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But what do we call “music theory”?

I open here a question that appears much needed, not only because it was formally raised by Stephen Soderberg in several postings (https://discuss.societymusictheory.org/discussion/277 ; https://discuss.societymusictheory.org/discussion/279; https://discuss.societymusictheory.org/discussion/275), but also because SMT, after all, is the Society for Music Theory and as such should be aware of what it is about… My hope is that this may turn into a truly general discussion. To this end, I’ll try to avoid biased statements, but not polemic ones — and I hope that reactions will follow.

In a first approach, “music theory” might seem to be that which most of us teach under this name. However, if music theory were only that (or if it were all that), the question would hardly be worth raising. It is because music theory may not (exactly) be what we teach that the question must be raised. We teach both theory and practice, i.e. not only theory itself, but also how it can be put to use in musical practice. A scientific theory, in general, is some kind of hypothesis made about the world; and a musical theory, to me, similarly must be some kind of hypothesis about the musical world, or about specific aspects of it – music theories, in short, are hypotheses about how music works.

The fact is that, when we teach music in practice, we don’t really, or not often question our theoretical assumptions; and rightly so, many of us would think, because otherwise our students would soon get lost. But the risk exists, then, to teach what is but a theory, a hypothesis, as if it were a truth, a certitude. This raises the question of scientificity: a theory, according to Popper, must be "falsifiable" to count as scientific — that is, its formulation must not prevent it being proven false. Are musical theories scientific?

Let’s consider a concrete example, Roman numerals. Am I right to suppose that most of us do use Roman numerals at some point in our teaching, but that fewer of us would consider them a theory? How many of us are aware of the theoretical, i. e. the hypothetical background of such a simple device? The hypotheses involved include, among others, the following:

– Chords are built on a root, they can be inverted without losing their root or their identity.

– The role of chords in tonality is heavily dependent on the root on which they are built, and rather less on their real bass.

– The seven possible roots in the tonal scale produce roughly seven distinct functions, even if these usually are not further defined.

– Some root movements are particularly significant, especially those allowing to build another theory —let's leave it for later—, that of cadences.

Is it reasonable to teach on such bases without stressing that these are but hypotheses, and that alternative theories do exist? Can we reasonably believe that students who might later be confronted with the theories of Rameau, Riemann, Schoenberg, Schenker, and so many others, can be dispensed from realizing that Roman numerals do express a theory? And what if we were later in charge or teaching, say, Renaissance "theory"? We teach music theory, but do we teach music theories? And can we do so without at least some consideration of their history?




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  • 35 Comments sorted by Votes Date Added
  • I'm not going to comment (yet) on the specific issue of defining music theory.  But I would add to Ildar's comment that it may be helpful to move beyond a simplistic Popperian falsificationism (or even Popper's real theories, which are quite a bit more nuanced) in our search for an applicable philosophy of science pertaining to music theory.

    There are of course Thomas Kuhn's critiques of Popper, though some consider them to go too far.  I personally kind of like Imre Lakatos's notion of a research program to describe how science actually functions in practice.  (Despite the fact that many scientists are taught naive falsificationism as a criterion for scientific hypotheses, it's really not a very good description of how actual science works at all.)

    And with something like a Lakatosian "research program" in mind, I think we can begin to see how music theory can fit in.  There are various "research programs" within music theory that have existed or are ongoing (e.g., Schenkerian, set theoretical, etc.), each of which comes with a "hard core" (as Lakatos calls it) of theoretical assumptions.  Researchers working within these areas don't often spend a lot of time questioning this set of "core" assumptions; instead, we work on resolving various details within our program while taking the "core" mostly for granted.  (Thomas Kuhn would perhaps refer to this as "puzzle solving" within the paradigm.)

    Of course, there are plenty of music theorists who do spend more time delving into meta-theoretical problems, which implicitly or explicitly question some of these "hard core" assumptions.  (And I suppose this discussion is supposed to be one of them.)  This may be somewhat different from scientific practice a bit in the size of the fraction of theorists who do this compared to "normal science" (or "normal music theory").

    Or it may be -- as is probably likely -- that some of our research programs have been destablized in recent years due to the pluralism now manifest in both modern approaches to theory and due to the recognition of historical modes of understanding and theory which may differ significantly from a current model (while perhaps being closer to the way the actual composers of historical music may have thought of their own music).

    All I will say about Roman numerals is that I've spent a number of graduate seminars now with students trying to get them to step "out of the box" of Roman numerals.  It's very challenging for many of them to dig through arguments about harmony in 16th-century theory or Rameau or even 19th-century theory without bringing a long a lot of their baggage about Roman numerals and modern functional harmony.  But -- for better or for worse -- Roman numerals have become part of the "core" assumptions of tonal harmony today, and generations of theorists and composers now simply conceive of chords that way.  Are they the best tool to analyze 18th century music?  Probably not.  Are there other repertoires where they are better suited?  Yes.  Should we critique their problems?  Sure.

    But until we have an alternative "core" set of assumptions about harmonic description to overtake Roman numerals in the discipline, we'll all probably keep using them since it's a common "language."  As in all language, research (and science) requires communication, and communication requires common understandings of meanings of core concepts.  I may despise and deplore the fact that 6/4 chords came to be treated as "2nd inversions" rather than the unstable sonorities they almost always are in common-practice harmony, but the theory of inversions has so many other useful features that we're unlikely to abandon it anytime soon.  So we live with it -- even while criticizing it -- until somebody comes up with a better theory that is just as easy (or easier) to communicate and has similar (or greater) levels of explanatory power.

  • A few replies.  @Nicholas writes:

    Are we conscious enough of all the implications of the theory behind Roman numerals? John McKay writes: "until we have an alternative 'core' set of assumptions about harmonic description to overtake Roman numerals in the discipline, we'll all probably keep using them since it's a common 'language'." But are we enough aware that music theory teachers in several countries in the world do have alternative assumptions and never use Roman numerals?

    I would say: No, most people who employ Roman numerals -- which includes not only professional music theorists and college theory teachers, but likely books for much wider audiences from Music Theory for Dummies to elementary guitar manuals -- tend to worry continuously about the kinds of issues you bring up.  Are we aware of what happens in other countries?  Again, it depends on who "we" are.  If "we" are professional American music theorists who constitute the central membership of SMT?  Probably some of us worry about it more than others.  If "we" includes the audiences of Music Theory for Dummies and primers for various instruments (particularly keyboard and guitar) that might include some discussion of chords, then almost certainly not.

    I left off the necessary qualifier in the statement you quoted that should have said that Roman numerals seem to be a "common language" for discussion of harmony for a lot of Anglo-American theory.  Replacing Roman numerals with an alternative method of chord description would require significant advantages for students and teachers, and there is certainly much to be learned from already existing alternative theories.  And I'd frankly be okay if Roman numerals were deprecated and replaced myself.

    You mention "axioms" -- I certainly believe Roman numerals are pretty much assumed axioms.  They probably continue to influence my thinking in ways that I'm not always conscious of, because I encountered them first when I was fairly young, but I just think of them as one possible (and flawed) model of harmony that evolved at a particular period of time.  (And, as is true of much -- though certainly not all music theory -- they are often used to describe older music that was probably not composed with the same axioms in mind.)

