Daniel Walden
Enter just about any room of a Western-style conservatory or music department, and you will probably stumble into a piano. Nearly everyone on the teaching and research staff has a use for them. Composers, improvisers, and performers employ them in searching for new artistic possibilities. Theorists use them to work out the properties of musical harmony. And pedagogues are almost certain to employ them when teaching students the laws of harmony, as well as for developing aural skills, score reading, and critical listening. In short, the piano keyboard is a classic example of what Alexander Rehding (2016a and 2016b) calls an “instrument of theory,” shaping how we conceive and interpret music, and playing an integral role in defining the discourse networks by which musical knowledge is stored, transmitted, and reproduced.[1]
But challenges have arisen to the sovereignty of the keyboard. Consider recent developments in music theory pedagogy. Departments across the US and UK (and perhaps Europe?) have started removing keyboard skills, once considered foundational, from their undergraduate curricula. Just this year at Oxford, Keyboard Skills was converted from a compulsory course into an optional one; at Harvard, it was eliminated as a requirement several years earlier; at Durham University, it has been absent from the formal curriculum for decades, at least. (These are the institutions I have been a part of and can thus speak about from personal experience, but I am sure they are not the only ones.) Driving these curricular adjustments are a set of social, political, and institutional concerns: for the advantage it gives to students of means who were able to afford private training on the keyboard; for the marked gender inequalities in grading outcomes, seemingly indicative of unconscious bias; for the possibility that it might act as a deterrent to prospective students; and so forth.
Yet another affront has been mounted from the side of theoretical research. In my own work (2019), I have examined how the keyboard acted as a filter in the investigation of non-Western and Indigenous music—not only because it quantized pitch values to a one-size-fits-all scale of twelve divisions per octave, but also because it was instrumentalized as a training device that would tutor musicians in how to pay attention to certain highly valued parameters (i.e., pitch) over others of supposedly secondary value (timbre). I am not the only one to raise these sorts of questions. Bryan Parkhurst and Stephan Hammel (2020) have issued a bracing Marxist critique of the piano (and piano-making firms) for its historical role in instantiating the exploitative paradigms of capitalism. And Martin Scherzinger (2016) has written about how the lion’s share of computer software remains grounded in “claviocentric digital patterns,” with MIDI logic creating a “path dependencies” in both collaborative and interpretative settings. The pitch sequences of the world, the notes, are “gradually coalescing around the MIDI standard” of twelve-tone equal temperament—leading him to paraphrase the software engineer Xavier Serra in speculating as to whether keyboard-based digital protocols might constitute “a kind of colonialism.”
Anxieties about the social and cognitive effects of the keyboard are not exactly new. Legend has it that harpsichords were scorned as relics of elite culture during the French Revolution, and were eventually rounded up and chopped into firewood by the hundreds. So should we emulate the sans-culottes and burn all the pianos? As a pianist myself, my answer is obviously “no” (although there may be a few practice room pianos out there that would be better as kindling). But the lessons of curriculum redesign and recent keyboard studies clearly suggest that it is worth questioning its legacy and enduring centrality, and that we should begin applying our energy to the development of new instruments of theory that are designed to highlight our current path dependencies as musical researchers, pedagogues, and creators and to offer new ones. By “new,”I don’t necessarily mean “original” or “as yet unseen” (although instruments that are new in that sense would also be welcome). In fact, many of the “new” instruments of theory I have in mind are historical. I would nevertheless call them “new” because they are capable of jolting scholars and pedagogues out of their “path dependencies,” and into new modes of thinking and communicating that are more flexible, creative, and socially inclusive.
What might such an instrument of theory look like? Perhaps like the instrument you see in figs. 1 and 2—almost like a piano, but not quite. This is the “Demonstration Harmonium,” built by Oskar Walcker for the Japanese music theorist Tanaka Shōhei in 1892—and then neglected for over a century, until it was restored to playing condition by the builder’s great-grandson, Gerhard Walcker, for the inventor’s grandson, Dr. Tanaka Tasuku. This instrument features not twelve equal divisions of the octave, but twenty divisions tuned in just intonation and distributed across split sharps and naturals. This makes it impractical for performance—it only works in C Major, for one thing—but its purpose was not for practice but for pedagogy and research. As Tanaka outlines in a four-page advertisement that accompanies the instrument, explaining its objectives and providing a sample pedagogical program for young pupils, the goal of the harmonium was to break intellectual habits formed by the piano and encourage new ways of listening and thinking, sensitive to the significance of microtonal discriminations of intonation and the alterity of tonal relations within unequal pitch spaces. It is extraordinarily effective to that end, as I discovered five years ago when I had the chance to try the instrument myself, and put myself through Tanaka’s pedagogical program. I found it a defamiliarizing experience, in the sense that it introduces minute alterations to the acoustical and haptic feedback one would expect from a keyboard instrument, and those alterations ultimately challenged me to rethink in productive ways all that was familiar to me from daily practice on the piano.
