Open Strings: Manipulations of Time, Distance, and Pitch Space

Abstract Open strings are a central compositional-aesthetic feature in a range of repertoires, from overdriven guitar parts in early rock music to stopped-string passages in Western European classical art music. Despite their ubiquity, existing fretboard-space models are currently underequipped to consider their use—open strings are either simply ignored or treated as an unreachable position outside the range of the instrument. Such an approach complicates Cartesian analyses, presents additional caveats to voice leading, and ultimately decouples fretboard theory from real-world practice. To address these latent issues, I adopt a range of interdisciplinary analytical techniques to propose a series of modifications to existing fretboard spaces such that open strings are treated as a point of indeterminacy between a grounded physical fretboard space and an underlying pitch network. Analytical vignettes of popular-music guitar performances by Brushy One String, Sister Rosetta Tharpe, Celisse Henderson, Kurt Cobain, and Lenny Kravitz showcase this indeterminacy, demonstrating that open strings are primarily used in two ways: to instantly access otherwise unreachable fretted notes without shifting the fretting hand, or to facilitate otherwise difficult lateral leaps by “borrowing” time from adjacent rhythmic values. Both techniques are manipulations of distance and travel speed as factors of Fitts’s Law during goal-directed physical movement. In this way, I argue open-string usage is analogous to Lorentzian wormholes—interstellar gateways that can act as a shortcut between time and space—that share similarities with other common pitch-space transitions such as modulations between distant keys. Such considerations inform a proposed set of modifications for transformational fretboard spaces that provide a more accurate summation of distance calculations between fretted- and open-string events. I then showcase the utility of the proposed modifications when estimating performance difficulty in a computationally assisted analysis of the first movement, Allegro Moderato, from the Concerto in G major for double bass by Édouard Nanny. There, I apply the proposed modifications to open strings in fingerboard space to offer an accurate perspective on lateral transitions and their influence on shifts in a performer’s bodily balance as it relates to formal organization, fretboard transformations, and sonic clarity.