    @S_Soderberg writes:

    John McKay, I appreciate your summary of some of the issues that arise in the question of whether or not music theory is a science & I eagerly await your comments on "the specific issue of defining music theory." Right now, as far as I can tell, you are headed for: (theories) = (analyses) U (speculations about analyses), which to my mind would still ignore the elephant in the room. I may be misinterpreting your prefatory remarks.

    First off, I agree that "Mersenne's mailbox" is indeed a high standard to aspire to.

    I still don't know that I actually have a definition of music theory other than it's what people say it is (which sort of returns us to Nicholas's initial conundrum).  Perhaps that's not a satisfactory definition for this discussion, but music theory, like music or even like science, is a cultural practice.  It does vastly different things for different people.  In some ways it perhaps makes hypotheses about how musical practice works.  In other ways it can assert and create possibilities for how music could work.  And, both historically and today, in still other ways some parts of music theory can be a product of particular theorists' preoccupations and assumptions which may have little to do with musical practice.

    As to the question about whether I'm heading toward the idea that theories are analyses (and/or speculations about analyses), well I'm not asserting that.  In some cases and for some people, I suppose that that may be a somewhat accurate definition.  There is certainly an empiricist mindset in much theory that seeks to create models which describe existing music.  But that's not really saying that "theory = analysis" anymore than Kepler's laws of planetary motion are simply observation of nature.  The abstraction process of theorizing of course creates new understanding that is somewhat different than the sum of all analyses.  Of course, there's also a long history in the field of music theory (dating at least back to the Pythagoreans) for bringing in a priori assumptions external to musical practice (i.e., not analytically based) as a basis for theoretical models, too. 

    Anyhow, I have to apologize and say I really don't know what exactly your particular "elephant in the room" is.  If you kindly direct me to it, I might try to address it (or at least have a better look at its trunk, ears, and other features).

    In sum -- my only definition of music theory is that it is what it is, which is complicated and involves a whole of lot of people doing a whole lot of different things.  If we're looking for a definition to actually describe what theory is in the real world, that's my view.  If we're looking for a way to define what music theory ideally should be or how it could be better, that's a rather different project.  (And perhaps that project is partly what the original question could be about.)  

    As for the relationship of theory to practice that also seems at the heart of the question originally posed, I think we could (and should) all be more conscious of where theory actually works as a "good model" of musical practice and where it fails.  (But given the diversity of "musical practices" one could potentially be describing with a theory of harmony, I'm not sure any theory of harmony is up to task of being a good fit for all of them.)  And I personally am very upfront with my students -- both graduate and undergraduate -- that things like Roman numerals are simply one possible model which is good for certain tasks.  I spend a great deal of time emphasizing many of the places where they are a bad model and trying to give them hints at better models for those cases.  That's a pragmatic approach to the issue, and perhaps if we move toward a different common theory of harmony, chords, and keys, I'll do the same thing with whatever new theory comes along.

  • @Nicolas,

    Yet I consider that even there, the fact that the debate is opposing different forms of "falsificationism" shows that Popper may not have been completely understood. The question is not one of falsification, but merely of falsifiability, that is, of the possibility of being shown false. A scientific theory is one formulated in a way that allows proving it false, or at least trying to. Good examples of unfalsifiable theories include these: "God exists", or "God does not exist". How do you answer that? How do you even begin discussing that, unless by opposing one of the two statements to the other?

    Popper says more, of course. His theory of falsifiability does not concern mere statements, as these above, but theories built of statements — Lakatos' notion of "research programs" may be a better way to define these, but in the end it is the same thing: a theory can be considered a research program.

    I would say the Kuhnian critique of Popper, though, is really important to consider.  Perhaps I am understanding this wrong, but the implicit argument seeming to be made here is something like: by paying more attention to falsifiability and falsifiable statements, we would somehow be able to allow the field of music theory to make "progress" or make music theory better or whatever.

    However, as both Kuhn and Lakatos (and others) have pointed out in various ways, science does NOT treat its core assumptions as falsifiable.  Historically, it can also be argued that science has not made major progress through direct falsification of core assumptions, but rather, following Kuhn, through incommensurable "paradigms" with different core assumptions.

    My point being: the specific philosophy of science does matter here.  If we accept some of the critiques of Popper, the falsifiability criterion only tends to function for scientific progress at the level of minor hypotheses (or "puzzle solving").  If we do not take certain core assumptions for granted, we have no coherent body of theory to apply to a given task, and we end up with methodological anarchy.  (And some philosophers of science, e.g., Feyerabend, are happy to go down that road.)

    What seems to be proposed in the question here is that we treat the foundations of one major contemporary theory (Roman numerals) as falsifiable.  But is that actually a coherent methodology for "progress" in the field?  There are many philosophers and historians of science who would argue that this is not the way science usually progresses.  Rather, we can do "normal science" (or "normal theory") and basically act like our core assumptions are reasonably valid, OR we can claim that Roman numeral theory "misses the point" and propose an alternate set of core values that can supplant it and allow us to do "normal theory" once more within a different paradigm.  (Ian Quinn has tried this, for example, at Yale about a decade ago when he dropped Roman numerals and instead taught functional harmony using a hybrid system involving bass notes, scale degrees, and basic functions -- rather than a chord-root and Roman numeral system.)

    But I'm not sure how we can actually make much real "progress" within Roman numeral analysis/theory by questioning its core assumptions.  All we end up doing is making ad hoc "patches" to the theory and amendments of exceptions to "rules" -- unless we actually jettison some of the major tenets and start anew, in which case we no longer have "Roman numeral theory" as it is commonly understood.

    I don't mean to take this discussion too far out on a philosophy of science tangent.  But since it was brought up in the question, I think it's useful to think about what falsifiability can and can't do in science, since I'm not sure it could actually achieve the goals intended in the question (and many philosophers of science might agree).

    However, of course being conscious of the limitations of a theory/model is still extremely valuable and important.  I'm just not sure whether treating such broad theoretical statements as falsifiable can help.

    And are we really talking about falsifiability (i.e., whether something can be true or false) or simply imprecision in language?  To take some offered examples:

    – a chord can be (fully) characterized by its root

    To me, this is obviously false, especially with the word "fully."  But can some aspects of chords be characterized this way?  Sure.  Let's be more explicit about what they are.  For example, since Rameau came up earlier, we might look to Rameau's own discussions of the usefulness of inversion theory.  By saying a dominant seventh chord in any inversion is "the same chord," we can offer a reasonable theory of voice-leading -- sevenths resolve down by step, leading tones go up.  That's probably less convoluted than a theory of figured bass which tries to explain proper voice-leading for individual figures like 7, 6/5, 4/3, 4/2 all in their own specific case.  Inversion accomplishes something specific here in describing reasonable voice-leading.

    But is that the only thing that such sonorities do?  No.  And some of those other things may be modeled well by a root-based theory that equates all of these sonorities, while other things may not be modeled as well (e.g., metric placement and placement within a phrase is not generally the same for all of these).

    – a V always is a dominant chord

    – a dominant chord always is a major chord

    Again, these strike me as a statements that are definitely not true for all possible interpretations.  But for some definitions of "dominant" and "chord," we could probably say this is an accurate statement or an efficient way of modeling harmony for a certain circumscribed set of musical repertoire.

