MathJax

Wednesday, January 14, 2015

Notes from the Pluriverse {2–6}


{2}

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.



{3}
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.



{4}

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, Fauré, 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]

{5}

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.



{6}

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}

{1}

THREE HATS

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]


A.
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.




B.
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.



C.
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.







            Thursday, November 20, 2014

            Desperately Seeking Relevance: Music Theory Today (6.2)

            Rubbish Theory
            and Music Theory Today

            2. Maverick Integration
            [Previous Post: 1. Tripping over Rubbish]


            There are many ways to jump into this. The most direct way is to replace music-theory-today's presumed equal sign with a question mark and start from scratch.

            Diagram 1


            Preliminarily, analysis is how theory probes the real world. As much as theory needs analysis if it wishes to stay grounded, analysis needs theory or it is nonsense. Without theory, analysis is at best a collection of disconnected hunches. The moment a connection appears, we know that theory is lurking in the background.

            Theory with no view to application is similarly sense-less. (Nevertheless, theory can develop in the abstract, and this is often desirable and even necessary when navigating possibility's garden of forking paths. But for now, put this garden out of your mind. For the present, while it lasts, there is only certainty's garden path.)

            Theory applied yields a necessary ground for analysis; each analysis provides theory with a confirmation. Each confirmation strengthens our confidence in theory as it edges toward "truth," i.e., appears incontestable. (Diagram 2.)

            Diagram 2

            If we leave it here, we're stuck in a loop: apply–confirm–repeat. We have yet to ask: Just what is it that analysis analyzes? The theory–analysis transaction (Diagram 2) assumes a supply of motivating objects or artifacts we call musical works. Think of this supply as a library of objects available for analysis to draw from to perform its theory-mandated analytical operations. (Diagram 3.) This draw can be made in one of two ways, either randomly or selectively.

            Diagram 3


            If the draw is selective, it can bias in favor of the theory, i.e., analysis is free to select just those works (or portions of works) that confirm the theory (cf. "procrustean intonations"). This is always tempting, but it's cheating. We assume no user of the model would want analysis to cheat.

            But a work randomly drawn (analysis is blindfolded for the draw) might not confirm the theory. In that case analysis looks for ways to "save the theory" by suggesting adjustments to theory in order to accommodate the new information supplied by the maverick work. The theory is not replaced – it is effectively the same theory[*] corrected, improved, expanded, with essential core invariants remaining untouched. Now on future draws the model can handle similar works previously considered as mavericks.
            [*] In the present context, two theories are the "same" in the sense that they are both versions of one abstract theory defined by a core set of invariant features (propositions, rules, objects, patterns, etc.) "Core feature" is left undefined at this point. Some may think of it as common sense, others a consensus of experts, others a structural sine qua non, still others audience expectation, cultural norm, etc. The important thing is that, were theory's core to be breached, either it would morph into something unrecognizable or unpalatable, or it would collapse entirely taking its model down with it (see previous comments on Euclidean"axioms").

            This is evolutionary adaptation. Theory has built-in room to grow. A constant supply of works chosen randomly fuels (challenges) the analytical pump which in turn confirms or improves or corrects the theory which then allows analysis to encompass a wider, more varied selection of works. While the model in Diagram 2 represents a homeostatic system, the model in Diagram 3, simply by including the adjustment function, represents a homeorhetic[1] system.

            Note posted at the library's circulation desk: The works library is a public lending library. After a work is removed and analyzed it must be returned to the library. No exceptions.

            Continuing to work backward, the next question emerges: Where do all those works come from? This consideration might appear to be redundant for the model. We sense that adding unnecessary weight is asking for trouble, and, as we shall see, adding a third role does add a big dose of complexity and discomfort. It would be easier  to stop here. Using a wave-of-the-hand strategy, we could call the question an irrelevant nuisance. But relevance is the game we've decided to play. We cannot not look. So....

            If we add a composition (synthesis, assembly) arrow to those arrows labelled application, confirmation and adjustment, we still have to decide on composition's source and that source's relationship to the model. Composition commonly implies a composer[2], but the model encourages us to continue to focus on function and process over flesh and blood actors such as theorist and analyst. This suggests that the work source in the model ought to focus on the more technical craft of composition rather than how the craft is employed or who employs it or what the employer's motives might be. Drawing on a venerable tradition, let's call the source of any work techne.[3] (Diagram 4.)