I found that tonic triads, for example, required a subtle pronation of the wrist so that the pinky lands correctly on the back split G; the requirement to pronate every time I returned to the tonic served as a tactile reminder of the peculiar geometries of a just-intonation system, in which fifths and thirds are tuned by separate chains. Progressing further through Tanaka’s pedagogical program, I discovered that virtually every harmonic function had some sort of small peculiarity built into it, and that this choreography was guiding me towards carving new and alternative “paths” through tonal space, breaking my dependencies upon those I had inscribed through piano practice and theory training. Once I completed Tanaka’s pedagogical program, I continued to learn simply through play with the instrument, following the pleasure that accompanied the discovery of new types of harmonic relations (what is the sound of a limma + a major third?) and tactile sensations (what is the best hand position for a just diminished ninth?).[2]
This is why I would call the Demonstration Harmonium a “new” instrument of theory—even though it is of course old, in the sense that it is historical. There are doubtless many other “new” instruments we could identify through historical research, with different affordances for different areas of theory: monochords, tuning pipes, sirens, rhythmicons, etc. And as every instrument has its limitations—Tanaka’s keyboard may break path dependencies, but could it free us from claviocentrism?—it seems to me that it would be quite useful to start identifying and reconstructing such instruments in order to develop a new theoretical instrumentarium. And so, with support in the form of a Small Research Grant from the British Academy and Leverhulme Trust, I have begun assembling an interdisciplinary laboratory I call NIFTY—after New Instruments for TheorY—that will bring together theorists, instrument builders, and computer scientists interested in the research and development of new instruments of theory modelled after both historical and entirely original designs. My objective for NIFTY is to make these instruments as widely accessible as possible, by ensuring that all digital instruments are open-source and available as free downloads, and that all acoustical/analog instruments can either be 3D printed or constructed from simple DIY kits using cheaply available materials. In this way, I hope to remove as many constraints as possible on the potential for these new instruments to have a meaningful impact on the ways we teach and research theory.[3]
NIFTY will start in the coming year with a series of workshops. Attendees will have the opportunity to select a new instrument of theory—one they have discovered in their research, or one they have conceived themselves—and work closely with the other participants in determining potential research and pedagogical applications for the instrument, as well as a plan for how to render that instrument as broadly accessible as possible. In future stages of the project, we will start to build those instruments, and develop a website to host them. My own focus will be on developing digital reproductions of the just-intonation and microtonal instruments of theory I have discovered through my research—ranging from Tanaka’s instrument to the Euharmonic Organ of Henry Liston, built in 1817 for St. Andrew’s Presbyterian Church in Calcutta, to the “Oriental Piano” built in the 1930s by Lebanese musician Abdallah Chahiné to demonstrate the Arab maqām system. I expect these instruments to take the form of a software application that can take input from any standard MIDI keyboard, as well as a set of guitar pedals, and output the intonation systems to which these historical instruments were tuned. But I am hopeful that other projects will take very different forms. I am currently looking for new collaborators—so please get in touch with me if you might be interested in being part of this project!
A final thought about how this project may prove useful for assistance in other projects underway in the discipline, focused on decolonial and anti-racist ends (see for instance Jade Conlee and Tatiana Koike’s recent post on this site): if music theory is stuck within the “path dependencies” of colonial ideology and the white racial frame, the problems music theory face must lie as much with the mediums as the message. How then can we ever seek to effect substantial changes in music theory discourse, if we allow the current discourse networks to remain unaltered?
Bibliography
Conlee, Jade and Tatiana Koike. “Reimagining Formalism for an Antiracist Music Theory,” Part I and Part II. Blog for the History of Music Theory SMT Interest Group & AMS Study Group, dated 8 March 2021 and 18 March 2021. Accessed 17 October 2021. Link here.