    For myself, I prefer not to think of music theory in terms of what things "are" or "are not," but rather in terms of what our descriptions can tell us, how they provide a model for looking at particular musical structures, and what sorts of interpretative acts (and compositional acts, if we admit that theory can offer practical advice for composition) are made possible by making use of such concepts.

  • This is indeed an interesting discussion.  Thanks to all for your comments.

    @Nicolas wrote

    This brings us back to the Popperian question of "falsifiability", which certainly is not concerned with questions of "truth" — questions which have no place in any science. Popper is not concerned whether a theory is true or false (because he believes that any theory will eventually be proven false by a better theory which in turn, etc.), but whether it is formulated in terms that will permit discussing its validity.

    Yes, you are certainly correct to point out that I misspoke when I said "true" or "false."  Popper is, as you say, not concerned with "truth," and that was a slip on my part that I'd happily correct if we could edit older posts.

    However, I believe it is somewhat incorrect to say that Popper was not concerned with truth and falsity at all, for certainly the very heart of falsifiability is the notion that one can say with relative certainty (i.e., a logical truth) that something IS false.  That is to say, according to Popper, that we may never be able to come up with a "true" theory with certainty that describes the universe (though we might produce accurate descriptions within the bounds of a theory).  But Popper is rather convinced that we can utter "true" statements with certainty about what does NOT describe the universe.

    (This may seem to be quibbling, but it's actually a rather critical feature of his notion of scientific progress.)

    One of the problems with trying to characterize music theoretical statements in falsifiable terms is this very problem of assuring absolute falsity to a statement.  Music theoretical systems are often more like mathematical or logical systems in this regard than empirical science systems.  That is to say that you may be able to prove a statement false with the boundaries of the given axioms of a particular music theory, but you may often also be able to modify your axioms in such a way that a statement which was formerly false might now be true (or, rather, "true" in the sense that it coheres with the rest of the logical system). (I am here perhaps making similar arguments to Ildar's but from a different perspective.)

    Actual musical practice, to my mind, is simply too "messy" to correspond directly to most of our theoretical models.  It seems to me that if Nicolas is serious and wishes to produce something like "falsifiable" statements, we'll need to (1) narrow the focus of such statements significantly, and (2) add quantifiable variables to their predictions.  It's not enough to declare a statement like "A chord can be characterized fully by its fundamental" as "falsifiable."  That would never pass muster as a scientific hypothesis, since it is not testable in any meaningful way.  It's simply not specific enough.

    We could, however, make up a statement like: The voice-leading of a dominant seventh chord (defined as a sonority which has a certain intervallic qualities and could be given the bass figures 7, 6/5, 4/3, or 4/2 and perhaps having certain metric or durational features) can be accurately described 90% of the time (or whatever number) as having certain features (e.g., leading tone goes up by step, seventh goes down by step) in extant Common Practice pieces of the period 1750-1800.

    We can then do a corpus analysis and test such a statement to determine whether it is accurate.  If it is accurate, we have shown that a root-based characterization of such sonorities is at least useful for describing voice-leading in these particular sonorities in a particular stylistic and historical period.  If it is inaccurate, we will have falsified our hypothesis (in a Popperian sense), which could lead us to try a different model or to modify the older one with additional stipulations.  Those involved in music informatics and "empirical musicology" are now and have been engaged in testing such questions in recent years.

    To me, that's closer to what a "falsifiable" way of approaching music theoretical claims looks like.  Declarations like "A dominant seventh chord can be completely characterized by its root (implicitly: for all time and in all places and cultures)" are simply not falsifiable in any meaningful sense, and they never will be -- since they are more like statements in logical or mathematical systems, not subject to direct empirical reasoning.  I'm not quite sure what it would mean to even attempt to treat such statements as "falsifiable."  The discussion seems to be equating "falsifiable" with "having room for doubt," but that's certainly not what Popper meant by the term.  He meant that a statement was specific enough that it could actually be shown to be false.

    On a related thought:

    One specific aspect of music teaching in France (and Continental Europe) that you don't have in the US is the distinction between Conservatoires and Universities. I tend to consider that Conservatoires are places were certitudes are taught, while Universities are places for the teaching of doubt. As a violin or piano student, you are not supposed to doubt anything that your teacher tells you (teachers, for the same reason, are often called "Master"). As university student, you are invited to doubt anything taught (or anything printed).

    I would say that we do have something akin to this, if some of the reports I have heard from those who attend conservatories in the U.S. are somewhat true.  As someone who teaches at a School of Music within a university, I certainly find that one of my roles (as academic faculty, as opposed to applied faculty) is often teaching students about "doubt."

  • Dear Nicolas, perhaps I am slightly poisoned by the study and conversations with Derrida and that leads me to think that music theory is not a science. Fortunately, in English usage, it does not have to be and most commonly it is not called a science. To Popper's criterion of verification I can counterpropose Greimasian veridiction. The latter involves the subject of analysis together with its object. In fact, I cannot make any musical work an isolated object of scientific study because I cannot exclude myself from the experiment. Yes, I know that such exclusion is the must for any precise scientific research. But, no, I do not think that this is the case for music study. Here we stumble upon major ontological distinction and the necessity to deconstruct Being-as-presence situation. Music analysis is always a bit of self-analysis. Carol Krummhansl provided an astounding example of objective probe-tone method of key definition, using the questionnaire with hundreds of virtually untrained listeners. However, I prefer to analyze my own perception, at the risk of being subjective. Yes, I rely upon my own understanding of music because I have trained myself quite extensively. Roman numerals and roots are the part of my personal idiosyncratic perception of music; therefore I trust them. Hoping that my students will follow, though this is not an ultimate requirement.

  • For me, musical theory is the direct investigation of conceptual matters for individual musicians be they composers, performers, historians, theorists, educators, etc.  Obviously as evidenced by this group, musical theory is an academic/technical discipline in it's own right.  As a composer, my initial interest in musical theory was necessity - I needed to understand harmony, counterpoint, form, orchestration, post tonal comtemporary language, technology, etc.  As a composer I need to understand the scalar material Debussy is using, or the modal usage of Renaissance compostion, or the principles and physics of acoustical sound that may inform my ideas and creative thinking.  I understand that I could spend a life time studying "musical theory," but I have limitations and my interface with theory is a much more practical one - I need to understand certain things which are relevant to my own creative work and musical interests.  Gustav Holst remarked (and this is not a direct quote but easily found in his biographical material) upon leaving the Royal Academy of Music early that he wanted to compose music, not study it.  

    Regarding Roman numerals, they do have the advantage of denoting major, minor core qualities: iv, IV, V+, v(o).  All basic triad primes (major, minor, diminished, augmented, and the various suspensions) can be symbolized effectively and probably why still in usage.  My Patterns For Jazz books use Roman numerals to denote chord possibilities/progressions (for non diatonic progressions as well common in Jazz).  

