Wednesday, January 14, 2015

Notes from the Pluriverse {2–6}


Why do so few people get the distinction between "rule" and "rule"? One is confining, the other is liberating. There are "laws," and then there are "laws." Some divide, others unite.

Already we behave as if we live in a world that holds only a remnant of what there actually is .... I believe the major cause of this more mental than physical rift lies less in the folly or onesidedness of our societies and educational systems, or in the historical evolution of man into a predominantly urban and industrial creature, a thinking termite, than in the way we have, during these last hundred and fifty years, devalued the kind of experience or knowledge we loosely define as art; and especially in the way we have failed to grasp its deepest difference from science.
– John Fowes, The Tree.
That there are rules is a fact of art. That the rules are immutable is not.


In a 2002 program note[1], I included a summary of that exciting/nightmarish (take your pick) period in Western music (roughly 1890–1920) and referred to it as "The Crisis" (Fragment A below). It was during this remarkable short stretch of time, that the line of European music history finally broke out into three lines of Euro-Anglo-American music history. (It's important to note that I'm using the word "crisis" here not so much in its original sense of the "turning point of a disease," but in the sense of passing through a critical point of no return. Surviving The Crisis, you can still look back and perhaps learn from the past, but any continuity, real or imagined, has been broken: you can't regain either the innocence or the ignorance of the past.[2]) At the same time that The Crisis was working out publicly in concert halls, there was a related crisis in music theory that was at work below the surface, not so much among analytical theorists but primarily among theorist-composers[3] (Fragment B). While remnants can occasionally be found, today the three lines have mostly disappeared, replaced by a riot of musics and their theories: a pluriverse of possibility.

Anyone who claims the crown is a fool.

Fragment A: Praxis
If we ignore most of the fascinating detours, forget the dead ends, remain blind to other cultures or treat them as irrelevant – in a word, if we squint hard enough at European music history – we can just barely draw a straight line that traverses a millennium and a half from the Middle Ages right down to Brahms and Wagner on the verge of the twentieth century. Unfortunately, right at that point, our straight-line project fails completely. American musicologist Charles Seeger put it this way:
Since sometime before the First World War there has been a general realization among both conservatives and radicals that the great romantic tradition of nineteenth-century Europe was in difficulties. It had become encrusted with so many bypaths that some sort of revision seemed inevitable, either to set it upon its feet again or to form from its honored remains a new style.[4]
Seeger’s student and friend, composer Henry Cowell, was not as circumspect, leaving much less room for a comfortable conservative outcome:
Let us, however, meet the question of what would result if we were frankly to shift the centre of musical gravity from consonance, on the edge of which it has long been poised, to seeming dissonance, on the edge of which it now rests.[5]
Indisputably, Schoenberg and Stravinsky at this point were at the heart of the crisis in Europe; more importantly, a musical revolution that officially began in Europe was now heavily “in the air” on both sides of the Atlantic. Seeger capsulized the beginnings with due credit to Europe and then summarized what came next with a single word:
Certainly a revolution began, but a gradual one – perhaps a series of small revolutions: first Satie, Debussy, Strauss; second Scriabin, Schönberg, and Stravinsky; then the deluge.[4]
After the “exquisite elaborations” [Seeger's words] of the nineteenth century with figures such as Debussy and Strauss, the line of history forked into three main branches. The traditionalist branch attempted to set European music “upon its feet again,” stretching the use of the old material by insisting that it wasn’t yet exhausted. As critic and scholar Eric Blom noted, FaurĂ©, Elgar, Vaughan Williams, and Sibelius remained “fundamentally loyal to their key signatures.” The other two branches, setting off in radically new directions and causing riots in the concert halls, were the “atonal” branch – centered in Vienna and identified with Arnold Schoenberg – and the “neo-classical” branch centered in Paris and headed by Igor Stravinsky.
Fragment B: Theoria
In 1985, Schoenberg scholar Severine Neff was visiting her friend, composer Otto Leuning, then 87, in his New York apartment. While helping him sort through his papers, Neff spotted an unfamiliar journal called The Monist published in Chicago in 1917. When she picked it up it fell open to an article entitled "Our Musical Idiom" by Ernst Bacon [see also prior E&EN entries on Bacon]. Among other things, the article included what appeared to be a complete list of all the chords possible in the twelve-tone chromatic scale. But the year––1917––was all wrong. Prior to Neff's discovery, 1960 [Howard Hanson's Harmonic Materials of Modern Music] was the date generally associated with the first publication of such a list. As Neff later wrote,
Five years before the debut of twelve-tone music and over thirty years before proliferation  of mathematically based theories of non-tonal music, Bacon was working on order permutation, invariance, and symmetrical inversion of non-tonal music.[6]


