Monday, September 24, 2007

Schenker's tonality, Part I

Yesterday I realized that it has been eight years since I thoroughly reviewed the various theories of tonality, when I was studying for my qualifying exams. So I thought I'd create a regular series of posts going through the details of some theories, though the posting schedule will definitely be aperiodic. First I will look at Heinrich Schenker's theory of tonality, as explained in his final monograph, Free Composition.

First, there was the tone. This tone creates overtones, the images of which create the triadic chord, called the Chord of Nature. Most contemporary theorists ignore the chord of nature part of Schenker's theory, for reasons that I listed here. Instead, we accept that Schenker's tonality is based upon the triad, and upon major or minor modes. These postulates are accepted because the music literature of 1600-1880(ish) exhibit this behavior and the analyses based upon Schenker's theory work with this starting postulate. Recent theories suggest that jazz tonality is based upon the seventh chord rather than the triad.

This triadic chord is unfolded through time by stepwise descending motion in the upper voice, from either the third or fifth* of the chord to the root tonic, which Schenker calls the fundamental tone**. Schenker equates this melodic motion, the fundamental line(Urlinie) with our own life-impulses, striving towards a goal. The melodic motion is accompanied by an arpeggiation in the lower voice up a fifth and back down again, as a foundational counterpoint. Why the fifth? From the overtone series, but also from contrapuntal practice: in three-voice strict counterpoint, if the closing scale degrees 2 and 7 are in upper voices, only scale degree 5 is allowable to complete the triad, and was the only leaping bass line found at the close (same as a cadence) in modal counterpoint.

Schenker has a few terms for this counterpoint: background, fundamental structure (Ursatz), and diatony. This fundamental structure is further expanded through middleground and foreground levels by transformations, prolongations, and elaborations, until the actual musical composition is realized (the surface level). The fundamental structure provides the unity, the primary identity of the tonal piece, by marking the goal and the direct path to that goal. Schenker defines "tonality" as the sum of the fundamental structure with all the elaborations and prolongations.

I'll stop here for the first part, quoting from p. 5 of Free Composition:
As the image of our life-motion, music can approach a state of objectivity, never, of course, to the extent that it need abandon its own specific nature as an art. Thus, it may almost evoke pictures or seem to be endowed with speech; it may pursue its course by means of associations, references, and connectives; it may use repetitions of the same tonal succession to express different meanings; it may simulate expectation, preparation, surprise, disappointment, patience, impatience, and humor. Because these comparisons are of a biological nature, and are generated organically, music is never comparable to mathematics or to architecture, but only to language, a kind of tonal language.

Next time I will describe dissonance as it affects the fundamental structure, and begin to explain the transformations that elaborate this fundamental structure.

* Schenker does allow for the traversal of an octave, from root down to root, but later analyses show that he doesn't think it is very common.
**Or at least that is how Ernst Oster translates it from the german.

8 comments:

james cook said...

Yesterday I realized that it has been eight years since I thoroughly reviewed the various theories of tonality, when I was studying for my qualifying exams. So I thought I'd create a regular series of posts going through the details of some theories,

This is a good idea; I look forward to reading more.

First, there was the tone. This tone creates overtones, the images of which create the triadic chord, called the Chord of Nature. Most contemporary theorists ignore the chord of nature part of Schenker's theory, for reasons that I listed here.

I don't quite see how the points you raise in that earlier comment explain why contemporary theorists ignore Schenker's "chord of nature" theory. After all, Schenker's derivation of the elements of tonal music is quite distinct from that of people like Hucbald (the commenter to whom you were responding). For instance, Hucbald says "Harmony is a product of nature, and not artifice." This is quite contrary to Schenker's position -- for Schenker, harmony (and art in general) is the result of applying human artifice to the raw materials given by nature (through such principles as repetition, development, inversion, and abbreviation). In particular, note that Schenker does not derive the diatonic collection directly from the overtone series, as many others have attempted to do; in fact the only use of the overtone series he makes is to derive the "boundary interval" of the fifth, from which he then constructs the diatonic collection in basically the standard way. See Harmony, Ch. 1. (Note the title of §11: "No Overtone Beyond the Fifth in the Series Has Any Application to Our Tonal System")

These postulates are accepted because the music literature of 1600-1880(ish) exhibit this behavior and the analyses based upon Schenker's theory work with this starting postulate

This sounds like Pistonism, i.e. the view that music theory consists of "observations reported"; of course as I have noted in several places before, such "observation" is the task of the historian, not the theorist. The task of the latter is to explain how notes are (or should be) conceptualized; information of this kind does not necessarily follow from information about their behavior. Indeed, for a theorist to fall back on behavioral description as explanation is to commit the fallacy of limited depth and cop out of his/her actual job.