  • Ildar,

    "I'm just a caveman. ... Your world frightens and confuses me. ... Sometimes when I get a message on my fax machine, did little demons get inside and type it? I don't know. My primitive mind can't grasp these concepts." In other words, here's my problem:

    Derrida & Cie must necessarily make one existential assumption: the TEXT. No text, no Derrida. It's a radically non-generative theory. What is truly erased (ignored) there is the creative act. This is especially true in music. You can accept everything in Derrida and at the end of the day you won't have a single note of music. The text, the musical work, is assumed. It appears, in virtually all postmodern accounts, as if by magic - because the mechanics that enable it to appear are not what the Derridist wants to (or can) talk about.

    To return to Nicolas' question, "SMT, after all, is the Society for Music Theory and as such should be aware of what it is about." If you are going to hold up the Derrida shield, especially if you simply name drop him as if it's too tiresome to have to make the connection yourself, you may not realize you are taking a position you may not want or be able to defend. In effect you are saying that music theory is "analysis," no more & no less. In other words, theory has no need to provide a generative function because the text is "just there" & your job is to pick it apart in a variety of ways. I think Derrida & his desciples have made interesting points, but here is the one question I have yet to see addressed, let alone answered, in that camp:

    Where do the notes come from? The actual notes.

    How does a Bach go to Greimas and Courtés' "veridictory square" and come up with a fugue? An actual fugue. Perhaps someone can explain this to me, because after many years of reading and listening I have come to the conclusion that musical Deridists are all closet creationists who believe that angels whisper the notes into the ears of composers. That's what any theory looks like that starts with all the notes already on the staff and, rushing breathlessly to tell us what the notes mean, remains doggedly incurious as to how they got there.

    (Before we discuss whether or not music theory is a science it may be beneficial to get our terminology straight. Popper brought "falsifiability" into the picture as a distinguishing mark of science. "Verification" is related but is a very different animal & it's important not to confuse the two.)

  • Let me ask further questions.

    David Feurzeig writes: “Roman numerals are labels, theoretical claims. Functional categories (dominant, pre-dominant, tonic) represent yet a further level of theoretic abstraction.” But some consider that Roman numerals describe six or seven functions (depending on whether vii or vii° is considered an independent function), while Riemann’s theory of functions properly speaking considers that there are only three functions, dominant, subdominant, and tonic. How does one pass from the one to the other, and it what sense would Riemann’s theory be more abstract?

    How could one reconcile with this abstraction the fact that II may not always represent the same function as V/V? As to 6/5 or 6/4 chords, or even II–IV, should not one involve in the theory some consideration of the voice leading? Is it enough to conclude that Roman numerals and functional labels are subjective, or must one recognize shortcomings in these theories themselves? Also, what is the point of labeling chords? For sure, labeling IV or iv says whether the chord is major or minor, but to what purpose? And how can Roman numerals denote chord progressions – or, more precisely, what do they have to say about progressions? What is the difference between these various progressions by a 4th or a 5th: V-I, IV-I, VI-II, I-V, I-IV, II-VI?

    And if the root is the important aspect in a chord, how comes that chords were used before the advent of the idea of root and the real bass at times considered more important? And why do so many of us believe that the idea of root is an idea of Rameau, several years after, say, Corelli who sometimes is said the first tonal composer?

    Many of these questions are mere rhetoric, fore sure. Yet, are the answers so obvious? Are we conscious enough of all the implications of the theory behind Roman numerals? John McKay writes: "until we have an alternative 'core' set of assumptions about harmonic description to overtake Roman numerals in the discipline, we'll all probably keep using them since it's a common 'language'." But are we enough aware that music theory teachers in several countries in the world do have alternative assumptions and never use Roman numerals?

    My purpose here, of course, is not to refine our understanding of Roman numerals, but our understanding of what music theory is. I’ll leave the questions of falsification and scientificity for another posting.



  • Dear Nicolas, It seems to me that the problematics of scientificity (its relevance or irrelevance) can help answering to your questions. John's precise definition of our theoretical hard positions as core assumptions is the key, for example. You seem to criticize the idea of the roots of chords as secondary and subjective to voice leading. You know that I have exactly the opposite core views. The problem, as I see it now, is our desire to construct a super-core, the one that will provide a final solution to these ideological questions. Is it possible, at all? What will it look like? Will it be a tree-like hard system, or something more like a rhizome? I have strong suspicions that we are not ready for that (concider, for example, David's idea that Derrida is all about text--which is complete misinterpretation of philosophy of the XX century, with phenomenology and postmodernism lumped together in some superficial thematization). In this situation, I would leave this meta-theorizing to composers. I agree with Carson.

  • Dear Ildar, just a few rapid answers; I'll come back on the question of scientificity later.

    I repeat that I have nothing for or against the theory of roots, I merely chose it as an example to ask whether we were enough aware of the theoretical assumptions behind what we teach. Like everyone here, I do use Roman numerals.

    I did not criticize the idea of the roots as secondary and subjective to voice leading. I merely said that when II goes to IV, it might be best to examine the voice leading (which, let me be more precise now, probably involves a descending chromaticism). And I do believe that labeling a 6/4 on the tonic either as a V with suspensions or as an inverted I may have to be decided in consideration of the voice leading.

    The problem may concern our "core assumptions'' — that I'd call more simply our axioms. I hope that, for the majority of us, what Roman numerals say is not merely axiomatic. The problem of a theory usually is not in its axioms themselves, but in the laws that are inducted from them. And I certainly do not believe in final solutions.

    I am a fervent reader of Derrida's Grammatologie and I am not so sure that the idea that Derrida is all about text is "complete misinterpretation". I don't think that one can oppose Greimas' concept of veridiction (which is about saying the [apparent] truth, not about verifiability) to Popper's concept of falsifiability (or testability). But as I try not to speak without knowing, I'd like to reread a few things and make a few verifications (;-)) before answering more completely. Be patient.



  • I apologize, dear Nicolas, for being impatient! This is not a good quality for a theorist, I agree! Few small remarks, though, without finalizing anything. In his last decade Derrida gave seminars in Irvine, California. So many of his students were eager to quote his earlier works, including De la grammatologie. He ouvertly rejected these references. It seemed to me that he was disappointed with his earlier writings, centered around text and semiotics. I would not jump into conclusions about his philosophy, though. At this point I am rereading Le toucher. Interesting stuff. David's black-and-white verdict that Derrida's thought is non-generative does not make sense to me. It is exactly the opposite: one can find the source of music somewhere outside the notated score. Within Husserlian transcendental reduction, perhaps. I, actually, whanted to know exactly that: how do you, my colleages, see the source of music, its generative agency? Note heads? Lines? Hierarchy? Voice leading? Are you serious?


  • Thanks again to Nicolas for starting this thread. Whether it will help SMTDiscuss rise to the level of Mersenne's mailbox still remains to be seen, but it's a good start.

    Some may not have noticed that Nicolas made a relevant comment in another SMTDiscuss thread (see: https://discuss.societymusictheory.org/discussion/comment/312#Comment_312) about the need to accept the coexistence of (at times radically different) theories to accomodate the appearance of (at times radically different) musics – a point I have been trying to make under the rubric "possible models in a musical pluriverse." Maybe we can coax another voice into this discussion: a premise (and accompanying frustration) similar to Nicolas' vis-a-vis Schenker & pluralism was taken by Rick Cohn in an article from quite a few years ago. I associate it with Rick because I remember exchanging emails with him about it at the time I first read it, but I believe it was co-authored & the other author's name escapes me, as does the article title & cite. Rick, if you're out there, any help on a cite or any comments on this thread?