A note on post-tonal voice leading. There is a vast area ripe for research re note {4} which I will not even try to pursue in the detail it deserves. Both Bacon and Luening were greatly influenced by Bernhard Ziehn's theories. Busoni called Ziehn "Die 'Gotiker' von Chicago," and was inspired by him to take up the study of counterpoint once again. John Alden Carpenter studied with him also. In Howard Pollock's bio of Carpenter, there is this intriguing passage:
Carpenter wrote hundreds of harmonic and contrapuntal exercises under Ziehn. Most of the harmonic exercises involved short progressions; starting from a given triad or seventh chord, he would quickly move to some distant triad via passing tones, a whole-tone bass, or some other designated way. Some of the results sounded like Wagner or Franck, some like Reger or Busoni, some like modern jazz, and some like nothing recognizable.
There is a growing literature on Ziehn, but Neoriemannians looking for some new connections during this stormy period (I believe Ziehn was not too keen on Riemann's work, but that's irrelevant) might start by looking at his 1911 Five and Six Part Harmonies with reference to the above passage quoted from Pollock.


Harmonices Mundi Mod XII


[1] The "program note" was an extended essay titled "Toward an American Music" included in a season (2002-3) booklet celebrating the forty-year residency of the Juilliard String Quartet at the Library of Congress (also the end of JSQ's residency at LC –– but that's another story). I chewed off way more than I could manage in anything less than a book. I said nothing in the essay I would retract even today, but overall the essay doesn't make the points I had hoped to make.
[2] There must have been a sense of fear and loathing for many people during this key period –– a fear and loathing that appears to survive to this day in some composers, performers, audiences, and musicologists. The Online Etymology Dictionary humorously notes that a German term for "mid-life crisis" is Torschlusspanik, literally "door-shut-panic," fear of being on the wrong side of a closing door.)
[3] Previous posts are predicated on my contention that some analytical theorists may be composers, but all composers are theorists.
[4][5] I have lost the exact citations for these quotes, but as I recall, the two Charles Seeger quotes are from Studies in Musicology II, 1929-1979 (ed. & intro. Ann M. Pescatello. Berkeley, UCal Press, c1994) & the Henry Cowell quote is from his New Musical Resources (orig. pub. 1930, but I probably used the 1969 repub. [NY], Something Else Press)
[6] Severine Neff. "An American Precursor of Nontonal Theory: Ernst Bacon (1900–1990)." Current Musicology 48: 5-26.

Monday, January 12, 2015

Notes from the Pluriverse {1}



It was around 6:30 in the morning on July 18, 1997. This is one of those dates that I can pinpoint, not because I remember the exact date (I have a lousy memory for facts), but because it was the first day of the second Buffalo Music Theory Symposium – the dates are easily found on the web. I was there to present a paper on an unlikely topic, "The Z-Relation in Neo-Riemannian Transformations."

I didn't really know why I was there. In the first place, I had (and have) no qualifications that would put me in the company of the small and highly distinguished group of scholars invited to attend, and I had no expectation that what I had to offer would be of any interest to anyone there. In the second place, I have a phobia involving euphemistically named "conferences" where you suddenly realize you've been trapped inside someone else's fable.

