What key are we in? Where is the downbeat? What is this song's tempo? The music theory classroom is full of questions that presuppose single correct answers. It is also built around a repertoire that makes such questions seem like the right ones to ask in the first place. Western thought has a long history of privileging qualities of fixity, hierarchy, and coherence, and this has undoubtedly trickled down to inform current ideas about what sorts of music are (and are not) worthy of study. What might happen if we feature music in the classroom that challenges the most foundational premises of this historical tradition? In this essay, I discuss how I have used certain recordings by free jazz musicians Ornette Coleman and Sun Ra to introduce my students to alternative forms of musical organization that relativize these Western frameworks and decenter music theory's long-standing Eurocentrism. I make the case, in short, that there is much to be gained from teaching free jazz.

Free jazz refers to a range of Black experimental musics that arose in the late 1950s and 1960s as a reflection of (and reaction to) contemporaneous sociopolitical conditions in America (Kofsky 1970, Carles and Comolli 1971, Wilmer 1992). It has been referred to by a variety of names, from "avant-garde jazz" to the "New Thing," but I choose to use the label "free jazz" to highlight this music's intimate connections with particular notions of freedom that emerged in the era of civil rights and Black nationalism. In contrast to Euro-American ideas of freedom as something only attainable within a predetermined structure of rules and constraints, emergent Afrocentric conceptions of the term merged a freedom from predetermined constraints with a freedom to pursue one's own path (Monson 2007, Anderson 2007). Free jazz can be considered a sonic enactment of these Afrocentric ideas of freedom. The music emphasizes collective improvisation, eclecticism, and pluralism while distancing itself from aesthetic markers of music theory's hegemonic whiteness such as fixed chord changes, hierarchical metrical templates, and functional tonality. For those trained to regard Western Euroclassical systems of harmony and meter as normative defaults, encountering free jazz can be a jarring experience, to say the least.

Studying free jazz is therefore a productive way to shine a light on the field of music theory's traditional values and priorities, and it is for this reason that I am lobbying for the music's more widespread inclusion in the undergraduate theory classroom. If the college experience is ostensibly about stepping outside of one's comfort zone, being exposed to differing ideologies and viewpoints, and learning how to hold multiple positions at once, then is there any better music to do the job? Free jazz is far from "unstructured chaos" (Tymoczko 1996, 76). Its organizational trajectory is simply of a different kind—one that is not always describable by traditional metrics of "governing key," "ensemble downbeat," or "global tempo." Indeed, much free jazz operates in a manner that exposes such alleged musical "facts" as matters of perspectival contingency. Individual ensemble members often approach these referential orienting devices in different ways, but crucially, no one is more "correct" than any other. The music is thus an effective tool to teach students that moments of apparent ambiguity or interpretive plurality need not always be reckoned as instances of conflict (or competition) in which a "winner" must be selected; rather, they can profitably be regarded as instances of vital coexistence (or collaboration) in which plurality is precisely the point.

Ornette Coleman's music furnishes an instructive starting point for discussion. I have asked students to transcribe the horn line of "Lonely Woman," and then compare their efforts with those of Block 1990, Westendorf 1994, Folio 1995, and Vickery and James 2017. This leads into a conversation about the politics, pragmatics, and inherent partiality of the transcriptional act, and how certain scholars prioritize certain features of the music in their transcriptions while downplaying or even erasing others (Rusch, Salley, and Stover 2016). I pay special attention to the approaches of Folio 1995 and Vickery and James 2017, in which the aesthetic of perspectival contingency plays a central role. Folio is the first scholar to argue that the song's tempo is not a collectively agreed-upon fact, but rather varies across members of the ensemble. She posits a 6:7 ratio of structural polytempo between parts, with Coleman (alto saxophone) and Don Cherry (pocket trumpet) playing at 150 BPM while Charlie Haden (bass) and Billy Higgins (drum set) play at 176 BPM. Vickery and James postulate not just a contingent tempo, but also a contingent meter: they hear the horns in 3/4 and the drums in 4/4. Each excerpt they discuss thus receives two distinct transcriptions of the same music—one from the composite perspective of Coleman and Cherry, and another from the perspective of Higgins. I like to conduct a "perspective-taking" activity where I first ask my students to tap along with the drums, and then to flip frameworks for a subsequent listen and tap along with the horns. Doing so allows them to viscerally experience how each hearing affords its own set of qualitative subtleties; eventually, they learn to switch back and forth between the two at will. But they cannot entrain to both at the same time, thus making this situation an auditory analog to the well-known rabbit-duck illusion reproduced below:

I am far from the first scholar to invoke this analogy in reference to musical ambiguity (see Lewin 1986; Guck 2017), or to suggest the image's utility as a pedagogical tool (Carmona 2017). But what is unique about its application to free jazz is that the interpretive plurality it describes is not just a momentary phenomenon that eventually clears up and gives way to consensus; rather, it is something that is aesthetically built into the music on the most foundational level. The upshot of this scenario, ultimately, is ideological and ethical: to encourage students to "snap out of [their] customary or habitual trance of encountering things" (Kemp 2017, 256), and to foster "an awareness that [their] current perception is not the only possibility" (Dubiel 2017, 234).