    John McKay, I appreciate your summary of some of the issues that arise in the question of whether or not music theory is a science & I eagerly await your comments on "the specific issue of defining music theory." Right now, as far as I can tell, you are headed for: (theories) = (analyses) U (speculations about analyses), which to my mind would still ignore the elephant in the room. I may be misinterpreting your prefatory remarks.

    Ildar, I assume you are confusing names -- David Feurzeig may not appreciate having my position confused as his. So this is me (Stephen) answering you. You are charging me (I assume it's me) with saying that Derrida is all about text. I accept that that is honestly how you interpret my words. But that's not what I intended. To say that text is a necessary condition for deconstruction is not to say it is sufficient. I'll try again. The existence of a text is a sine-qua-non for Derrida for him to say anything at all. Enlarging, this is to say that any analytical theory requires an analysandum prior to the analysands coming in to do its work. I consider this is uncontroversial - correct me if it is not. Now, of course the source of music is somewhere outside the "notated score" (or performance or recording of a performance -- today there is often no notated score at all). I don't believe anything I wrote contradicts that. So the question is: From where? Locate for us  music's Helicon in relationship to music's Parnassus. I would like to learn more about your idea of where that source is that results in that score/performance/recording and the relation of that source (some call it composing) to your idea of music theory; and while I don't mind quotes to speed a conversation along it would be preferrable to go beyond mere name dropping and assuming we all know what you understand Derrida said. None of what I say here should be taken to mean or imply that I believe Derrida or his accolytes are wrong. But I am saying that my present incomplete understanding of deconstruction and related/competing analytical theories relying on a pre-existing text leads me to conclude that they are  incomplete. (You see there, I didn't mention Sokol's name even once.) But until then I'm left with an empty wave-of-the-hand response. I still have nothing more than what appears to be your belief in an analytical angel who conjures texts for analysis, and the "theorist" in this world has nothing to do but sit and wait for the next work to appear. I refer to your incredible statement "I would leave this meta-theorizing to composers" which is a bit like Pilate washing his hands. So, until you can make some connections, the following is for you:

    I am currently writing a blog entry whose starring actors are Fux and Rameau. Leaving to one side the issue of whether what I conceive turns out to be an historically accurate account or a convenient fiction or some mix of the two, one of the questions I will pose in that E&EN post – a question that has an easy answer simply by reading the first few lines of Gradus Book 2 – relates directly to the question of what ought(!) to be included or not in any music theory. I feel that anyone bold enough to walk to the front of a freshman theory class to "profess" should first confront this easy question:

    Why did Josephus come to Aloysius?

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  • Interesting that in jazz the function or identification of a II or V/V is less important than the quality of the chord itself.  In other words it doesn't matter what you call it, it only matters what it sounds like!  In that regard Jazz is more compressed than the functioning of the music from the classical common practice period.  Modulaton can be instantaneous in jazz, while requiring preparation and pivot chords in the common practice period (and thus requiring theoretical analysis).  As a composer, a chord quality for me is an option of sound possibility, not a function.  In a tonal sense, any ii, II, V/V, 2 chord has a myriad of options (and resolutions) for that root or inversional root. So in essence there are many possibilities for the 2 position, the 3 position, etc.  Modern usage relies less or hardly at all on diatonic relationships so if C is the predetermined tonic, Db minor, major, diminished, augment, or suspension of some degree (as core triad) is a musical possibility despite analytical function.  The same is true for any quality of D or D#.  In this regard jazz is more direct and less concerned with harmonic functions and more concerned with substitutes and harmonic variation.  

    In reality there are few choices (in the chromatic 12 tone scale) for any degree on 2 (b2, 2, or #2), b3 or 3, 4 or #4, b5, 5, or #5, b6, 6, b7 or 7.  This is how jazz musicians view the degrees and interchange them freely as harmonic possibilities for modern usage (I can't speak for all jazz musicians, but my training in jazz theory leads me to this assumption).  To my mind it's less complicated and more direct than determining a chord's function in the tonality.  Musical notation has limitations as to what it can convey, so voice leading would depend on a performer's knowledge, the style of music, the written notation, figured bass, etc.  Jazz notation also has the advantage about being direct about a chord's identigy, root, suspension, quality, etc.  It may not denote voice leading, but a good jazz player would have that knowledge intellectually and at their fingertips.  

  • Correction:

    Jazz notation also has the advantage of being direct about a chord's identity, root, suspension, quality, etc.  

  • Dear Carson, your training in jazz theory, indeed, does not cover all that is jazz. You are talking about more or less modern forms, something that falls into the category of modal jazz, or atonal jazz. It seems to me that we are forgetting about traditional jazz, the reflection of Afro-American folk music. There, functionality was not only present, but it was sharpened and pointed by times more than in the late-Romantic harmony. Think of great masters of New Orleans. They could distinguish between supertonic and double dominant (without knowing the RNs, of course, by ear). Or, think of The Sunny Side of the Street: on the word Your hat one can, theoretically, chose either iii, or V/vi. Try both--the functional choice here is absolutely clear. They knew substitutions and doubles, but then they were called functional substitutions and functional doubles. Function is not an abstract concept. It is an animalistic attraction of one chord to another, the sense of breathing of a phrase, tension-relaxation patterns, gravitation, resolution, an exchange of tonal energy. That all is gone in today's academic school jazz, which is a pale shadow of the old one. I keep listening to endless asyntactic reshuffling of chords and scales. It is so boring!


  • I won't after all comment about Derrida (but see below), nor on Greimas, because I don't think either is really relevant to the present discussion (but I might participate in another thread on the semiotics of music theory, is anyone were interested in opening it).

    A few words about my mention of Popper and falsifiability: I am perfectly aware that the whole debate about it mainly concerns exact sciences. Yet I consider that even there, the fact that the debate is opposing different forms of "falsificationism" shows that Popper may not have been completely understood. The question is not one of falsification, but merely of falsifiability, that is, of the possibility of being shown false. A scientific theory is one formulated in a way that allows proving it false, or at least trying to. Good examples of unfalsifiable theories include these: "God exists", or "God does not exist". How do you answer that? How do you even begin discussing that, unless by opposing one of the two statements to the other?

    Popper says more, of course. His theory of falsifiability does not concern mere statements, as these above, but theories built of statements — Lakatos' notion of "research programs" may be a better way to define these, but in the end it is the same thing: a theory can be considered a research program.

    What I meant is that chord root theory might involve statements that could be presented as falsifiable, or not, such as:

    – a chord can be (fully) characterized by its root.

    – a V always is a dominant chord

    – a dominant chord always is a major chord (Schoenberg)

    – etc.

    I don't really think that presenting these as falsifiable (i.e. not as mere truths) really can turn our discipline into an truly "scientific" one in the sense of the "hard" sciences, but I do believe that our discipline can be said a "theory" only if it allows for some doubt about all this.

    I must however revert to the question of the text. The fact is that a theory, even in human sciences, needs an "object". If we are to write, or even merely to think of, theories, they must have an object — that is, something given outside us. If this object is music, it is our object only insofar as we think of it as something external that can lead to a theory. I can understand Ildar's argument that he cannot exclude himself from the musical experiment, or Stephen's argument that we need to know the "source" (although I am not very sure of what that might mean). But music theory, for me, can only be about something already given: theory is an act of contemplating, not of creating. (This is the definition of the term, by all means!)