            Diagram 4


            Tracing back from theory-analysis through the work and then to techne suggests the next obvious question: What is the source of techne?

            Within the confines of the model, techne has only one real option for a source: theory. This is represented by the arrows and overlapping green box in Diagram 5.

            Diagram 5

            Theory might be "informed" by techne directly, short-circuiting the work→analysis→theory chain by going right to the work's source for confirmation and adjustment. This would suggest that techne in turn might apply theory as its source of acceptable patterns and objects – an authority/guide to be followed in order to compose a work that stays within the status quo and maintains the consistency of the model. 

            So techne might draw from theory in ways roughly parallel to the two possible ways analysis draws from the works library, but with reverse effects. On the one hand, techne might slavishly accept everything in theory's list of objects and patterns – somewhat akin to analyzing anything a random draw proffers. Or techne might pick just those items in theory's list that are "relevant" to its work-in-progress and ignore or reconfigure the rest in ways that still leave theory's core untouched – acceptable variation somewhat akin to a biased analytical draw. 

            This possibility, despite a circumscribed freedom of choice given to both analysis and techne within their domains, envisions theory as a Janus-faced overlord within the model, one face governing analysis, the other governing techne. In principle, any time analysis comes across a maverick work, it would no longer be a mystery where the maverick came from – only a puzzle whose solution lies within the model. Either techne misunderstood or unintentionally misused theory (a mistake), or theory in its navel-gazing abstract mode ("speculative theory") spontaneously expanded within its self-imposed bounds of internal consistency and directly encouraged techne to choose freely from the new menu of possibilities provided by this expansion.

            Strangely though, closing the circuit – staying within the confines of the model – implies that theory and techne aren't really compelled to talk to one another directly at all (which can be helpful when they're separated by three centuries). Certainly techne can "read" theory directly, but a lecture from theory – especially one that does no more than rehearse techne's own past – is hardly conducive to discovering new procedural approaches. (For some reason, techne is averse to running in ruts.) For its part, theory can always get at techne the long way around via analysis of techne's works. (For some reason, theory finds analysis' company more amenable.) Similarly, given that techne stays within the model, there is no need for a direct path between techne and analysis. That particular transaction – if it is ever necessary at all – is adequately mediated by theory.

            In another world we might expect to find a triangular model with three co-dependent and interacting roles. In music theory today the model more closely resembles the interaction between two pairs of roles that share one of those roles. Let's now separate those pairs to see if this is really the case.

            With time (four or five centuries ought to be more than enough), theory reasonably comes to assume that it can always count on a relatively well-behaved techne to express itself within theory's rules or helpfully expand those rules via the enrichments of "clarifying violations"[4] which will sooner or later be caught by analysis as they appear in maverick works whence, it is assumed, these violations can be folded back into the model. Theory, again quite reasonably, comes to assume that its model is the only model: there are no other models that techne can escape to – indeed, why should techne even want to escape a benevolent dictator? And even if techne is unhappy with its prospects within a fully mature model, there are no other options. Resistance is futile.

            Theory now feels safe in ignoring techne altogether because it can get all its developmental needs from the work via analysis, with no particular need to know anything more than it already does concerning the work's source. At this stage, the works library has become huge, and it continues to grow in quantity if not in quality. Analysis detects no more mavericks. The overstuffed library now appears to consist almost entirely of centuries of artifacts that conform to a maximally expanded theory that can take no more adjustments if it is to maintain an intact core (i.e., if it is to be itself). Obviation of the need for analysis' adjustment function means the model has effectively collapsed back into its archetype (Diagram 3 above minus the adjustment function).[5] Apply–confirm–repeat. There are plenty of artifacts to go around to support a homeostatic model without techne having to produce any more of them. This has made life easier for analysis whose only task now is to confirm the theory. In the now vanishing possibility that analysis comes across a stray nonconforming work, analysis will simply reject it as a monster.[6]

            Diagram 6


            Diagram 6 shows the situation. Rather than overlapping pairs we see one pair and a detached singleton. Techne – know-how – is now unemployed – or, to be accurate, can find no meaningful employment beyond music's version of a fast-food chain, which is to say that techne can continue to produce as many model-conforming works as it likes. New-to-my-generation is fine and may get a pat on the head from theory, but new-to-the-world is no longer in the cards for the model or, evidently, for the library it has created. A submissive techne can only look back nostalgically at the days when it was able to produce those reinvigorating mavericks – when it was relevant to the model.

