Playing with Tuning in bitKlavier

Combining a new software system with the familiar interface of the MIDI keyboard, bitKlavier is a versatile instrument for exploring the nature of tuning and temperament. We describe a number of approaches it facilitates, including composed tunings, moving fundamental systems, and a novel adaptive tuning system. All of these are characterized by the overarching design priority for bitKlavier to be a context for musical play and exploration, as opposed to finding singular, “correct” solutions to particular tuning “problems,” as has often been the case historically. Introduction Previously, we described how John Cage’s prepared piano has served as an important inspiration and metaphor for bitKlavier, a new instrument that combines a flexible software tool with the powerful constraints and ubiquity of the MIDI keyboard (Trueman and Mulshine, 2019). This inspiration has nothing to do with the sound of the prepared piano and everything to do with the kind of creative process that it inspires. Specifically, bitKlavier aims to provoke a practice that is both playful and generative, by leveraging the hard-earned embodied feedback loop between player and instrument, and subverting it through an engaged process of preparation. In our earlier paper, we focused on the development history of the instrument and its time-domain machine-inspired virtual preparations; here we explore the Trueman, Bhatia, Mulshine, Trevisan 2 Computer Music Journal tuning possibilities of the instrument, with an emphasis on composed tunings and dynamic adaptive systems. We can think of the act of tuning as the original “preparation” for keyboard instruments: it requires design, planning, and significant time to implement, without requiring rebuilding the instrument itself. While the actual retuning can happen instantaneously in bitKlavier, the tuning systems themselves require preparation, and these preparations in turn profoundly shape the creative process. As such, the goal of experimenting with tuning systems in bitKlavier is not primarily about finding exact solutions to tuning problems. Rather, it is more about creating interactive, responsive, and dynamic systems that encourage new possibilities for creative expression via a playful, real-time feedback loop between the musician and the instrument. Tuning poses long-standing and deeply consequential challenges to musicians and instrument designers, particularly in the case of keyboard-centric instruments (like bitKlavier) with their discrete keys—the division of the octave into twelve static steps creates intractable conflicts with the physics of the overtone series, forcing us to choose from innumerable imperfect (if fascinating) possibilities. Given that bitKlavier is at heart a keyboard-conceived instrument, we will be focusing on this particular 12-key case, and while this is related to the history of temperament, we are freed from some of the constraints that acoustic instruments impose (it is impossible, for instance, to instantaneously retune an acoustic piano). There are many resources for learning more about this history (Keislar, 1987; Duffin, 2008; Barbour, 2004; Isacoff, 2003), as well as learning about just intonation (Doty, 1999) and tuning from around the world (Forster, 2010). A recent article by Stange et al. (2018) provides an overview of the challenges of tuning, while Polansky et al. (Polansky, L., D. Rockmore, M.K. Johnson, D. Repetto, and W. Pan., 2009.) presents a rigorous mathematical approach to tuning and temperament. Finally, Wooley (2018) Trueman, Bhatia, Mulshine, Trevisan 3 Computer Music Journal is a fascinating collection of articles about tuning and the various ways a number of composers and performers are wrestling with it today. Composed Tunings What we call composed tunings are in some ways primitive, but nonetheless compositionally powerful. In the chorale at letter D in Nostalgic Synchronic Etude #5 (“Wallumrød”) by Dan Trueman (Figure 1; see also the collection of audio examples available online for this paper), the fundamental for a simple just-intonation system changes periodically throughout, ensuring that each sonority is just tuned while still liberating the progression to move through sonorities that would sound strongly out of tune otherwise. In this example, the slashed notes are played ever so slightly before the other notes, setting the tuning fundamental as indicated by the circled letters (via a modification in bitKlavier). Figure 1. Moving fundamentals (circled). Offsets from ET are indicated only for the first appearance of individual notes, or when they change (for instance, the D# in m7, changing from the D# in m5). Slashed notes are played just before other “simultaneous” notes, ensuring (in this case) that they all use the same new fundamental. Trueman, Bhatia, Mulshine, Trevisan 4 Computer Music Journal Consider measure 5, for instance. Here, the B has a slash through it, indicating that it should be played