    In other words, I am fully of the side of those who think that theory is of the order of analysis (and reciprocally). Theory needs a given, a text, a Dasein [I hate these German words]. This needs not be a written text, but it must be something already given. This, to me, is essential even in musics of oral tradition, modality properly speaking, where the game always is about something already heard, already there, to be both respected and negated. After all, the situation is not really different for our music, otherwise we would not spend so much time studying the music of the past.

    This also is to say that theory, properly speaking, in my opinion at least, can only be retrospective and descriptive, never prescriptive. Not all of what we teach as "music theory" may be so, and that, once again, is the very reason why the whole matter deserves a discussion here. There is an essential distinction between "music theory" as a description of classes to be given alongside "music history", and "music theory" as an object of speculation since music exists.



  • What a fascinating discussion! The core assumptions are not detected by their carriers, indeed. It is even more a case if the core assumtion is inherited from the previous generation. Husserl managed to deconstruct the core assumtions of metalanguage of natural sciences in 1935 in his text Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie. Very often a science is moving with full force toward discovery of absolute truth while its basic premises are hiding in the subconsciousness! In this case, I can criticize (and deconstruct) my own axioms, as well as the axioms of my opponents. I say that tonal-harmonic function is sacred, it is absolute and universally pertinent. But, ask me, what do I know about its psychological mechanism? Nothing! Others believe in Schenker as if they just came from the private meeting with Mr. Jesus Christ. If I start asking questions they will be clueles about their most basic terms! There are some who prefer figured bass and voice leading as the main criterion, but these assumptions are based on a shaky ground, to say the least. What is music theory, then, after all?

  • [Thanks to Rick Cohn who passed along the cite for the article I mentioned:

    Cohn, Richard, and Douglas Dempster. "Hierarchical unity, plural unities: Toward a reconciliation." Disciplining music: Musicology and its canons (1992): 156-181. I doubt whether Rick will want to weigh into this discussion.]


  • Dear Stephen, thank you for the link, I will read carefully this important text. As for the elaboration of John's post and questions of philosophy of science, I would like to say few things about our "science", which is music theory. False or true really matters in physics, I guess. But there must be a difference between physics and music study; the latter is a part of sciences of man, humanities. Magnificent French culture discinguishes that: there is  even the Maison des Sciences de l'Homme.   It is different and serves different functions from CNRS, Le Centre national de la recherche scientifique. Have we decided to ignore this difference? If not, why do we have to follow the problems of les science naturelles? What will we get from such following? Publications in Science or Nature? I suggest that we stay within our own field of humanities. And for that field, the problem of scientific truth is solved differently from Popper's concept. For us what matters the most is not what is said, but how it is said. We are talking about the same thing--the chord progression--but what matters to us is the question How. This is roughly the same as the question of modalities and moods of the spoken statement. Each statement can be pronounced and interpreted differently, even though grammatically it will be the same. In addition to vocabulary meanings there is fonction narratif (according to Greimas). Four or more modalities. So, progression I-ii6/5-V8-7-I is the same grammatical and syntactic substrate, yet there are at least four musical-theoretical interpretations-modalities: - 6/5 8-7 - (figured bass), T - S - D - T (Riemannian functions), C -  Fadd6 - G7 - C (commercial chord notation) and I ---(V)---I (prolongation). It is obvious that Roman Numeral notation is the least theoretical, yet is the most unimposing. It functions as a simple grammatical structure. However, it is not sufficient to generate the musical enonce. The latter needs modal variation. The simple grammatical structure is neither false, nor true. All possibile enonce's are false by default (according to Umberto Eco). Yet, who cares, if we managed to create rich artistic meaning. Its truthfulness is guaranteed not by verification, but by veridiction.

  • Dear Ildar and all,

    One thing that appears certain to me, is that this thread really is about theory, and I am very happy with it. I 'd like to remind that my initial intention had not been to question Roman numerals, but to discuss whether we were aware of the theoretical implications of our teaching of theory. I took Roman numerals as an example, and it turned to be a very good one, but it was not meant to be more than that, an example.

    As to the progression I-ii6/5-V-I, Ildar, let me stress that all SchenkeriansI know, and Schenker himself, would describe it as just that: I-ii-V-I. I know that you would like to prove that Schenker neglected subdominants, but he did not. He merely tried to hierarchize and he considered that in I-ii-V-I, ii was of a lower hierarchical level, I of the highest, and V in between. I am not sure Riemann would have disapproved.

    As to the Maison des Sciences de l'Homme, the link that you give is not that of the French MSH, but of a very recent one (2013) in the University of Liège, Belgium. There are at present 22 Maisons des Sciences de l'Homme in France, most of which closely linked with the CNRS (http://www.cnrs.fr/inshs/recherche/msh2.htm). I agree with you that there is quite a difference between the human sciences and what we tend (in France) to call the "inhuman sciences", but we share with them, I hope, a common idea of what a "science" should be, in the best meaning of the term.

    After the first European Music Analysis Conference in Colmar in 1989, an argument arose between Yizhak Sadaï and myself, of which traces were published in Analyse musicale 18 (January 1990, pp. 83-85). I had claimed, in my short talk concluding the conference, that "music analysis is a science, not an art", and Sadaï, quoting Schenker, argued that a good analysis always results from an intuition, from a personal sensibility. In my answer to Sadaï, I stressed that "Analysis is not an art because its productions cannot have the closed and definitive character of the work of art: it must remain a science because its productions always must remain open to refutation". [Sadaï and I, after that, became very good friends.]

    This brings us back to the Popperian question of "falsifiability", which certainly is not concerned with questions of "truth" — questions which have no place in any science. Popper is not concerned whether a theory is true or false (because he believes that any theory will eventually be proven false by a better theory which in turn, etc.), but whether it is formulated in terms that will permit discussing its validity. You had said in a previous posting that "tonal-harmonic function is sacred, it is absolute and universally pertinent." I cannot figure out what you really meant by that but, if you meant it seriously, let me stress that such a statement is inherently irrefutable. That does not mean that it is true, nor that it is false, merely that it leaves no space for discussion. As such, it is not "scientific" in Popper's sense. This is not a value judgement on your statement, merely a demarcation.

    One specific aspect of music teaching in France (and Continental Europe) that you don't have in the US is the distinction between Conservatoires and Universities. I tend to consider that Conservatoires are places were certitudes are taught, while Universities are places for the teaching of doubt. As a violin or piano student, you are not supposed to doubt anything that your teacher tells you (teachers, for the same reason, are often called "Master"). As university student, you are invited to doubt anything taught (or anything printed).

    My conception of theory, in the end, would be that a theory is something eminently, inherently doubtful — and that doubt is the most entertaining aspect of it.