I feel I can now admit that more than once I have fled a conference presentation on a topic of interest to me and rushed back to the sanctuary of my hotel room with a Snicker Bar and a Coke to watch The Price Is Right or Jerry Springer.

Milton Babbitt may have had a touch of this phobia as well. I was once told, by the organizer of a smallish invitation-only conference, that when the first scheduled meeting was ready to begin, Milton was nowhere to be seen. They waited for a while, then the organizer called his room. Rather annoyed, Milton said to go ahead and start without him – he would be there as soon as the game he was watching was over. Well, maybe this wasn't my phobia, just a matter of Milton's priorities. In either case, the organizer who told me the story didn't seem to appreciate the humor and was obviously inviting me to share in his indignation. But I digress.

The Buffalo conference was to turn out to be one of those rare meetings out of the admittedly few I have attended that lives up to the name "conference" (thanks to the synectic mix of participants & John Clough's sensitive planning ear). My mounting anxiety was to prove unfounded. Still, when I walked in to the hotel restaurant for breakfast the first morning, I was relieved to find no one else there yet. I just wanted to sit alone, eat my breakfast, and gather my thoughts while pretending to read my free copy of USA Today. I had just taken my first sip of coffee when a voice said, "May I join you?" I looked up to see David Lewin.

Although we had corresponded, I had never really had a private conversation with David before that – only small talk at a conference dinner once. I can't say exactly that he grilled me, but he was curious and managed to get me to tell him about some of my adventures as a closet theorist (defined as a non-academic theorist who knows enough to keep his mouth shut when visiting the academy). Then came a question no one had asked me before.

"Steve, do you compose?"
Big G.P. while I chewed on a bite of toast.
"Well, no, I don't ... I mean, not much any more. ... I used to. I used to try. ... There was a. ... It's not so easy with a 9-to-5 job. ... I just can't find the time. ... It's different than ...."

He interrupted, quietly, almost conspiratorially:

"You should make the time."

No one had ever before gotten to my well-guarded core.

Others began to straggle in and join us, and then we were all shuttled off to Buffalo (U) for the day.

I had breakfast alone with David the next morning as well. Evidently we were the only two early risers in the lot. Over the few years left we never talked about "a composing life" again. So I never got the chance to ask the same question back at him – to get at the core that I now realized we shared – more importantly, to get at how he got over the wall of that amazingly beautiful cloister he had built and into the more dangerous exoteric world of personal expression. It was much later, after his death, that I got an answer of sorts.

As I looked through his relatively sparse collection of compositions and noted the large gaps between their dates I realized that David's advice to me was advice he must have repeated again and again to himself. He wanted it all, but even he just couldn't find the time.