slightly before the other notes in that chord. A keymap (with this B enabled) is connected to a modification object that in turn changes the fundamental of the tuning to G# when this B is played (see the companion paper to this one, Trueman and Mulshine (2019), for further information about how this sort of signal flow works in bitKlavier), so this entire chord will now be just-tuned relative to G#, resulting in a B that is 15.6 cents sharp to equal-temperament (ET) (a 6:5 minor-third relative to G#), a D# that is 2 cents sharp (a 3:2 perfect fifth), and a G-natural that is 11.7 cents flat (a 15:8 major seventh). From there on out, the fundamental changes in each measure. Note that some pitch classes end up being tuned differently over the course of the chorale (G# in m.1 vs m.5, for instance). It is this ability to manually configure tuning, in composition-specific ways, that motivates that term “composed tuning.” In Nostalgic Synchronic Etude #2 (“Undertow”), we experience a horizontal, melodic kind of composed tuning (Figure 2). Here, the D in the left-hand is what changes tuning, so the slashed-F in the right-hand is played just before the D (to be clear: the slash is a performance indicator, not a preparation indicator; it tells the performer to play that note slightly before the others at that moment, but bitKlavier may be prepared so that any of those notes cause the fundamental change), and therefore is tuned according to the prior tuning (C-just). Then, a reverse note (the nostalgic preparation type in bitKlavier—backwards piano notes with durations dependent, in this case, on the length of preceding sustained note, triggered on note release) which begins when the F is released (notated with a parenthetical note and dashed swell) will be tuned according to the new system, which is an overtone tuning of A, so the F is treated like the 13th-partial, 40.5c sharp to ET (13/8). We end up with a kind of micro-voice leading, where the F moves up by almost equal increments of ~40c before reaching a just tuned F#. Trueman, Bhatia, Mulshine, Trevisan 5 Computer Music Journal Figure 2. Micro-voice leading, resulting from moving fundamentals, from Trueman’s Etude #2, “Undertow.” The tuning of first F on beat 4 is set by the C-fundamental, so is 2c flat to ET (4:3 over C), and the A-fundamental (triggered by the D in the left-hand) sets the tuning of last reverse F (13:8 over A, or 40.5c sharp to ET), which then continues to the last F# (5:3 over A, or 15.6c flat to ET). Horizontally, then, the first F shifts up 42.5c (40.5c + 2c) from beat 4 to the offbeat of beat 4, which then shifts up another 43.9c (100c 15.6c 40.5c) to the F#. This might seem a complicated setup for a small gesture, but it is one of only five very similar configurations used in the piece, and, for perspective, is actually quite simple when compared to, say, preparing the piano for Cage’s Sonatas and Interludes. Crucially, this preparation wasn’t created in order to facilitate a gesture like this; rather the gesture was discovered through experimentation with the preparation. “Systerslått,” a movement from Songs That Are Hard To Sing for string quartet and percussion quartet by Dan Trueman, is based on a traditional Norwegian fiddle tune that is decidedly not equal-tempered. In the example here (Figure 3), we see the passage notated with Helmholtz-Ellis accidentals in the strings (Sabat and Schweinitz, 2004; Nicholson and Sabat, 2018), which efficiently indicates how each interval is just-tuned (the down arrows indicate just-tuned major 3rds (5:4) and 6ths (5:3), the up arrows just-tuned minor 3rds (6:5) and 6ths (8:5); notes with normal or no accidentals are tuned relative to a background grid of perfect 3:2 fifths) while this particular version of the tuning is not meant to claim traditional accuracy, it does reflect a reasonable hearing of how it might be played. The strings are in scordatura, with open C-G-C-G strings in the viola and cello and G-C-G-E strings in the violins; this open E is just-tuned to the G below, and so is flat by a syntonic comma (a ratio Trueman, Bhatia, Mulshine, Trevisan 6 Computer Music Journal of 80/81, or 13.7 cents), notated here by a single down arrow, as in m.2. In order for the viola and cello A’s to be tuned most consonantly to that E, they must also be a syntonic comma flat, hence the down arrow for the A’s. For bitKlavier to match this melody, its fundamentals must change in each measure, and note that in m.2 the fundamental changes to A, a syntonic comma low, in order to match the strings as described. Though the spelling of the bitKlavier part is conventional, simply to make it more readable for the player, the actual sounding tuning will match what the strings play—the right hand of the piano is in unison with the strings. This sort of reasonably complex composed tuning enables the strings to retain the crucial tuning aspects of the traditional melody and play with the keyboard, without rounding off the tuning to the mor