  • Hi IIdar, thanks for your comments.  My point in reference to Roman numeral usage as related to jazz studies was that they are used in jazz pedagogy as means to quickly memorize complex changes for jazz musicians and that despite modulations or key shifts which are often unprepared in jazz - the Roman numeral system can convey any harmonic progression in a kind of shorthand if you will.  For instance in a common turn around: C7 - Eb7 - D7 - Db7 - C.  Jazz musicians can easily think of that as I7 - bIII7 - II7 - bII7 - I.  In a way it's easier (at least for me) to process a few Roman numeral degrees in an otherwise complex progression by referring to the Roman numeral degrees.  This is apparent in examples from "Jazz Improvisation 1 Tonal and Rhythmic Principles" by John Mehegan and "Creative Jazz Improvisation" by Scott D. Reeves (a text used for jazz studies at the University of Washington).  Unfortunately I am having no luck pasting the examples into this message! I did not mean that Roman numerals denote chords without harmonic functioning, I meant that Roman numerals are used to [more easily] memorize and conceptualize complex changes by directly understanding what scale degree (within the 12 chromatic tones) is being used and it's quality (major, minor, diminished, augmented, suspension, etc.).  I-bII-II-#II-bIII-III-IV-#IV-bV-V-#V-bVI-VI-bVII-VII (and of course minors (as well as diminished and augmented chords) can be represented as well: bii, V+, iiiø, etc.  I do understand you comments regarding earlier jazz.  I was not referring to a quality judgement of early or later jazz, rather the way Roman numerals are used in jazz theory and by musicians.  


  • Dear Nicolas, thank you for your poignant remarks. It seems that you started this discussion and provided the answers that we all, perhaps, should agree. Yes, theory is the place for doubt. As for Sadai, I envie you for having an opportunity to converse with him! His book on harmony is one of the best I have seen. Tonal harmonic function is a scientific category, pertaining to music theory. Of course, I was joking by saying that it it sacred. On the other hand, I asked so many experts in function, icluding Dr. Harrison, but the answers were far from being conclusive. So, this one remains an open question. I also think that definition of tonal function is not so much logica, as ostensible--that is, available by point out to it. It also requires great deal of preliminary aural training of a very special kind.

    To summarize, your assumptions concerning voice leading are not provable (or falsifiable). They do not have even a pure verbal definitions, on the level, required by the unhuman sciences (:)). Schenker's definitions are  very thoughtful, but they belong to esotheric kind, like Buddist or Taoist statements. Only Roman Numerals are neutral enough not to cause raised brows. And, from my experience, most theorists use them, all over the world. So, perhaps, your choice of example was exceptionally good! By the way, one other modality--your theory of tonal vectors--seems more and more useful to me. I will apply them in most of my analyses of Russian music.

  • [I'm a philosophy/logic Ph.D. I've seen many struggles to define/characterize various abstract disciplines. With this as a background, I offer a humble contribution:]

    A practical way to define/characterize Music Theory is to look at the ways in which it can be used:

    [a] It can help composers to compose

    [b] It can help performers to perform and producers to produce

    [c] It can help listeners to enhance their perceptions and to increase their enjoyment of music.

    [d] It can help everyone who is interested in music to think and talk about music more articulately and with better organization.

    Regarding [d]: I think it is a natural part of musical experience for people to want to think and talk about music. Musical theory can help people in that activity.



    Isaac Malitz, Ph.D.




  • How about this:  the sum of the squares of the lengths of the catheti is equal to the square of the length of the hypotenuse. This statement is verifiable because the opposite is falsifiable. Or, two straight parallel lines on a flat plane never cross. I see the point of Popper exactly as helping to find the truth. Scientific truth, without which no unhuman science can function. What is an equivalent of such truth in music theory? Could anyone provide a single example?


  • John, I think we should better drop the matter of falsifiability altogether, lest everyone would get really bored. Let's recognize that my statement about music theories being falsifiable was in itself ... hardly falsifiable.

    On the other hand, I believe that corpus analysis and empirical studies are important. They may become one of the major aspect of our discipline, now that our computers make serial studies (i.e. studies of large series) so much easier.

    One theory that we very much need, to remain in the domain of Roman numerals, is one that would explain why I-ii-V-I makes sense in tonal harmony, while I-V-ii-I does not (or almost) — why the first is "grammatical", as Ildar would say, and the second is not.

    Ildar mentioned my own theory of harmonic vectors (thank you, Ildar), which tries to answer this question (see http://nicolas.meeus.free.fr/NMVecteurs.html). Dmitri Tymoczko also produced interesting results in this direction, in his case more specifically as the result of corpus studies. And my web page just quoted provides links to recent PhD works (by Paul Scott Carter or Bryn Hugues; there are others) concerning pop music or blues, that go beyond the use of Roman numerals as mere labels — and that show that pop or blues harmony does not function exactly like common practice harmony.

    The question (about the grammaticality of I-ii-V-I), I am afraid, Ildar, cannot avoid questions of voice leading: there certainly is a relation between the grammaticality of such a progression and the downwards resolution of dissonances or the upwards resolution of the leading tone, but this relation still needs to be explained.

    It has been said, on SMT-Talk I think, that the reason why dissonances resolve downwards had to do with gravity. This certainly would pull music theory towards hard sciences, and the reason would then appear universal. But our human sciences cannot (and/or should not be allowed to) make universal claims — even although some of us may think otherwise.




  • I'm not ready quite yet to go out and buy a bumper sticker that reads "God Composes – Theorists Analyze – And There's An End To It" (although it would be a big seller at the next annual meeting if SMT wants to buy rights from me), nor can I add my voice to the strains of Kumbayah I'm beginning to hear in the background (-- & I don't hear a soprano voice at all; maybe my lack of proper ear training, but another time on that).

    For one thing, consider that the theorists who set up SMTDiscuss saw fit to include two categories: "Theory" and "Analysis" -- not "Theory, i.e., Analysis". Surely this was not a thoughtless choice & it was made with a very large, varied, at times unruly community in mind. I write this in part to remind myself that I'm not alone, but my main point is that a half dozen contributors to the current discussion so far about "what is music theory" should not consider themselves (ourselves) representative of the community at large (let alone being objectively "right"). We represent only our own viewpoints regarding a very complex issue and thus we should be judicious in using the qualifiers none, few, some, many, most, all, never, always, etc. The emergence of a conciliatory idea here is not impossible (one can always hope), but for me the larger issue is encouragement of a more inclusive discussion that takes in the entire theory community.

    So to continue, let me point out the elephant in the room: It is, simply, everything that is NOT in the room. Scientific fact: relative to other mammals, elephants are really, really big.

    For our little group here, I don't think it's now going to be that easy to shut off the Roman numeral spigot that Nicolas chose to open when he suggested it as an example to work out from (as he recently reiterated). I know Nicolas meant it as a spring board, and that's the way I, at least, understood it – even while knowing from experience where it was almost certain to lead. I then held my breath and just watched as the example invaded the argument like a virus – example morphing seamlessly into epitome. I should have objected earlier, but I felt the only thing to do was let it play out. But I'm now thinking it may be a good thing to keep diatonic functions available as we proceed, especially those Roman numerals, not to show what tricks they can do within their model, but what they can't do outside it. So let's keep what we have so far & bring it forward with us as we move on to Boulez, Crawford-Seeger, Ferneyhough, Indonesian gamelan, Ewe drumming, microtonal systems ("natural", ethno & synthetic), even our old friend & whipping post, classical duodecaphonic serialism with its dozens of offshoots still very active today -- in short, all the wonderful musics that can't be stuffed into the common practice glass slipper. 