Dabin, Matthew, Terumi Narushima et al. “3D Modelling and Printing of Microtonal Flutes.” Proceedings of the 16th International Conference on New Interfaces for Musical Expression (NIME 2016), 286-290. Brisbane, Australia: Queensland Conservatorium Griffith University, 2016.
De Souza, Jonathan. Music at Hand: Instruments, Bodies, and Cognition. Oxford: Oxford University Press, 2017).
Dolan, Emily. “Toward a Musicology of Interaces.” Keyboard Perspectives 5 (2012), 1–13.
Eidsheim, Nina. “The UCLA PEER Lab.” Accessed 17 October 2021. Link here.
Moseley, Roger. Keys to Play: Music as a Ludic Medium from Apollo to Nintendo. Berkeley: UC Press, 2016.
Gawboy, Anna. “The Wheatstone Concertina and Symmetrical Arrangements of Tonal Space.” Journal of Music Theory 53/2 (2009): 163–190.
Rehding, Alexander. “Instruments of Music Theory.” Music Theory Online 22/4 (2016). Link here.
Rehding, Alexander. “Three Music Theory Lessons.” Journal of the Royal Musicological Association 141/2 (2016), 251–282.
Scherzinger, Martin. “Software Physiognomics: Adorno’s Radio Analytics Today.” New German Critique 43/3 (2016): 53–72.
Sonevytsky, Maria. “The Accordion and Ethnic Whiteness: Toward a New Critical Organology.” The World of Music 50/3 (2008), 101–118.
Parkhurst, Bryan and Stephan Hammel, “Pitch, Tone, and Note,” in The Oxford Handbook of Critical Concepts in Music Theory (2020). Link here (paywall).
Walden, Daniel. “Pitch vs. Timbre.” In The Oxford Handbook of Timbre, ed. Emily Dolan and Alexander Rehding (Oxford: Oxford University Press, 2019). Link here (paywall).
[1] See also Sonevytsky 2008, Gawboy 2009, Dolan 2012, De Souza 2017.
[2] My idea of creative “play” as a valuable research method is shaped by Moseley 2016 as well as Nina Eidsheim’s work with the UCLA Practice-based Experimental Epistemology Research (PEER) Lab (click here for more info).
[3] This is not the first project of its kind. See for instance Terumi Narushima’s collaborative project focused on 3D printing of microtonal flutes, described in Dabin/Narushima et al. 2016.
History of Music Theory 
As this SMT group invites comments (on its Facebook page), let me react to this. I fail to see how replacing the piano by Tanaka’s enharmonium in any way could achieve the results mentioned above, reducing “the exploitative paradigms of capitalism,” leading theorists to “new modes of thinking and communicating that are more flexible, creative, and socially inclusive,” and the like.
Tanaka’s enharmonium, and its simplified version the “Demonstration Harmonium,” is an instrument of fixed pitches meant to illustrates possibilities of just intonation. Both these aspects, fixed pitches and just intonation, are very much characteristic of Western music theory. Just intonation in particular requires sounds with harmonic partials, which have been particularly cultivated in Western music. Just intonation has been an utopy of Western music theory from the Renaissance up to the late 19th or early 20th century.
The enharmonium had been presented in Berlin in the late 1880’s and was praised by several Western musicians including Joseph Joachim, Phillip Spitta, Hans von Bülow, Anton Bruckner, Hans Richter, and many others. It was never meant to emulate Japanese music which, mainly pentatonic, has little use of 20 fixed pitches in the octave. The harmonium, in addition, might be considered as a colonial instrument as it was forcefully introduced in India and surrounding countries in the second half of the 19th century.
The idea to reduce non Western musics to a number of fixed pitches (usually more than 12 in the octave) is a characteristic Western view on Oriental music. One well known example is the Cairo Congress of 1932, called by European music theorists, who convinced the Arab participants that their music could be described as based on 24 quarter tones in the octave.
If music theory is to become “decolonial and anti-racist,” this must be taken seriously and in full knowledge of all aspects.