Why the fifth? From the overtone series, but also from contrapuntal practice: in three-voice strict counterpoint, if the closing scale degrees 2 and 7 are in upper voices, only scale degree 5 is allowable to complete the triad, and was the only leaping bass line found at the close (same as a cadence) in modal counterpoint.

See above; the "practice" of modal counterpoint may be part of the "explanation" for contemporary theorists, but it isn't for Schenker, who (in this matter at least) correctly understands what his task is. Schenker's derivation of the bass arpeggiation does not depend at all on the mannerisms of Renaissance composers; in fact, Schenker accounts for such mannerisms by the very fact that the composers in question were dimly perceiving and "groping toward" the principles of music as Schenker conceived them!

Schenker defines "tonality" as the sum of the fundamental structure with all the elaborations and prolongations.

To the contrary, I'm not sure that Schenker defines "tonality" at all; remember that as Schenker conceived it, his theory is not a theory of "tonality"; it is a theory of the "musical artwork".

Scott Spiegelberg said...

Free Composition, Chapter 1, Section 3: "In contrast, tonality, in the foreground, represents the sum of all occurrences, from the smallest to the most comprehensive – including illusory keys and all the various musical forms." (Emphasis in the original translation.)

Chapter 2, Section 2: "I have used the term tonality to include the various illusory effects in the foreground; yet the tonal sparseness of diatony in the background and the fullness of tonality in the foreground are one and the same."

Chapter 2, Section 3: "Contrapuntal practice provides an additional reason for the descending arpeggiation V - I, specifically in the setting-up of the close in three-part strict counterpoint. When both leading tones appear in the upper and inner voices there is only one tone, the root of the dominant, which permits the complete triad to occur in the penultimate measure."

james cook said...

Chapter 2, Section 2: "I have used the term tonality to

Fair enough. Amend my comment by striking out "I'm not sure that Schenker defines 'tonality' at all". The point remains.

Chapter 2, Section 3: "Contrapuntal practice provides an additional reason for the descending arpeggiation V - I,

See Equivocation. You know (or should know) perfectly well that by "contrapuntal practice", Schenker means the theoretical system that he elaborated in Counterpoint (the citation he gives at the end of that paragraph proves as much, in case there was any doubt). He's not talking about "modal counterpoint", i.e. the musical procedures of the Renaissance. (Surely you are familiar with his views on the church modes and pre-Baroque music?). To reiterate: for Schenker, the practice of ("genius") composers derives from the fundamental principles of (his) music theory; not the other way around.

Remember: Free Composition, though it may be the final and most complete presentation of Schenker's theory, is not self-contained; Schenker expects readers to be familiar with his previous work (in partcular with the first two volumes of New Musical Theories and Fantasies -- namely Harmony and Counterpoint.)

Scott Spiegelberg said...

James, how does your point stand? By that very statement Schenker is showing that his analysis is one of tonality. Yes, he uses the theory to argue for the supremacy of the German canon, but through the "fact" that they perfectly express this tonality. From Norman Anderson's dissertation "Aspects of Early Major-Minor Tonality: Structural Characteristics of the Music of the Sixteenth and Seventeenth Centuries": "On a practical level, Schenker apparently sought to rationalize the bases for his music criticism and of his teaching of musical composition. On the other hand, since he viewed compositions that failed to meet the standards of his theory as non-music, one can surmise that he took his theory as embodying a complete definition of music." (p. 24) "Schenker's theory is particularly appropriate for the study of tonality in that it, unlike the theories of music that preceded it, addresses the question of how a piece expresses a particular key." (also p. 24)


As for your claims about counterpoint, where do you think Schenker got the rules in the first place? He started with Johannes Fux's Gradus ad Parnassum which was the synthesis of many previous attempts at species counterpoint to explain how Palestrina and contemporaries composed their music. Schenker does add the organic elements as a reason for these rules: "It was the human voice alone that taught the contrapuntal era a priori to distinguish the true and right from the unnatural. Since its limited range (an average of little more than one and a half octaves) and its emotional involvement in forming intervals results in the truest representation of musical tension, it is - now as centuries ago - best suited to assume the role of guide and judge in the conduct and blending of melodies." (Kontrapunkt Vol. 1, p. 17)

Thus Schenker does attempt to attach psychological explanations to compositional behavior, but he still starts with said compositional behavior as the data, and with Fux's distillation of this behavior. You should read Hellmut federhofer's "Fux's Gradus ad Parnassum as Viewed by Heinrich Schenker" in Music Theory Spectrum Vol. 4, 66-75.