            Knowledge (knowing-that) is now encapsulated in the perfectly self-contained, teachable red box. Pedagogically at least, theory and analysis can go on forever, perennially renewed as succeeding generations are presented with the same library of new-to-them works to learn from. New-to-my-generation requires no more than a good curator to pull off the illusion of newness. And if perchance theory, in its navel-gazing mode,  comes up with a new "approach" to some of the artifacts in the library, verification of that approach means no more than instructing analysis to do a "search of the literature."

            The model is perfected.
            The world is one.

            Ite, missa est?





            ___________________________
            [1] Homeorhesis: "The condition of a flow process which remains canalized within limits in a growing system. ... [A homeorhetic] system turns homeostatic (i.e., acquires dynamic stability) when it reaches its full development, in accordance with its archetype[!]" More at the on-line Encyclopedia of Systems and Cybernetics.
            [2] Since music is a performing art, a work may also be construed as a performance-of-a-work, and so a performer may be construed as a composer. This identification, which is my own position, still raises practical issues that remain open for discussion and development. Whichever position one takes on this would not significantly change the model; but such a discussion here would obscure the issue at hand by taking us off into a maze of sidebars.
            [3] Other candidates in naming this role are the more highfalutin poiesis and synthesis. My preference for techné comes from a desire to maintain the earthbound "workshop" essence of the model which is intended to emphasize the toolbox nature of theory and the tool-use nature of techne. Both art and kitsch emerge from tool-users whose activities are circumscribed by the tools available within the model. Also, identifying the work's source within the model as techne has the added advantage of interpreting the model as yet another variation on the old philosophy–etymology game played between genesis (doing, making, craft, techné) and knowledge (theory-analysis, epistémé). Knowing-how vs. Knowing-that.
            [4] The phrase is Charles Wuorinen's ("Toward Good Vibrations" originally pub. in Prose, reprinted in Elliott Schwartz' Electronic Music; a listener's guide, p. 257). While Wuorinen was making a point about the contribution of interpretation in the composer→score→performer context ("clarifying violations of the text"), I find it also neatly summarizes techne's contribution to enriching the closed normative model presented here.
            [5] "Growth of a system is normally homeorhetic, because it is the only way to maintain its identity[!] The system turns homeostatic (i.e., acquires dynamic stability) when it reaches its full development, in accordance with its archetype." (Encyclopedia of Systems and Cybernetics)
            [6] "Monster" is Thompson's word for such a reject. It is particularly appropriate in our present discussion given it's etymology. In the 14th century "monster" was associated with any creature afflicted with a birth [read "compositional"] defect. As the discussion proceeds it is important to keep in mind that such a work rejected by analysis as irredeemably nonconforming was nevertheless conceived in the womb of techne. The monster's story will be told in the next post.

            Tuesday, October 14, 2014

            Desperately Seeking Relevance: Music Theory Today [6.1]


            Rubbish Theory
            and Music Theory Today

            What is it to supply a theory? It is to offer an intelligible, systematic, conceptual pattern for the observed data. The value of this pattern lies in its capacity to unite phenomena which, without the theory, are either surprising, anomalous, or wholly unnoticed. [my italics]
            Norwood Russell Hanson, Patterns of Discovery 


            1. Tripping over Rubbish

            I was on my way out of a used book store when I spotted a spine title that made me stop. I pulled the book off the shelf and began to thumb through Rubbish Theory: The Creation and Destruction of Value [1] by Michael Thompson. I had never heard of the book or the author before. It had a lengthy section on catastrophe theory and a foreword by E.C. Zeeman. The used book price of $9.50 seemed a bit steep, but how could I resist having the title Rubbish Theory on my book shelf?

