Fretboards

While recent publications exploring the instrumental affordances of the guitar through transformational theory such as De Souza (2017; 2018) focus on the concept of embodiment, the explanatory power of such transformations with regard to voicings has yet to be examined. In this paper, I develop a methodology involving the interaction between pitch content and fretboard transformations to investigate the limited number of voicings used by Tōru Takemitsu in “Rosedale” from In the Woods (1995). I introduce fretboard prime forms (fbsets), which are generic hand shapes that can be transposed up and down the fretboard while maintaining the same intervallic pitch relationships. Fbsets thus correspond to voicings, with each voicing yielding several fbsets when plotted on the fretboard GIS. Furthermore, I discuss various fretboard transformations that model chord successions in fretboard space such the the SINT transformation, which preserves same-shapedness across strings, and the S and A operations, which adjust the “soprano” and “alto” voices respectively. Using these transformations to map fbsets, I construct a network that demonstrates the proximate relationships of the voicings that Takemitsu selects.

Ultimately, these results clarify that the close relationships among pitch sets in this piece are related to fingerings on the guitar. Specifically, these relationships are manifest in idiomatic chord successions that allow phrases to be performed smoothly and with legato execution. Thus, by choosing proximate voicings throughout “Rosedale,” Takemitsu demonstrates a deep understanding of the relationship between pitch content and the classical guitar’s affordances. 

Despite the ubiquity of open strings in popular-music guitar performances, fretboard-space models are currently underequipped to address their use—open strings are either ignored or treated as an unreachable fret. This can complicate Cartesian analyses, present additional caveats to fretboard voice leading, and ultimately distances fretboard theory from practice. 

This paper reconceptualizes fretboard space by qualifying open strings as a point of indeterminacy between Lewin’s Generalized Interval System and De Souza’s fret-string network. I argue the entire horizontal vector of the fretboard is activated when a performer articulates an open string. This action simultaneously evokes a single pitch from the GIS from any point in the fret-string network. 

By linking the component universes of fretboard space via open strings, I suggest that open strings are not unlike Lorentzian wormholes—portals that allow one to manipulate time and space to efficiently traverse great distances. Gestural analyses of performances by artists such as Sister Rosetta Tharpe, Brushy One String, Nancy Wilson, and Kurt Cobain explore how open-string operations mirror the two classes of wormholes. Thin-shell wormholes are infinitely thin and take virtually no time to traverse. Guitarists similarly use adjacent open strings to instantly access otherwise unreachable fretted notes without shifting their left hands. Thick-shell wormholes meanwhile require some distance to traverse, but still mitigate time as a factor of travel. This matches along-string transitions, where guitarists use open-strings to “borrow” time from an open string’s rhythmic value and facilitates otherwise difficult leaps on the horizontal vector of the fretboard.

Viktor Zuckerkandl remarked that “Whatever else music may be, one thing it must be: motion.” Yet the idea of music as a composed succession of discrete elements has limited the ways in which musical movement has been theorized. This study focuses on what is arguably the quintessence of continuous musical motion among polyphonic instruments: the steel guitar. Aside from synthesizers, this instrument is particularly well-equipped for exploring continuity multidimensionally. It is fretless, it can produce full harmonies, and with pedals, it allows for smooth changes in dynamics and pitch, in multiple directions at once. Unlike a keyboardist or fretted guitarist, whose fingers lock into the atomized, itemized logic of set theory and elemental harmony, the steel guitarist can move undividedly in myriad ways.

Less about the exact succession of musical elements, the steel guitar sounds out movement from, through, and toward them while also illustrating a phenomenon of moving in place. This presentation will feature live demonstrations on the instrument, which can create a vertiginous effect when the tone bar, pedals, and levers proceed in different directions at different rates of change, confounding notions of “up” and “down.” Analyzing movement in music by performers including Frank Ferera, Gabby Pahinui, Buddy Emmons, and Susan Alcorn suggests a theory in which, rather than an attitude whereby music transforms abruptly from one spatial position to another, music is a kinetic process shared among those creating and experiencing it.