Once students become more comfortable with contingent tempo and contingent meter, I usually proceed to Coleman's "All My Life," which combines moments of these with what might be called an overarching "rabbit-duck tonality." I begin with a homework assignment, sending students a recording of the song and asking them to write 400 words describing its tonal orientation. I then open the next class by posing an intentionally reductive question—"So, what key is this in?"—that typically garners some laughs. This sets the stage for a lively discussion about the continual interplay of C-centrism and G-centrism, and how neither of these tonal areas is meant to be heard as globally/structurally more important than the other (though there are local moments where the interpretational scales might be heard as tipping, so to speak). Asha Puthli's opening vocal melody, transcribed below as Example 1, displays a gradual shift from C-centrism to G-centrism. But this apparent "arrival" on G is ultimately negated by the song's strophic form, which dictates a return shortly thereafter to the opening C-centric material. Since neither key is dignified with particularly strong (hyper)metrical support, the song's governing tonality appears to be an open question by design.

This tonal dualism takes on new significance during the song's instrumental strophe beginning at 1:17. Its opening line—essentially a superimposition of Puthli's vocal melody in mm.1–3 and mm.12–14 of Example 1—is transcribed in Example 2:

I have chosen to represent this rubato horn line as unmoored from any governing metrical framework, since it floats recitationally above the emergent duple meter of the drums, refusing to capitulate to their proposition of strictly isochronous phrasing. As such, the rhythmic values in my transcription are meant to be loose approximations of "short" and "long" durations, not rhythmically exact lengths.

This moment provides the perfect opportunity to introduce students to Coleman's original philosophy of "harmolodics," which is part musicking approach, part compositional method, and part cultural ideology (Rush 2017 contains the most extensive treatment). Harmolodic philosophy, which Coleman developed during the US civil rights movement, is rooted in the idea of human equality and mobilized through music that enacts this fundamental equality—concretely, among performers and instruments in an ensemble, and more abstractly, among musical domains. It is marked by what Peter Niklas Wilson (1999, 68 and 70) calls an "egalitarian spirit" in which no one thing dominates over any other; its end goal is to create a musical space "in which the partners [in a] dialogue can articulate their own worldview without any pressure to compromise." One distinctive feature of this philosophy is Coleman's expansive concept of "unison," which explicitly "reject[s] the hierarchical notion of 'concert pitch'" (Harbert 2018, 149). He would often write out a melody and instruct each musician to play it as if it were written in the clef they were accustomed to reading. The result would be a unique kind of parallel motion that seemingly merges the qualities of polytonality and heterophony, as if suggesting multiple potential referential centricities while simultaneously acting as a unified elaboration of one basic, fundamental melodic line.

The instrumental strophe partially transcribed in Example 2 above can be conceived as a textbook example of Coleman's "harmolodic unison." Consider the opening B-E dyad, for instance. Even though it sounds as two separate notes, its constituent elements—a concert-pitch B played by a tenor saxophone and the concert-pitch E a fourth above played by an alto saxophone—would both read as the same C♯ on Coleman's harmolodic clef (see Morris 2012 and Rush 2017). Since most of the ensuing instrumental strophe proceeds similarly, in parallel perfect fourths, this offers a clue that Coleman may have conceived of it as a single, unison melody in harmolodic terms. As such, the instrumental strophe (and with it, the song as a whole) is a sonic encapsulation of the central harmolodic credo: to always "respect and celebrate differences within unity" (Rush 2017, 21). To pigeonhole this music into the either/or confines of C-centrism versus G-centrism, put plainly, is to miss its point.

Bringing music like "All My Life" into the music theory classroom gives instructors a valuable opportunity to decenter several foundational assumptions that have become ingrained in Western music-theoretic thought. Such music exposes the notions of monotonal determinacy and structural coherence not as universal aesthetic ideals, but as biases resulting from a particular cultural worldview (and conception of history) that keeps out more than it lets in. It reveals the idea of a single agreed-upon meter (or tempo) to be just one among many equally valid ways to play "in time." It shows that there need not be a determinate relationship between part and whole, the demonstration of which is the end goal of a musical analysis. It suggests that music can still sound tonal without containing anything like traditional harmonies or harmonic functions. And it illustrates rather cogently that aesthetics and ideologies are two sides of the same coin, and that the former cannot be discussed without the latter.