            The little gray book I purchased was the 1979 first edition – actually, it remains the only edition as far as I know. Thirty years later, I still have the book. Unknown to me at the time I purchased it, the book had created somewhat of a stir among anthropologists and economists when it came out. The reviews were mixed. It clearly rattled some cages. In some cages it went unnoticed.[2] Google Scholar currently lists over 650 citations for the book. It's now a collector's item with prices varying between $250 and $500. But even if I wanted to sell it, which I don't, I could never get near those prices. The reason? The used book I bought in nearly pristine condition (a discard from the "Army Library"(?) that appeared to have never been checked out) now has my pencil and ink scribbles on half the pages. Another book ruined by my overwrought conversations and arguments with the author.

            Despite all those cites, I'm not certain of the status of either the book or its author within the social sciences at this point (I've only taken the time to check out a relatively small sample of the citing articles). Still, it has become clear to me that Thompson's work was among the first in cultural anthropology to recognize rubbish as an indispensable object category in the study of "the creation and destruction of value." Curiously, as I write this, neither Rubbish Theory nor Michael Thompson have an entry in Wikipedia, the final word on stuff to be taken seriously. The book's lack of an entry in Wikipedia (making it invisible to the bulk of on-line humanity) coupled with its increasing market value and citation history (suggesting it has a persisting value to collectors and scholars) is an ironic demonstration of Thompson's central thesis.

            In this final relevance-thread entry (due to length I've broken it into two three parts) I'm not going to attempt to "apply" Thompson's rubbish theory directly to music theory today. Rather (in part 2) I am going to steal some of Thompson's ideas and adapt them into a meta-theoretic model to help focus on some significant blind spots in music theory and the wider field of musicology. My intention is to lay the foundation for an actual discussion/debate, or at the very least, to demonstrate the need for a serious reexamination of the discipline. In today's climate, I doubt any of that will happen, and my essay will be no more than a passing curiosity at best.
            .    .    .    .    .

            Here is what rubbish theory is all about.

            On page 9 Thompson gives an introductory summary:
            [The two overt categories,] the durable and the transient, do not exhaust the universe of objects. There are some objects (those of zero and unchanging value) which do not fall into either of these two categories and these constitute a third covert category: rubbish.
                  My hypothesis is that this covert rubbish category is not subject to the control mechanism (which is concerned primarily with the overt part of this system, the valuable and socially significant objects) and so is able to provide a path for the seemingly impossible transfer of an object from transience to durability. What I believe happens is that a transient object gradually declining in value and in expected life-span may slide across into rubbish. In an ideal world, free of nature's negative attitude, an object would reach zero value and zero expected life-span at the same instant, and then, like Mark Twain's 'one hoss shay', disappear into dust. But, in reality, it usually does not do this; it just continues to exist in a timeless and valueless limbo where at some later date (if it has not by that time turned, or even made, into dust) it has the chance of being discovered.
            He then gives a diagram that represents a first approximation of his theory:


            Thompson contends that these arrows represent the only allowable transfers between the three categories –– no left-pointing arrows are valid, and no transfers between transient and durable can occur directly. At creation, objects start out in the transient category where, at varying rates of decay, they begin to lose value until they fall into the rubbish category. Here they not only have no value, they are so worthless as to be invisible.  Any rubbish object will remain at zero value (invisible) theoretically forever unless it is "discovered" (made visible) in which case it pops into the durable, value-increasing category where it remains (theoretically forever).

            In a 2003 article, John Frow gives a helpful summary from a different vantage point:
            Rubbish is a zero-degree of value; and as such it's either the invisible limit point of social value, or it's something we actively conspire not to see. It is thus in an asymmetrical relation to the two major categories of value, which Thompson calls the transient (this is the normal state of things: a state of decreasing value) and the durable (an exceptional state in which objects have permanent and increasing value). Consumer goods are the paradigm case of the former, works of art, perhaps, of the latter.
            ... [T]he corollary to this view of function as a matter of use rather than an entelechy of intrinsic properties of the object is that objects are likely, in a complex world, to have a number of actual or potential overlapping uses. No single game exhausts their function; no single description exhausts the uses to which their properties might appropriately or inappropriately lend themselves. Indeed, objects don't simply occupy a realm of objecthood over against the human: they translate human interests, carry and transform desires and strategies.[3] [my underlines]

            Before noting all the problems that immediately come to mind, and trashing the theory before it's fully unwrapped, the reader should note that the summary just given is a "naive" first-approximation which works quite well in ideal applications, especially for physical objects traded on the market. It's beyond these applications (where the theory at first might seem to fail) that it provides an expanding analytical framework for less tractable examples.  Thompson takes most of the rest of the book exploring many theory-related complications, explanations, caveats, and implications.

