JAVS Summer 2025

This contrast between vertical expanse and horizontal simplicity contributes to the piece’s ethereal, timeless atmosphere. Pärt’s repeated use of the same chord to harmonize identical melodic tones reinforces this sense of unity and oneness—a harmonic mantra that grounds the listener in spiritual stillness. VI. Neo-Riemannian and Set-Theoretic Dimensions Neo-Riemannian theory, which examines transformations between triads rather than their functional roles in a key, is particularly apt for analyzing the gentle shifts in Arvo Pärt’s tintinnabuli textures. In this framework, motion between chords—often through minimal voice-leading— can be understood as transformations (such as Parallel, Leading-Tone Exchange, or Relative) that prioritize smooth voice motion over tonal hierarchy. Though Spiegel im Spiegel may not engage triadic relationships in the Romantic sense, neo-Riemannian tools help illuminate the subtle harmonic interplay between static tonics and gently shifting consonances. Set theory, by contrast, abstracts pitch content from tonal context entirely, treating collections of pitches as unordered sets and focusing on their intervallic relationships. This approach is useful in Spiegel im Spiegel not because the work is atonal, but because its surface simplicity belies a deeper structural economy. The recurring pitch collections in the piano’s right hand, for instance, can be grouped and analyzed for their interval class content and invariance, revealing a spare but deliberate architecture. Set theory also aids in understanding the symmetrical pitch structures and mirrored gestures that contribute to the piece’s meditative symmetry. Together, these analytical approaches allow for a richer engagement with Pärt’s minimalism—not as a negation of complexity, but as a redirection of attention toward subtler harmonic and spatial relationships. Consider Phrase Eight (see Figure 2: measures 102–112), which harmonically traverses the diatonic palette of F major: • m. 102 – G minor 6/5 (ii⁷ in 1st inversion) • m. 103 – F major 6/4 (I⁶⁴) • m. 104 – B ♭ major 6/5 (IV⁷ in 1st inversion) • m. 105 – A minor 6/4 (iii⁶⁴) • m. 106 – D minor 6/5 (vi⁷ in 1st inversion) • m. 107 – C major 6/4 (V⁶⁴) • m. 108 – F major 6 (I⁶)

• m. 109 – G minor 6/5 (ii⁷ in 1st inversion) • m. 110 – F major 6/4 (I⁶⁴)

These chords form an elegant, almost circular harmonic progression. When viewed through the lens of neo Riemannian theory, transformations such as P (Parallel), R (Relative), and L (Leading-tone exchange) illuminate the triadic shifts between adjacent harmonies. For instance, the move from F major to D minor reflects an R -transformation; from G minor to B ♭ major, a P -transformation; and from A minor to C major, an L . These relationships generate a non-functional but internally coherent logic—one that privileges smooth voice-leading and tonal proximity over goal-oriented progression. At the same time, a set-theoretical analysis reveals how the viola’s ascending scale accumulates pitch classes methodically. Starting from a dyad, the line expands to triads, tetrachords, and ultimately to a heptachord. The center of symmetry lies around A4, and the motion of pitch classes mirrors itself across this axis. In this way, Spiegel im Spiegel structures its material with fractal like precision, where symmetry, reflection, and gradual revelation are primary compositional tools. For the violist, this theoretical architecture translates into a physical and spiritual challenge: how to render a seemingly simple line with depth, direction, and balance. Intonation must be centered; bow pressure and speed must remain consistent across registers; and one must resist the temptation to inflect each interval with romanticism. Instead, the goal is balance—between resonance and restraint, dissonance and resolution, movement and stillness. Ultimately, Pärt’s harmonic world is one of unfolding revelation. Each chord, though familiar, is heard anew through its placement, inversion, or voicing. As in religious iconography, repetition does not dull the sacred image—it refines it. In Spiegel im Spiegel , harmony becomes not merely a backdrop to melody but a sacred text unto itself, slowly recited, prayerfully intoned. Conclusion The Viola’s Prayer For the violist, Spiegel im Spiegel is less a performance than a meditation—a contemplative act in sound. Its demands are not technical but existential. The tone must be pure and centered, as if suspended in prayer. Each phrase is a step into silence, and each return to A4 a re-

Journal of the American Viola Society / Vol. 41, Summer 2025 Online Issue

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