I find it useful to start with Coleman's music when teaching free jazz in the undergraduate classroom because it makes enough contact with the "common ground" of Western music that it provides an accessible inroads to some of the more radical instantiations of the genre. Coleman's musical language reveals the fundamental constructedness of several oppositional binaries that enable Western music and Western musical thought: consonance versus dissonance, strong versus weak beats, and closure versus open-endedness, to name a few. But it does so while situated on the familiar terrain of song forms such as AABA and the blues. Coleman's flexible relationship to these inherited song forms (see Charry 1997–98), together with the harmolodic egalitarianism of his approach to them, make for a compelling introduction to alternative music-organizational and music-expressive frameworks that are non-hierarchical and non-Eurocentric, yet still approachable to Western-enculturated ears.

Later in the semester, I present my students with music that even more pointedly escapes the metaphysical enclosure that structures Western thought. One example I have used with great success is the aptly titled "Outer Nothingness" by Sun Ra and his Arkestra. This collective sonic exploration features several distinctive timbres that are set into even greater relief by the frequent silences that surround them. Musical time is often regarded in terms of space; silence, in this reading, can be reflective of emptiness. Indeed, the very first few seconds of the recording, which feature a timpani part not unlike the opening bars of Maurice Jarre's "Overture" to Lawrence of Arabia (written earlier that decade), evoke the idea of the echoic void. Sun Ra's musical aesthetics are inextricably intertwined with his ideological project to reframe and reclaim Black consciousness. As Daniel Kreiss (2008, 58) writes, Sun Ra envisioned a "'mythic consciousness' of technologically empowered racial identity that would enable blacks [sic] to recreate and invent technologies and construct utopian societies on outer space landscapes." Demonstrating control over a potpourri of timbres is one way Sun Ra performs this reclamation of Black technological agency through sound. His music thus exhibits what theorists of Black art call an aesthetic of "multidominance" (Douglas 1991, Lewis 2009): an intense array of coexisting colors and textures.

By this point, my students have become familiar with metrical multistability as an organizational principle. But in the collective group improvisation of "Outer Nothingness," the musicians seem to control the very emergence and dissolution of pulse itself. In the absence of regular pulsation to temporally organize pitch information, other musical parameters structure ensemble interaction in its place—and timbre is no doubt a central one, far from the "secondary parameter" that Leonard Meyer (1989) considers it to be. A representative excerpt begins at 4:02, when a four-second silence is broken by a sonically beckoning "doorbell" line played by Sun Ra on bass marimba. The door is "answered" at 4:04 with a ten-second outburst in winds and horns, a salient characteristic of which is what I hear as a "rubbing" sensation created both by the superimposition of timbres and by the microtonal crunch of simultaneous pitches. Double bassist Ronnie Boykins's harshly bowed response, beginning at 4:14, is a conceptual reduction of this "rubbing'' idea, its essence transferred abstractly from several instruments to one. By 4:20 the friction seems to be too much to handle, and a bouncy col legno emerges—thus completing the process that Ekkehard Jost (1974, 95) calls the "gradual emancipation of timbre from pitch." I like to assign students other short excerpts from this recording and ask them to describe, as specifically as possible, how ensemble members manage to coordinate with one another in a world where conventional musical "facts," as we typically know them, seem not to exist. This gives students the opportunity to showcase their creativity by employing original organizational metaphors and coining their own descriptive neologisms to characterize ensemble interaction. Effectively analyzing free jazz comes down to knowing what to listen for (and knowing which formerly trusty guideposts will no longer serve as reliable perceptual anchors). Once students get the hang of hearing differently—and thinking differently about musical hearing—they are less likely to dismiss free jazz as bothersome noise or dissonant randomness.

Stepping out of one's musical comfort zone can provide an invaluable perspective on how that comfort zone came to be in the first place (and how one is often instinctively inclined to seek refuge in it whenever it is put under pressure). It can also help one think with greater nuance and self-awareness when "stepping back in," so to speak, to analyze familiar Western music. Free jazz reminds us that our judgments of consonance and dissonance are more so the products of our culturally conditioned expectations than they are the products of numerical ratios. It reminds us that, in Western music, tonal stability is metrical stability (and vice versa): that much of what makes downbeats "strong" is the expectation that certain types of tonal events tend to occur on them, and much of what makes tonic chords "stable" is the fact that they tend to occur in predictable temporal contexts. It reveals many of the implicit biases we tend to hold about how music "should" sound (and what constitutes "music" in the first place). And perhaps most of all, it encourages us to become more attuned to the persistent visual, auditory, and discursive traces of Eurocentrism, and more attentive to the ways they continue to lurk in those places we might not expect—from the disciplining bar lines of staff notation, to the sound of the piano, to those seemingly innocuous questions like "what key are we in?"