            When I first began to read this book 30 years ago, I started out being mildly amused and slightly bored. I have no abiding interest in snot (yes, you read that correctly) or Stevengraphs. But about 50 pages in, when he started talking about the Knockers-Through vs. the Ron-and-Cliffs, I started to perk up. (Readers wishing to decode the last two sentences will just have to read the book –– sorry.)

            At Chapter 4, "From Things to Ideas," he had me. Metaphors became apparent, and I began to test rubbish theory for its applicability for music. By "applicability" I mean, first, does it conflict with any well-established historical models? It seems to pass this first test. As an obvious example, using what is known about the reception history of J.S. Bach's music from the 18th century to the present, Thompson's model doesn't yield any new facts; but it does provide a complementary interpretive framework to hang those facts from, taking Bach's music from creation as it descended quickly through the transient category down into rubbish where it remained (to general audiences) at the "invisible limit point of social value" for a century –– and then popped into the durable category where its value began to climb to its present value. But does rubbish theory add anything new to acceptable approaches in musicology? Here, it seems to me, comes the big crunch. It's time to leave musicology's –– and music theory's –– comfort zone.

            There are two sides to the "canon" problem. First is the obvious: how does an object get into a "canon"? This is effectively identical to the question and example just discussed of how an object escapes the rubbish heap to become durable. But there is a dark side to selection: to select something we must not select other things. Selection is necessarily biased. Whether it is unintentional or an "active conspiracy not to see" (Frow), the only way to create and maintain a "canon" is by keeping out the majority of candidates according to some written or unwritten rule or constraint. This brings me to this statement at the opening of Thompson's Chapter 7, "Monster Conservation":
            [T]he charm of rubbish theory is that it seems always to lead straight into illogicality, anomaly, and paradox. Regrettably, there are many who find these qualities not so much charming as monstrous, and there 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, and repressive. At its best, it reveals a dubious prettifying intent that leads to the pretence that things are tidier than they really are.
                 Monster exclusion is a distinct, and often dominant, intellectual style. (p. 131)
            . . . .
            [M]onster exclusion can all too easily become monster extermination. Monster extermination can result in the permanent removal of the exceptions to a social theory and, in consequence, monster exterminators are particularly prevalent in the social sciences. The result is that social processes that rely on contradictions for their very existence are almost invariably described by theoretical models of impeccable internal consistency. (p. 133)
            We'll meet "monster extermination" up close and personal in Part 2 Part 3 which will be posted soon.

            I don't particularly look forward to walking the high theory wire from one praxis to another without the aid of a net.  Fortunately, I have such a net handy.  I'll end this part with an observation that indicates rubbish theory is grounded in an intellectual tradition more broadly based than its limiting sphere of application in the social sciences –– a tradition that echoes throughout the entire "cultural sensorium." This net is a general strain of criticism found in the philosophy of culture. It's nicely summarized by the late David L. Hall (my underlining):
            It is essential that one not succumb to the fallacy of completeness in either of its guises––namely, either in the sense that one claims completeness with respect to evidences employed, or in the sense that one requires completeness in the use of evidence. Some degree of specialization is essential. The question is this, however: Has the specialized employment of evidences determined the omission of important areas of experience which may in fact be seasonally relevant in our period of cultural activity? To respond affirmatively to this question involves one in the criticism of the manner in which the inertial character of the past has overdetermined the nature of the cultural present.[4a]
            .  .  .  .
            Strictly systematic theory is more often than not an ideological epiphenomenon functioning apologetically with respect to current modes of practice. Thus theory is practical by definition if one means no more by theoretical endeavor than that systematic, principled form of thinking shaped by the desire for application.[4b]
            .  .  .  .
            [T]he attempt to avoid contradiction leads inevitably to the exclusion of experiences or claims about experience which are consistent with alternative explanations of the way of things that, by virtue of their internal consistency and applicability to the world of experience, have an equal claim to be counted as theory.[4c]
            .    .    .    .    .

