and Music Theory Today
and Music Theory Today
How can the all-embracing logic which mirrors the world use such special catches and manipulations? Only because all these are connected into an infinitely fine network, to the great mirror. . . .
[Laws] treat of the network and not what the network describes.
3. The Monster Problem
[Previous Post: 2. Maverick Integration]
The previous post provided a slide show of stages in the life cycle of a hypothetical musical "system" which we will now continue to explore. The content (application) of this system is purposely left unspecified to suppress, to the extent possible, the aesthetic and political prejudices inherent in any specific application. It is presented as an abstract model to relate three fundamental conceptual roles: a model-defining theory, a generative techne, and a critical analysis. Theory and techne together are music's workshop: theory defines the model by providing the "allowable" materials and tools; techne offers ways to choose and purpose those materials and tools from work to work. Theory and analysis working together in this stable model provide ways for the model to evolve without jeopardizing its integrity. As long as techne works within the conceptual boundary identified by theory, there is no reason for analysis and techne to converse directly without theory being present – however, this is about to change.
From inside, this model is unaware of anything other than itself; it demonstrates (to itself) that it is capable of responding to any eventuality; it evolves over time before settling in to its steady state forever; its library, keeper of its works, is capable of infinite expansion; the model assumes it is the uni-verse. The previous diagrams traced the model's "phylogenesis" from birth (the initial state) through various stages of development until its final homeostatic state where a compliant techne, despite having exhausted its ability to provide mavericks to expand the model's theory, is free to continue providing model-consistent works till the end of time.
The question now is not whether or not the model can go on forever in its homeostatic state – it certainly can. Nor is the question whether or not the model can continue to challenge techne when acceptable variations on theory's core are exhausted – it certainly can not. Eternal life has its drawbacks, after all.
But the question is whether the model has judged correctly that it is the only possible model, which is to ask:
Is music a universe or a pluriverse?
If it's the former, then users (the finite actors playing the various roles in the model) are finally left with just one game to play:
The goal of the game is to create new combinations of knowledge within existing sciences and arts. This is also the very limitation of the game. No new knowledge is created, only new combinations of old knowledge. [Hermann Hesse's] "Glass Bead Game" is a symbol of culture in harmony and balance, but the price to be paid is high: "The most important consequence of this ... attitude, or rather of this ... subordination to the cultural process, [is] that men largely [cease] to produce works of art."
However, if it's the latter, if music is actually embedded in a theory pluriverse, then, given that as yet there is no known coherent description for this idea within music theory today, we must turn for help to recent conversations in philosophy animated by consideration of possible worlds and concomitant problems in modal logic. Here is arguably the most radical:
Are there other worlds that are other ways? I say there are. I advocate a thesis of plurality of worlds, or ['extreme'] modal realism, which holds that our world is but one among many. ... There are so many other worlds, in fact, that absolutely every way that a world could possibly be is a way that some world is. And as with worlds, so it is with parts of worlds. There are ever so many ways that a part of a world could be; and so many and so varied are the other worlds that absolutely every way that a part of a world could possibly be is a way that some part of some world is.
The one-or-many question is precisely where music theory is poised today – and with it, music itself.
In praise of monsters
In praise of monsters
Let's return now to the model and introduce Thompson's heterodox monster.
Cognition – our way of seeing and our way of not seeing – may, in the area I have termed 'overt', be subject to perfect control, but in the 'covert' area control can never be perfect since our way of seeing denies the very existence of this area. It is not possible to legislate effectively against that which it is held does not exist. The consequence of this inevitably imperfect control by the monitor [in our context, analysis] is that, despite all its efforts, some unruly elements get through into the world view domain. The arrival of such new elements is likely to mess up the ordering process, in some cases giving rise to quite serious contradictions between hitherto integrated patterns of value. If the world view domain becomes changed in this way then the operation of the monitor [analysis] will also change ....
The "overt" model developed in the previous post was indeed "subject to perfect control" by theory. Ignoring the implied contradiction, it even made provision for the possibility, however remote, that analysis might draw a work so deformed (incompatible with theory's core) that the model could not work with it at all. Such a work would have to be rejected as a monster. But we neglected to ask what would happen to such a work when it is rejected. Undisposed waste poses a threat to the balance of the model's ecology. So, if a monster did appear, what would analysis do with it?
It would make no sense to return a monster to a library that's set up for random draws because the monster would just keep popping up in future draws with no useful (model-supportive) purpose. Worse, the presence of such a monster in the library might cause embarrassing questions from neophyte users. So, in this isolated model, theory tells analysis that, if it ever does encounter a monster, it must ignore the library's requirement to return all draws and throw the monster in a rubbish bin. (Diagram 1). The onus is on analysis to get rid of monsters. Stuck on saving the theory within the model, analysis would have limited options.
The simplest of these, the passive "La-La" or "Hester Prynne" option, would be to ignore the monster – cover your ears – refuse to listen – shun it. This option would tag the monster with a scarlet M and throw it back willy nilly into the library, so that if the monster is drawn again, it could immediately be returned with no wasted analytical effort.