LikeLike
Dear Nicolas,
Many thanks for your comment, and for sharing additional background information about Tanaka’s instrument and just intonation. In fact, this is a history I am quite interested in and have studied in great detail, and I can refer you to my dissertation on the subject. (https://dash.harvard.edu/handle/1/42013088)
The point I am trying to make is rather different from the one you suggest. It is certainly not that Tanaka’s instrument is the instrument to decolonize music theory, and that we should replace all pianos with Demonstration Harmoniums! I do not believe that any single instrument would have the capability to single-handedly “decolonize” the discipline. (Nor for that matter do I believe the piano is inherently “colonial,” even if it has a history of being applied towards that end… if I thought this I wouldn’t play it!) My main point is rather that the legacy of colonialism should be traced not just through our discourse, but through our discourse networks—in other words, in the constellation of media that both transmit and shape the messages we put into them. We don’t always acknowledge the fact that the piano is not a transparent medium. And so if we are indeed to be serious about the goals of decolonialism (as you correctly observe we should be) we must pay equal attention to the instruments we use in the classroom as we do to the messages we try to communicate through them.
My second point is that every instrument has its constraints, and can afford us only a delimited set of observations about musical systems. And so my goal in organizing NIFTY is to work with colleagues in widening the range of instruments we use in pedagogy and research, in order to encourage diverse frameworks of thought—and this project is open to (even if not necessarily entirely defined by) sparking a search for instruments that could break colonial habits of thought.
The reason that I brought up the specific example of Tanaka’s harmonium was simply to demonstrate the power musical instruments have to shape the frameworks by which we make sense of music. My experience was that the Demonstration Harmonium radically defamiliarized my understanding of how music theory worked, and ultimately lead me towards radically new conclusions about musical systems. It broke certain “path dependencies,” so to speak, and breaking path dependencies seems to me a necessary first step of radical change. But one of the reasons I would like to organize NIFTY is to also start a conversation with colleagues about its constraints as a “new instrument of theory,” despite these remarkable qualities—for as I acknowledge in my post, I suspect it may not be the ideal instrument for breaking “claviocentrism.”
Two other points:
—I would never suggest Tanaka’s Demonstration Harmonium was intended for Japanese music. It was quite obviously intended for Western music, which is why I discuss in the post its applications for teaching Western music theory. However…Tanaka’s later harmoniums, built in the 1930s after his return to Japan and based on similar principles, were quite deliberately intended for Western and Japanese music. All of this is explained in his 1940 treatise, Nihon no wasei kiso.
—I would disagree that the Arab participants of the Cairo Congress were simply “convinced” by their European participants about the quarter-tone scale. In fact this seems to me an unfortunate way of putting it, as it divests Arab theorists of their intellectual agency. First of all, not all participants seem to have agreed. And second of all, the reason Chahiné, Wadia Sabra, and others adopted the 24-tone-per-octave keyboard seem to me far more complicated—connected more to a political strategy focused on establishing a platform for an active Arab participation in global modernity. Also in my dissertation, I draw on Homi Bhabha’s concept of colonial mimicry in describing an analogous situation in 1920s North India, when theorists like Krishnaji Ballal Deval proposed just-intonation harmoniums with 22 divisions of the octave as a direct response to the colonial history of the twelve-key harmonium within the subcontinent.
Many thanks for engaging with this post!
LikeLike
Thanks, Daniel, I see now clearer in this. The main point, I think, is that we don’t share the same view of what we call “music theory” – and the difference may more generally be between an American and an European conception. For you, music theory is a pedagogical discipline that includes, for instance, keyboard skills. In my point of view, I see no theory involved in keyboard skills. For years, I taught the history of music theory (or, perhaps better, of music theories). There was a piano in the class where I gave medieval theory and, as I am not a very good singer, I played examples on the piano. I would have done the same on a harpsichord, an organ, an harmonium, or any other instrument available.
Similarly, when I said that European participants to the Cairo Congres “convinced” the Arab participants that their music was based on 24 quarter tones in the octave, I mean that they convinced them that it was historically so, that traditional maqam used quarter tones, etc. You are perfectly right that the adoption of the system also represents an Arab participation in global modernity, as can be seen for instance in modern Arab jazz or pop music. But my former Arabic students and present-day colleagues in Tunisia or Lebanon prefer to think that Zalzalian intervals have known a complex history that cannot be reduced to quarter tones. There are historical treatises on the subject and national traditions to be taken in account.
This SMT Interest Group is about the “History of Music Theory,” but probably views it also in the sense of the pedagogical discipline that you envisage. I would rather consider that the “History of Music Theory” primarily means the history of (ancient) music theories, of treatises, etc. This seems at times forgotten in recent discussions in SMT.
LikeLike