally defined relationships" (internal/syntactic). Wilson collapses this opposition, prioritizing the "play of context."

Wilson’s Seven Contextual Functions

Wilson redefines the word "function" away from Riemannesque, major-scale positions. He identifies seven specific functions that must be argued contextually:

1. Goal event: The intended arrival point of a musical progression.

2. Initiating event: The starting material of a structural level.

3. Local dominant: An element that prepares a contextually argued goal event.

4. Interior tonal centre: A harmonic reference point within a section.

5. Local dominant preparation: Material preceding the local dominant.

6. Tonic substitution (of a goal event): An alternative arrival that replaces the expected tonic.

7. Extension (of an initiating event): Temporal or thematic expansion of the start point.

Note: The subdominant function does not appear in Wilson's taxonomy.

Critiques of Ernõ Lendvai's Axis System

Wilson identifies several "sleights of hand" in Lendvai's methodology:

• Change of Gamut: Lendvai extends three functions ($I$, $IV$, $V$) derived from the major scale to the total chromatic without sufficient justification.

• Extension of Relatives: Lendvai allows $F\#$ to function as $C$ based on tritone equivalence, but Wilson objects that this ignores the loss of key-signatures and diatonic identity.

• Alpha Chords: Lendvai classifies octatonic collections as "alpha chords" consisting of two diminished seventh chords. Wilson finds it aurally and theoretically difficult to discriminate traditional functions within these collections.

Symmetrical Structures and Interval Cycles

• Wilson’s View: Symmetry is prominent but only relevant where context "makes it reasonable."

• Richard Cohn and the TC-Property: Cohn introduces the "Transpositional Combination" ($TC$) property. A set has the $TC$-property if it can be divided into two or more transpositionally related subsets.

• Statistical Data on Set Classes: Out of $223$ set classes:

  • $65$ have the $TC$ property only.

  • $22$ have Intervallic Symmetry ($IS$) only.

  • $72$ have both properties (including the major sets significant to Bartók like octatonic, diatonic, and whole-tone).

  • $64$ have neither.

• Analytical Conflict: Antokoletz argues that everything in the music is explicable via interval cycles ($sum 5$, $sum 6$, etc.). Wilson views this as too abstract, leading the analyst away from the specific structural logic of the work.

Case Study: Fifth String Quartet, Second Movement

• Overview: An arch form centered on $D$. Wilson focuses on the interval of a fifth.

• Cycle of Fifths (Russ’s Alternative View): Russ proposes a cycle beginning: $F\#-C\#-G\#-D\#-A\#-E\#-B\#-G-D$.

• Cell Z (The 4-9 Tetrachord): Russ identifies the importance of cell $Z$ ($[0,1,6,7]$) in conjunction with octatonic subsets. At the cadence on $D$ (bars $4-5$), the $G-D$ motion is pre-imitated by $C\#-G\#$.

• Diatonic vs. Symmetrical Matrix: Russ proposes a two-dimensional matrix using inversionally related cycles of fifths aligned at $sum 10$.

  • Axes: $D-G\#$ and $B-F$.

  • Relationship: Diatonic elements (cycle of fifths) and octatonic elements interact as equals rather than one subordinating the other.

Case Study: Sonata for Two Pianos and Percussion, First Movement

• Duality of Thirds: The movement features a conflict between major and minor thirds.

  • Octatonic collection: Generated by cyclic transposition of the semitone by $T3$.

  • Hexatonic collection: Generated by cyclic transposition of the semitone by $T4$.

• The Matrix (Fig 2): Constructed from $T4$ cycles of interval class ($i.c.$) $1$ dyads horizontally and $T3$ cycles vertically.

• Introduction Analysis:

  • The motto theme ($4-3$ tetrachord) is octatonic and diatonic.

  • It interlocks with the hexatonic tetrachord $4-7$.

  • Transposition of the motto theme by an augmented fourth ($T6$) generates a full statement of octatonic collection $II$.

• Divergence from Wilson: Wilson interprets the introduction as a stepwise whole-tone ascent in the upper voice ($F\#$, $G$, $G\#$, etc.). Russ argues this minimizes the significance of the $T5$ and $T6$ entries and the functional retention of $A\#$ and $D$ leading into the Allegro molto.

Theoretical Critiques and Comparison of Approaches

• Linear Coherence vs. Intervallic Interaction: Russ challenges Wilson’s reliance on stepwise motion as the primary structural skeleton. Wilson himself admits that without modality, stepwise motion has no strong logical warrant in post-tonal music.

• Role of Folklore: Wilson’s focus on the "contextual" often ignores the influence of folk music (e.g., the Romanian augmented fourth). Russ argues that Bartók’s folk links often provide the "historical baggage" that allows minimal gestures to be perceived as explicitly functional.

• Final Assessment of Bartók's Style: Wilson concludes that Bartók "flowed slowly but irreversibly toward the traditional" in his later years. However, he maintains that the degree of hierarchical structure remained constant throughout the span of $1926$ to $1943$.