Schenker wrote a short article entitled "Geschichte der Tonkunst" published in an issue of Der Tonwille. Here he posits a history where music has evolved from modality to tonality, though he doesn't use those direct terms. He says "When did it happen that the triads attained their own ordering as regulators of composing-out and became harmonies of a system?" This attitude is also reflected in the first volume of Kontrapunkt and in the 1925 issue of Das Meisterwerk in der Musik.

And as for the psychological explanations, Schenker provides no justifications for these explanations beyond some philosophical musings on organicism. He gives no citations of experimental data, much less cognitive theories that would support his claims. Thus theorists accept that Schenker synthesized beautifully the behavior of compositions from the 17th-19th centuries, using a combination of 16th century species counterpoint with the tradition of Stufentheorie, as a means of describing this synthesis. But not accepting Schenker's theory as one of listener psychology (at least not as he laid them out). Read Davy Temperley's book The Cognition of Basic Musical Structures to get a feel of current research on actual listener psychology. Davy talks about Schenker's views within the book.

james cook said...

James, how does your point stand? By that very statement Schenker is showing that his analysis is one of tonality.

I never meant to claim that Schenker's concepts are of no relevance to modern theorists studying the concept of tonality; I was simply making the point that Schenker did not conceive of his own project in those terms. There is a difference between Schenker's agenda and that of, say, Westergaard (whose theory really is a "theory of tonality").

From Stephen Peles's review of Schenker's Argument and the Claims of Music Theory by Leslie D. Blasius (JMT, vol 45 no. 1, Spring 2001, pp. 176-190):

"It was, to put it mildly, a very selective reading of his texts that
made it possible to assume that our favored explanandum of the 1950s and '60s ("what does it mean to be 'tonal'?') was the same as Schenker's explanandum of the 1910s and '20s ("what does it mean to be a 'musical art-work'?')...There is, to be sure, a theory of common-practice tonality and its psychology to be found in Schenker (probably the best we have on offer), but in its native soil it was but one component of a very different project." (pp. 177-178)

As for your claims about counterpoint, where do you think Schenker got the rules in the first place?

That question is answered in Counterpoint, where each rule is justified in terms of general principles.(Whether or not you think his justifications are satisfactory is beside the point.) In no case that I know of is compositional practice alone invoked as sufficient to justify any precept.

Of course, that's no surprise, since Schenker specifically sets up strict counterpoint as a specialized setting that is distinct from "free composition" (actual music). The difference, on Schenker's view, between contrapuntal theory and actual musical composition cannot be emphasized strongly enough. He was fervently opposed to the idea (which you seem to be perpetuating here, or at least conspicuously failing to disavow) that the subject of contrapuntal theory is the compositional practice of some historical period. Do I need to prove this by quoting from the Introduction to vol. 1 of Counterpoint?

He started with Johannes Fux's Gradus ad Parnassum

What do you mean by "started with"? We're talking about logical dependence here, not historical influence. Nobody in their right mind would deny that Schenker was influenced by Fux; but his task was different from Fux's:

"Fux's goal, the Parnassus he wanted to lead the student to, was the ability to write imitation Palestrina. Schenker's goal...was the ability to understand the complex and varied voice-leading patterns of actual eighteenth- and nineteenth- century music in terms of the simpler patterns available under the artificial contraints of species counterpoint." - Westergaard, ITT, p.vii

You might equally well have said that Westergaard "started with" Fux too -- after all, where did he get the rules (and that old chestnut D-minor cantus firmus) from? But that would be missing the crucial point, which is the very different purposes served by those rules in these respective authors. For Fux, they are aesthetically-derived procedural dictates to be applied in composing music; for Schenker, they describe certain fundamental psychological laws of interaction among tones; and for Westergaard, they serve to delineate a rudimentary form of tonal music useful for pedagogical purposes.

This is not to suggest that there is no overlap among the goals of these theorists; but the context for each of them is different.

[Schenker] gives no citations of experimental data, much less cognitive theories that would support his claims.

It would be silly to demand such things of him, even if he could have accessed that kind of data. That simply isn't the kind of theory that he was proposing.

Scott Spiegelberg said...