            _________________________
            [1] Rubbish Theory : The Creation and Destruction of Value (Oxford UP, 1979) can still be found in many libraries. Those wishing to read a condensed version of Thompson's thesis as an introduction can read a pre-publication article he wrote in 1979 that was recently put on the web.
            [2] Michael J. Kowalski, "The Curatorial Muse" (In Contemporary Aesthetics, vol. 8, 2010) FN 34:
            The ramifications of the complex embedding of the system of aesthetic validation within a broader context of social validation are explored in Michael Thomson's brilliant and unjustly overlooked study, Rubbish Theory: The Creation and Destruction of Value (Oxford University Press, 1979). The fact that Peter Bürger's ponderously agued theories of avant garde literature, which appeared in English five years after the publication of Thompson's essay, should have become a canonic text for art critics, while the deft and humorous argument of Rubbish Theory was largely ignored, says a great deal about North American writers' knee jerk obeisance to Continental theory. I do not exempt myself from the charge.
            [3] John Frow. "Invidious Distinction: Waste, Difference, and Classy Stuff."   (In Culture and Waste: The Creation and Destruction of Value. 2003. Ed. Gay Hawkins and Stephen Muecke).
            [4] David L. Hall. Eros and Irony: A Prelude to Philosophical Anarchism.  (Albany : SUNY, c1982) [a] p. 41, [b] p. 45, [c] p. 46.

            Friday, July 18, 2014

            Desperately Seeking Relevance: Music Theory Today [5]


            Thus while it is commendable for composers to be concerned with the limitations of the senses, it is well to remember that music is directed, not to the senses, but through the senses and to the mind. And it might be well if more serious attention were paid to the capacity, behavior, and abilities of the human mind.
            –Leonard B. Meyer,
            Music, the Arts, and Ideas


            THE UBIQUITOUS TRIAD

            At conception, roughly 500 years ago, the tonal triad – barely defined, almost invisible – was all potential, a gift waiting to be unwrapped.

            Then came history. A lot of history. Today we've arrived at the end of that history.

            Now, the triad-as-we-know-it-today is ubiquitous, fetishized, decoupled, anthropomorphized, overused, tired.

            But most of all ubiquitous. This is the perfect word for it. It's not only that it is present everywhere, having invaded and pervaded the musics of virtually every culture on the planet. It's not only that its sound has captured the ears of most children even before they begin to talk. The concept of "ubiquity" originated as the Lutheran doctrine of the omnipresence of the body of Christ. The triad came to be heard as the omnipresent body of Music in the same mysterious sense. But ultimately came the whispering voice of the eternal devil lurking just outside the door of the Workshop, and of course the less subtle shout from the devil we invented:
            An idea in music consists principally in the relation of tones to one another. But every relationship that has been used too often, no matter how extensively modified, must finally be regarded as exhausted; it ceases to have power to convey a thought worthy of expression.[1]

            What chord is the robot playing, and why?
            (Image from  CS4FN, Queen Mary, University of London)

            As a fundamental compositional object, our triad has had a good run. But today its theory, now capable of speaking only through the many voices of analysis[2], has ossified into dogma. It's time to let it rest. Our composers–––not the gondoliers, but the explorers–––left it behind a century ago to map new coastlines and interiors. Now we all have to let go. But how?

            .    .    .    .    .    .    .

            Specific justifications for asserting the preeminence of the tonal triad, correctly but misleadingly referred to as the triad's multiple "natures," continue to multiply in the academic community. All of these natures/justifications taken together are considered by many analysts to be the basis for a demonstration of the inevitability of the tonal triad as the foundation for "our" music, coincidentally the music most amenable to extended analyses. It's as if there is a belief floating around out there that the more natures that theorists can identify or manufacture, the more solid a case can be made that the triad is a natural object whose status can't be challenged without bringing down the entire world of music. But there does come a day ––– "The lady doth protest too much, methinks." ––– when hollow echoes from that groaning tower of justifications makes us suspect that there's nothing left to justify (if there ever was a need). Except, perhaps, the justifications.