La-La's aggressive counterpart, the "Luddite" or "Tea Party" or "Zhdanovist" option, would be to campaign against any monster's right to exist and destroy it if possible. An urge to kill what is not immediately understood – what is perceived as prima facie malformed – would cause unending battles over the library's conservation mandate. Worst of all, it would institutionalize a policy of analytical intolerance.
And finally, the feel-good solution. The most ingenious option would be to build a separate room within the library. This is the enlightened "TBD" or "Academic Parking Lot" technique – to place all monsters into a special-access class of works within the library, in a room labelled "Unknown."
Also referred to as "Waiting for Einstein" or "Hedge Your Bets," TBD would treat the monster as an intriguing anomaly to be held in reserve for "advanced" research. Analysis would assume it may be able to deal with it some day by an approach awaiting discovery or one that is still under development. Then either the monster would turn out to be nothing more than a super maverick that the model can accommodate by making helpful extensions and adjustments to theory (as it has with other mavericks in the past), or it would remain a fading curiosity mostly out of sight in the Unknown and posing no threat to the majority of users' agenda of keeping the teachable Known in circulation. This approach is not only enlightened, it is reasonable and (above all) safe. It would protect the model without casting aspersions on TBD monsters that might later make analysis look like a fool.
These three possibilities echo Michael Thompson (quoted previously in "Tripping over Rubbish"):
[T]here are some who would go so far as to maintain that the proper aim and object of serious thought should be the systematic exclusion of such monsters. Monster exclusion is, at its worst, intolerant, puritanical [La-La], and repressive [Luddite]. At its best, it reveals a dubious prettifying intent that leads to the pretence that things are tidier than they really are [TBD].
Of course monsters begin to appear.
Not only that, they begin to accumulate. La-La can't continue to ignore them; the Luddite can't assassinate them fast enough; and TBD's parking lot is starting to overflow.
Our stable model is forced to admit that it is not alone. Unknown choices may exist outside the box.
The problem now shifts dramatically due to the knowledge that another – overlapping or entirely separate – competing model exists; and (finally it dawns:) this other model is the only thing that could possibly be polluting the library. But what kind of analysis is possible without prior theory to guide it?
This question puts us up against the discovery dilemma:
You can't assume nothing because then you don't know how to start looking, but if you assume too much then you're biased and you're not open to finding a lot of things that might be there.
By placing a monster in TBD, analysis is waiting to see if the purple box in Diagram 2 (the question mark is some unknown theory hypothetically related to unexpected moves in techne) will eventually merge with, or at least overlay, the red box, revealing that the monster was just a particularly knotty maverick all along – and this discovery will result in another adjustment in theory.
But the only way of getting at the question mark is by first finding a path lying outside the model that leads from the monsterwork back to (an unknown) techne based on an unknown theory, and then describing that path. If this reverse, outside-the-box analysis has done its job, this description will trigger a conjecture – an educated guess at some aspect(s) of the purple box's theory. Let's call this conjecture the proposition p. Analysis can then look in the red box's theory for a proposition r that will match or cover p. Given that such a proposition p can be established, there are two possible outcomes.
(A) If analysis finds such a congruence between p and r, then the purple box belongs to the model, the work is a maverick, theory is adjusted accordingly, and the red box's theory core is saved. It may not be immediately evident, but this is an "honest" version of the standard model-affirmation analysis as described in the previous post which is a weak form of confirmation bias. The distinction is that the type of analysis here doesn't begin by assuming an underived theory, but waits until the last step to "re-cognize" it. In the end, both approaches produce the same result: theory within the model is either confirmed or adjusted.
(B) If analysis can not find a match, the work is a true monster, and the purple box where it was spawned belongs to another, independent model, whose theory contains p. Rather than saving (i.e., confirming/adjusting) the theory-basis for the old model, M1, this procedure discovers a theory-basis for a new, autonomous model, M2. The work that is a monster to M1 is a normal work with respect to the discovered model M2.
NB: M2 does not supersede M1. Discovery of a new model does not imply replacing the old one since the independent library tenaciously retains all M1 works as well as M2 works. To avoid further confusion, the library must now expand to three rooms – M1 works, M2 works, and works of unknown origin.Both (A) and (B) are clearly music-analytic versions of what is commonly known as "reverse engineering," so we'll call this type of analysis that goes outside the model reverse composition. Reverse composition either re-derives previous theory – possibly in a new guise (version (A)), or discovers new theory (version (B)). This characteristic theory-discovery process (for both (A) and (B)) looks something like this (Diagram 3):
The engineering and music versions are alike in significant ways that suggest this is not simply an analogy or metaphor. First, they both begin with a known, accessible human-made work whose path from theory through techne has either been lost or hidden or purposely obliterated or was never recorded or even fully understood by techne. They are also alike in that their goal is to determine a path (not necessarily the path) that may or may not be identical to the original path but that can nevertheless ideally compose an identical or acceptably similar work or portion of that work. In both, the discovered path to the object is not necessarily the original one. Knowledge of the path to an object is never complete enough to reproduce all the decisions made by techne leading to the original work.