    So to continue, let me point out the elephant in the room: It is, simply, everything that is NOT in the room. Scientific fact: relative to other land mammals, elephants are really, really big.

    Recognition of the elephant presents a conundrum for any theorist who wants to apply a specific model or an adaptation of that model M1 to an object (work, text) that was conceived in a model M2 other than M1. (To keep it simple, we'll assume the theorist has somehow discovered or been told exactly what M2 is, so s/he has full knowledge of both M1 and M2. Often this is not a tenable assumption.) (A) If the intersection of M1 and M2 is not empty, they share some theory & there is a chance for reconciliation; but (B) if their intersection is empty, the theorist is unavoidably faced with two choices:

    (1) Discard M1 when analyzing this particular object.

    (2) Discard M2, thereby discarding the object as "illegitimate."

    I know of no other choice. The analyst who can switch between M1 and M2 depending on which is appropriate for a given work has a potential "multiple personalities" problem, especially as the number of possible M's grows beyond two. The analyst who doggedly sticks to M1 for whatever reason has a "reality recognition" problem as the pile of M2-, M3-, etc. objects grows and s/he begins to be taken up less with analysis and more with censorship; antidisestablishmentarians are not fun to be around. The former is the pluriverse model (multiverse if you prefer); the latter, the universe model (which has to include a really, really big trash bin). I almost admire those principled stalwarts who defend their universe. But I long ago noted that the biggest arguments take place among those who agree there is a (single) universe but end up screaming at each other, "Yours is not the correct description of the universe, mine is how the universe must be described." But I discovered there are pockets of pluralism within the theory community and the inhabitants seem quite content. Eventually I came to live with my own multiple personalities disorder which is what I've been writing about lately on E&EN (starting here). (I glanced at  the beginning of the Nov.20 post & was startled to read a premonition of our discussion so far.)

    I leave off here for right now to see if there are any comments/rebuttals. (And, yes, I realize that above I have violated or come close to violating a principle that was all but embraced by others here, to wit: theories (conceived as analysis) are not generative. A rebuttal on that later.)


  • This has been an interesting thread, at times, but also a complicated one. I went back to Nicolas' initial post, re-read it carefully. And here are brief comments in light of that and all of the other posts in the thread:

    [1] One of the more subtle and useful issues is: How is a theory/model/hypothesis in Music similar to or different from theory/model/hypothesis in other disciplines (e.g. chemistry, cosmology, wine connoisseurship, mathematical research, cardiology, psychoanalysis, cost accounting, financial planning, investments, artificial intelligence, courtroom litigation, ...) . These disciplines each function in somewhat unique ways; and the role/function of theory/model/hyothesis can vary.

    To put it another way: Why would we even want to try to force Music Theory to function like theory in the field of Chemistry (for instance)? Why are issues of empirical verification/falsifiability even important for Music Theory?

    [2] Whatever Music Theory is about, a large part of it is "value-laden", i.e. it is concerned with what is good, bad, sounds-good, doesn't-sound-quite-right, etc. Value-laden issues are not subject to empirical research.



    Isaac Malitz, Ph.D.




  • (In my previous post, repetition of the statement beginning "So to continue..." was not repeated for some sort of strange emphasis. It was an editing error. Please ignore the first statement. -- sorry)

  • Dear Isaac, you have expressed, more or less, the idea of our thread. In English-language tradition this problem is solved on the level of the usage--it is impossible to say that music theory is a science. In other traditions, though, it is different. I am not sure that Dahlhaus would agree with you and me. After all, he created a discipline of Musikwissenschaft--a university discipline that was supposed to function in the same way as other university disciplines. In Russian, the word nauka is even more flexible. My teacher Yuri Kholopov insisted that music theory is nauka--science, in the full sense of this word. I, as his student, was supposed to believe that, but I managed to hide my disagreement from him. Empirical research, pragmaticism--these are north American contributions to philosophy and to philosophy of science. In the global context the issue is more complicated.

  • There is not a rigorous definition for the term "science" !

    So in practical terms, the best we or anyone can do is to compare/contrast music theory with other disciplines. When one carefully examines various "scientific" disciplines, one discovers significant diffferences. The field of psychology operates differently from the field of mathematics, and so on.

    That being said, I think that mainstream music theory has a central characteristic that I think qualifies it as a largely "scientific" discipline:

    Music Theory deals with models of music.

    It builds, elaborates, examines, revises, applies these models.

    The most-developed model is what I call the "note-centric" model. This treats music as notes, and patterns of notes. It deals with motives, melodies, chords, chord sequences, counterpoint, larger structures that elaborate from these and so on. This is definitely a model (a "note" is an abstraction or simplification re musical reality). It is one of the most successful models of anything in history ! It has gone through steady elaborations for over 400 years! It has many variations that are of great interest.

    (btw, there are alternatives to the note-centric model, but that is for another thread)

    Are there methods to examine and even validate portions of the note-centric model? Yes. Two important methods: [a] Historical analysis (is a certain portion of the model consistent with the actual music written by Webern, or ...) [b] Evaluation against good-musical-judgement.

    Are [a] and [b] "legitimate"? Of course they are. Different scientific disciplines use different methods to examine and validate their models. If someone tells you that the only proper method to validate a model is laboratory experiment using textbook procedures, don't believe it. If you look at what scientists do, you will see that much activity concerns simply the development of interesting models. And depending on the subject matter, the "testing" of the model is of greater or lesser interest.

    (My formal academic background is in philosophy/logic. That background is relevant to the issues above. However, I am not a specialist in these issues. It would be good to get some input from a top specialist in History and Philosophy of Science.)









    Isaac Malitz, Ph.D.




  • @IsaacMalitz et al,

    The sub-digression on music theory & science is a blind alley as it is being approached here. The relationship, when it occurs, is not one of membership (as in fitting music theory into the family of sciences), but one of coincidence (as in finding how they inform one another at various significant points).

    Two examples ought to be familiar to everyone here, but it is doubtful that is the case. These connections have nothing to do with Roman numerals.

     (1) Quantum theory (statistical mechanics): Maximally even scales & rhythms are connected to the behavior of charged particles by the same abstract, mathematically identical structures first investigated in music theory; this was a case of music theory informing physics (article in Journal of Mathematical Physics).

    (2) Crystallography: In music theory Hanson first identified "isomeric twins" (also Lewin 1960; later Elliott Carter "residue different" 1965 (unpub.); Forte: "z-related sets" 1977). Around 2008 (Calender, Hall (et al?)) music theorists discovered that this relationship  had been identified & studied as "homometric structures" in crystallography beginning in 1939 with applications to problems in tomography & radar (chemistry & crystallography inform music theory). For nearly 50 years music theorists & scientists were working on the same problem unaware of its application in each other's field; this problem has "partial solutions"  mathematically - but it remains an open problem ... it is still unknown if there is a full solution.

    These are just two of the more startling examples. If you think these are just anomalies irrelevant to the main business, you're in the wrong business as far as I'm concerned. There are more examples especially within musics and between musics. But is it necessary to dot the i's? The name of the game is not name that chord, it's find the connections, both inside & outside, wherever they lead.