            As we shall see, other sonorities (I will work out just one in the next post to serve as an example) may also have interesting and compositionally suggestive multiple natures –– some natures will be shared with the old workhorse, others will be different. First, to know what we will be looking for and to be able to contrast and compare any new music theory with the established, we need to briefly discuss what I consider to be the closest thing music theory today has to a set of axioms. Of course, that is not precisely what they are (even less are they Euclidean requests!) but they do share the axiomatic sense of being proposition sets–––rules, if you will–––some version of which, however warped, is required for any pitch-based music game. A complete list of quasi-axioms for the tonal triad would be unwieldy, but I believe all of them fall into four basic categories that (unintentionally?) mix facts and claims. Remember, these refer to the triad, not its most compatible matrix, the diatonic system.
            1. Form inducing: The triad's structure invites characteristic compositional procedures and techniques such as "parsimonious" voice leading, modulation, chromaticization through decoupling from the diatonic, and so on.  It's in this category that some of tonal music theory's biggest claims and most bewildering terminological tangles are found. The triad's form inducing properties are arguably a sine qua non for tonal theories from Fux and Rameau through Schenker and Riemann as well as contemporary instructional manuals from Piston and the latest undergraduate harmony text to popular treatments such as those found in any guitar method book and Music Theory for Dummies.
            2. Extensible: The tonal triad is capable of combinatorially generating other harmonic objects such as seventh chords, whether by adding sevenths or sixths, by triad superposition, or by third stacking. There are different opinions as to the correct analysis of the way this generation works, but the end result –– new objects that are harmonically similar to their progenitor –– significantly expands available harmonic material.
            3. Matrix-defining: The triad's "shape" as a second-order maximally even structure connects it logically to the maximally even diatonic (I assume this recommends it based on our human aesthetic preference for symmetry, though I've never heard this argument specifically – only an amazement (which I share) at the triad's "fit" within a nested symmetry.) More importantly, beyond its symmetry and fit within the diatonic and other scales, the repetition of the triad shape at every level creates a defining coherence for the diatonic matrix. 
            4. Aurally preferable (apart from any system or matrix): The major triad appears in nature in the lower partials of the harmonic series. This fact is often cited in conjunction with the questionable notion that, presented with the choice, humans have a physical or psychological preference for "natural" over "synthetic." (Unfortunately, to get at the essential minor triad in the harmonic series requires some intellectual juggling.) Another nature-preference argument comes from noting the relatively smaller (ergo simpler) frequency ratios of the tonal triad's constituent intervals, and relating this to humans' alleged preference (again, presented with the choice) for simple over more complex structures. Finally, there is a claim that a natural preference for the triad's sound per se is internal –– somehow wired into the human brain/psyche. Cognitive science has been enlisted to demonstrate this claim which, if it could be done, would lend credence to the "We all like it" argument, a statistical syllogism that derives first-person plural status from a sufficiently large sample of first-person singular preferences. The unacknowledged underbelly of this attempt to ally with science in order to get to we, is that it can be easily confused with the discredited, but often employed, rhetorical argumentum ad populum with a little ad baculum thrown in for spice. At any rate, any applicable valid science here continues to be surrounded by a lot of big ifs. As far as I know, cognitive science is continuing to tell us that the innate preference feature will be thoroughly understood by next Sunday. So stay tuned if you believe the outcome might justify your personal listening preferences or provide rocks to throw at composers who refuse to comply with nature.
            This list resembles Euclid's axioms at least in the sense that each of the four basic categories (as proposition sets) is independent of the others. In particular (looking ahead), categories 1, 2 and 3 all offer pragmatic techne suggestions and useful game rules for composers of tonal works past and present and are easily seen to have nothing to do with the preference propositions alleged in category 4. The first three can stand untouched whether or not the triad object sounds good to you or me or anybody.