There is a Moses and Aaron tragedy that's played out by all those who seriously struggle through their art. The field for that struggle is what I've tried to describe quasi-metaphorically in the tri-partite model. I now confess my inspiration for that entire fantasy came from David Lewin. The following is from a letter David wrote to Oliver Neighbour that is now part of the David Lewin Collection at the Library of Congress.
Your overriding interest is in the man [Schoenberg] and his music.  Mine is too, when I have my analysis hat on.  That is when I make Dr. Jekyll type statements, from your point of view.  But I have at least two other hats which I wear on occasion, which is when I say those narsty things.  One I would call my Theory hat.  When you get around to Lewin/Cone [“Behind the Beyond: A Response to Edward T. Cone,” PNM 7:2 (Spring-Summer, 1969), pp.59-69], you’ll see what I mean by distinguishing this from my Analysis one.  You probably will not agree with me that it is possible (much less desirable) to distinguish the hats conceptually.  On that issue, you would be on Ed’s side and not mine.  Incidentally, I have a great deal of respect for EC also; among other things, I took several courses from him with great profit at P’ton (or, as we used to call it, the Six and Twelve Store).  Then I have still another bonnet which, however, I don’t wear in print: my Composer hat.  With that hat on, my interest in either AS or serialism is as completely self-serving as my interest in Mozart or tonality … more so as regards tonality in any case.  Baldly, what interests me then is “what’s in it for me to use.”  From that point of view, my tendency is also to try to separate “the system,” to the extent I can, from AS’s personal musical profile; I am interested in using “the system” as a matter of public domain, so to speak, but of course not interested in writing watered-down pastiches of  Schoenberg’s personal discourse.  And of course, in between “the system” and AS’s personal manner lies a large area which one could classify as the “usual” sorts of technical things a composer can learn by studying the work of a great composer of another generation.  This area contains such things as control of rate-of-change that you cite (here one can learn much from Mozart also, and beyond that, from concurrent study of both composers).  And this area merges fuzzily. For me, into “the system” at one extreme and personal manner at the other.  Now one of these fuzzy boundaries exists for any composer: the one between craft and personal manner.  It seems to me that what we are arguing, in this context, is whether or not there is also a fuzzy boundary at the other end, between craft and “method” (to vary the terminology) in Schoenberg’s case.  I am claiming that there is such, and you are claiming there isn’t (more or less, when all the endless qualifications are made).  A lot of the reason I am prepared to maintain and defend that position, personally, has to do with my intuition as a composer.  That is, I feel that I can use “the method” as a vehicle for my own expression, to a considerable extent without feeling bound not only by Schbg’s personal manner, but more significantly by his general “style,” the latter involving predilections for certain kinds of musical situations, and certain ways of treating and working out their musical implications.  I don’t pretend to Olympian stature as a composer, but I’m very sure that every composer who has ever written twelve-tone music has experienced a similar feeling, if he is worth his salt as a self-respecting artist, of whatever rank.  (At least until recently, when it has become possible and even fashionable to write serial music without having heard any of Schbg’s music … or any music at all, for that matter.)  I’m sure Webern felt this, and I’m sure Berg did too, though he probably would never have dared admit it to himself.  It’s more than obvious that Stravinsky felt it.  Were/are we all just kidding ourselves?  Very possibly, it may be that all “the method” amounts to is a certain means by which obscure electrical circuits in the brains, or endocrine secretions in the blood, of many composers at a certain period in history have been stimulated, in such a way as to inspire creative results when the composers play the appropriate mental games.  I’m not being completely sarcastic about this, I think there is probably at least a grain of truth in it, and possibly a good deal more.  I would however, argue that even to the extent composers have been and are fooling themselves, in considering that they can use “the method” without being bound by Schoenberg’s “style” (as above), the illusion was/is artistically necessary, in order to accomplish anything; and it has turned out to be quite productive.  And then, to what extent can one distinguish a tenet which is necessary and productive for artists, from one which is artistically “true”?
February 26, 1974

Sunday, January 4, 2015

Desperately Seeking Relevance: Music Theory Today [6.3]

Rubbish Theory
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.

Wittgenstein. Tractatus Logico-Philosophicus[5.511 & 6.35] (Ogden Translation)

3. The Monster Problem
[Previous Post: 2. Maverick Integration]

The choice

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."[1]
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[2], 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.[3]
The one-or-many question is precisely where music theory is poised today[4] – and with it, music itself.

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 ....[5] 

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?

Diagram 1

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.[6]

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.

Diagram 2

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.
NBM2 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):

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.

Diagram 4

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.[6]
  • (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."

            [1] Hans Hellsten, "Brief Reflections on the Organ Art, The Glass Bead Game, and Bengt Hambraeus." (In Crosscurrents and Counterpoints: Offerings in Honor of Bengt Hambraeus at 70, ed. Per F. Broman, Nora A. Engebretson and Bo Alphonse, p.35-38). Hellsten quotes a line near the beginning of Hermann Hesse's The Glass Bead Game. (I assume anyone reading this blog entry knows The Glass Bead Game, which ought to be required reading prior to beginning any undergraduate music curriculum.) 
            [2] 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.
            [3] 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.
            [4] (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.) 
            [4] Thompson. Rubbish Theory, p.147-8.
            [5] 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)
            [6] 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.