The schemata for M1 and M2 are the same, even though their respective contents (their core theories at the very least) are mutually independent and possibly incompatible. The discovered model, M2 (Diagram 4), can now be treated as an independent solitary model just as M1 was in the previous post, with analysis' job reverting to the confirmation and adjustment of M2's theory when/if it draws an M2-compatible work from the library's Unknowns collection.
But there is no guarantee that there is no work in the library that is not a monster with respect to both M1 and M2 resulting in the discovery of M3. Then, likewise, M4. And on and on.
In principle, there is no end to the discovery of possible models.
There is no reason to believe we will not be surprised again and again by the appearance of new monsters and their models.
Defining a music theory pluriverse
Here are some preliminary observations and conjectures regarding a pluriverse (possible models) approach to music theory.
- (1) Many possible music theory models exist – they are just as real as any current model.
This is a version of "modal realism" with respect to models. Positing that possible models are real implies that techne or analysis discovers an existing model rather than creating one. Theory offers, suggests or commands but is powerless outside its own model; theory is incapable of discovering anything.
- (2) Any possible model is the same kind of thing as any other possible model – i.e., all music theory models share the same schema.
The archetypal structure (schema) of any possible model looks exactly like the model posited in Diagram 4: the same three fundamental conceptual roles are present in the same internal relationship for every possible model, sc., a model-defining theory, a generative techne, and a critical analysis.
- (3) Possible models are independent which means the content of any one model differs in at least one aspect from the content of any other model; if there is no difference in content, they are the same model.
While this says possible models are distinct, it also implies models may overlap; e.g., theory in one model may contain proposition p while theory in another model contains not-p, but all other propositions in the two theories are the same. This suggests a way to define categories of models leading to a taxonomy of music theories.
- (4) The works library is built from the "output" from all possible models and does not properly belong to – or prefer – any one model to the exclusion of others.
Works are shared "public" objects available not only to music theory models, but to other kinds of possible music worlds as well (e.g., the class of possible music perception models).
- (5) Possible models may be compared, but one model cannot be evaluated (value-judged) in terms of another.
However: works, having been "released" from their model(s), may be compared and value-judged, fairly or not, based on criteria from other kinds of possible worlds (e.g., the class of possible music perception models, possible political models, historical models, cultural models, etc.)
This completes my thread on "music theory today." It is not intended to provide the right path (which I believe reasonable people know does not exist), but to lay out a very general plan for a future garden of forking paths.
I plan to return to this topic occasionally under the title "Notes from the pluriverse."
 Jumping from my exploratory fantasy (the abstract model world) to the real world for a moment: there are an increasing number and variety of analyses of "post-tonal works" that continue to fall out of the great tonal/post-tonal bifurcation, but these do not cohere into a descriptive account. (And by "cohere" I do not mean to imply the absurd idea of a single musical theory of everything.) I know of no attempt as yet to deal comprehensively (i.e., beyond ad hoc treatments) with the reality that nearly everyone seems to admit is not about to go away.
 David Lewis. On the Plurality of Worlds (Malden, MA : Blackwell, 1986), p. 2. As I implied, I am not going to "accept" Lewis' radical position but, as with Michael Thompson's theory, I will attempt to mine it as best I can for ideas that appear to be a "fit" for music.
 (Music theory today is stuck on the currently popular distinction made between "tonal" and "post-tonal" theories. This unfortunate bifurcation appears to have arisen in part as an attempt to improve on the term "atonal." But it has mostly caught on due to its pedagogical utility. In undergraduate music curricula, traditional "tonal" theory is unquestioningly required in all cases. "Post-tonal" theory – a potpourri of ideas about an increasingly large body of works that have in common only their inability (or mulish refusal) to fold into the comparatively well understood orbit of "tonal" works – is at best an elective or add-on. It is difficult to deny that this effectively ghettoizes all musics and their associated theories that lie outside the bounds of common practice "tonality" and its contemporary extensions to pop and jazz.)
 Thompson. Rubbish Theory, p.147-8.
 Jeffrey Scargle, NASA Ames Research Center, Moffett Field, CA, on the central dilemma of searches for extraterrestrial life (In New Scientist, December 13, 2014, p.41)
 Again, the concept of possible models introduced here is not necessarily intended in any of the senses that the various concepts of a possible world are used in philosophy and logic. However, to develop the idea of possible models with respect to music theory today, it is helpful to adapt some concepts from David Lewis' On the Plurality of Worlds just as some of the ideas in Michael Thompson's Rubbish Theory are being adapted for the discussion here. I have borrowed shamelessly (but not always obviously) from both these sources throughout this exposition. All mistakes, misunderstandings and inappropriately applied concepts from these works are mine alone.