            If this decoupling of sound from procedure is difficult to swallow, try this old philosophers' trick (usually done as an imaginary(?) conversation with the devil).
            Imagine an extraterrestrial visiting Earth who, when encountering chords as simultaneities,  experiences pleasure from those intervals found consecutively in the higher overtones (the higher the overtones, the more pleasant the sensation) and excruciating pain from intervals appearing in the lower partials. Our ET's hearing is so sensitive that she can clearly distinguish overtones well over the Pythagorean comma, creating a harmonic preference that is very odd to us: the higher the partials, the closer consecutive intervals get to unison; so she loves the near-unison, but the perfect octave down at the bottom is almost unbearable to her. On her home planet they also have consonant triads as verticals, but each triad's constituent intervals are so close together we Earthlings can only hear them as a single fuzzy tone. Well, this is unusual, but at least we can relate in that some of our own musicians and theorists have been investigating microtones for a long time, albeit not this radical an upside-down harmony preference. But then it gets really weird. She tells us that their melodies are generally stepwise with occasional leaps for effect and to avoid boredom; except that by "step" she means intervals from the lowest partials and by "leap" she means intervals toward the higher end. To illustrate she takes out something she calls a jPod and plays a recording of an old accompanied folk melody from her planet. To our ears it is a random jumble of sounds jumping all over the acoustic spectrum, but she smiles as it plays. We ask her to please turn it off. Her planet's way of forming "simple," enjoyable harmonic and melodic material is precisely the opposite of ours. We make one more try to understand and ask her to explain how her concepts of melody relate to harmony. She produces what she calls a jPad and we scroll through a document she tells us was written by an ancient philosopher-composer from her world named I. I. Fux simply titled Counterline. At first it makes no sense. Then gradually we realize that if we carefully switch certain words around, step <––> leap, consonant <––> dissonant, and a few more ––– and then if we re-read the teacher-student conversation, leaving the "rules" exactly as they are, just switching a few basic definitions ....... hmmm.... Our mind wanders out of music and into math for some reason ––– we vaguely remember something about duals, dual spaces, dual theorems, switching out points for lines .... hmmmm.  Our reverie is disturbed by an obnoxious sound like the rapid repetiton of the highest and lowest notes on a piano. It's our visitor's jPhone. She says she must return immediately. Her planet's North Polar Cap has declared war on the South Polar Cap again. Some things, beside the laws of physics, are the same across the universe. We ask her to accept a musical gift to remember us by –– an accordion. She politely refuses. We understand, of course, and wish her well. She steps into the old abandoned phone booth and disappears. Down on the ground we see the jPod she must have accidentally dropped. Hmmmmmmm.......




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            [1] Arnold Schoenberg (in Schoenberg, ed. Merle Armitage. 1937. p. 267)
            [2] It is my understanding that "music analysis" conceived as an independent discipline (and today considered as all but synonymous with "music theory") began in earnest only a couple centuries ago. This makes sense since music analysis is dependent on a sufficiently large body of artifacts that somehow managed magically to appear (as well as to be shared and enjoyed) without any independently coherent analytical theory to speak of. It took some time for these artifacts to accumulate before the professional analyst could make an appearance. This answers how (academy oriented) analysis became possible, but fails to address the question of why it was, and still is, considered indispensable. Or often why it's helpful at all. (And a host of other questions.) C.H. Langford, writing about G.E. Moore's "analytical paradox," sums up my own conundrum regarding analysis:
            Let us call what is to be analysed the analysandum, and let us call that which does the analysing the analysands. The analysis then states an appropriate relation  of equivalence between the analysandum and the analysands. And the paradox of analysis is to the effect that, if the verbal [music] expression representing the analysandum has the same meaning as the verbal [graphic, verbal] expression representing the analysands, the analysis states a bare identity and is trivial; but if the two ... expressions do not have the same meaning, the analysis is incorrect. (Langford, "The Notion of Analysis in Moore's Philosophy" in The Philosophy of G.E. Moore, ed. P.A. Schlipp, p.323)
            But the paradox didn't stop Moore from philosophizing. None of this is meant to say that I don't see a place for analytical work to inform theory and composition –– that would be absurd, even to me. If I were asked how I can then even make a distinction, I would be forced to admit that I see theory as the attempt to show how things might be (while knowing that all possible paths will not all be chosen) and analysis as the attempt to show how things are (with no attempt to provide a normative framework for either composer or listener).  Still it's in my nature to rebel against the latter, even (or especially) when I find myself faking that pose in a group portrait.