I'll point out that I never claimed Schenker called his theory one of tonality, you simply jumped on a very true statement I made in the original post, making a false counterclaim.

Schenker justifies his principles through caveats, and it is clear from his writings that he determined them from the actual compositional practices, rather than starting with fundamental principles based on their own merits and showing how they were then realized. Thus it is an empirical theory, like that of Weber, rather than a speculative theory like that of Rameau. In fact, Schenker complained to Bruckner about the disconnect between speculative theory and compositional practice, that the one did not reflect the actual music being composed. And you should read the Fux/Schenker article I cited, which shows that Fux's goals are not what you (or Schenker) thought they were.

As for cognitive theories or experimental data, how else does one support a claim for "psychological laws?" Psychological laws describe how people perceive something. One can debate whether Schenker meant how all people do perceive music, how all people should perceive music, or how all people could perceive music. Again, read Temperley's book for the pros and cons of these debates. You can also read Brown/Dempster/Headlam's article, "The #IV(bV) Hypothesis: Testing the Limits of Schenker's Theory of Tonality" in Music Theory Spectrum vol. 19, 155-183 to see one claim: "Although Schenkerian theory can be understood in many different ways, we view it as an empirical theory of tonality. [...]We would also expect to find that these derivations are confirmed by the responses of unbiased and suitably qualified auditors. [...] [the theory] tracks native judgments about what is grammatically - or in the case of tonal music, stylistically - well-formed."

So these three set up Schenker's psychological laws to describe how music should be perceived, after a person has become "suitably qualified." Other theorists (Ian Quinn, for one) have taken this article to task for repeating Schenker's failings to provide any such support for the perception claims, much less to provide a definition of what it means to be suitably qualified.

The data and theory Schenker could have accessed would be out-dated by today's standards, but it did exist.

james cook said...

I'll point out that I never claimed Schenker called his theory one of tonality, you simply jumped on a very true statement I made in the original post, making a false counterclaim.

All I said was that I wasn't sure that Schenker had defined tonality. Which was entirely true.

It's not merely a question of what Schenker called his theory; it's a question of how he conceived it. A theory that tells you whether something is a "musical artwork" is an essentially different kind of thing from one that tells you whether it is "tonal" (as opposed to "atonal").

Schenker justifies his principles through caveats,

I don't know what that could mean. To be sure, he gives plenty of examples to illustrate the differences between strict counterpoint and free composition (thereby explaining forces at work in the latter that are not present in the former, forces that he is trying to eliminate in strict counterpoint), but that is different from justifying the rules themselves.


and it is clear from his writings that he determined them from the actual compositional practices, rather than starting with fundamental principles based on their own merits and showing how they were then realized.

Again, you are asserting a proposition of the form "Schenker got the ideas for his theory from observing compositional practice", while I am asserting a proposition of the form "Within Schenker's theory, compositional practice is explained (and evaluated) in terms of fundamental principles". We are talking past each other.

Roger Sessions ("Heirich Schenker's Contribution", Critical Inquiry, Vol. 2 No.1 (Autumn 1975) pp. 113-119) understood the distinction very well:

"Sometimes his methods are logical and incontrovertible; too often, however, they seem arbitrary and speculative in the extreme, dictated by the impulse to find confirmation for an a priori assumption, even when one must admit that this assumption was arrived at only after years of painstaking research."
(p.117)

While I'm quoting this article of Sessions, here is a passage in which he demonstrates his understanding of what Counterpoint is about (emphasis added):

"Counterpoint is here conceived for almost the first time in two centuries, as the systematic and logically developed study of the fundamental problems of voice leading, considered in themselves and without reference to other elements of the musical language. In his view this is the only tenable approach to a real understanding of these problems; to consider (as is almost universally the case in current methods of teaching) the study of counterpoint as in any sense a study of composition is as futile as to regard the highly simplified exercises of a beginner in a foreign language as literature. He therefore rejects as superficial both the empirical and the specifically historical approaches to counterpoint, and devotes himself to the consideration of the facts of voice leading in and for themselves, with a result that is very close to the principles of counterpoint as originally formulated by Fux in the eighteenth century." (p.115-116)

As for cognitive theories or experimental data, how else does one support a claim for "psychological laws?"

I will let Milton Babbitt answer this:

"...the test of Schenker's conceptions is not whether 'one hears that way' but whether, after having become aware of these conceptions, the listener does not find that they may not only codify his previous hearing but extend and enrich his perceptive powers by making listening more efficient and meaningful, by 'explaining' the formerly 'inexplicable', and by granting additional significance to all degrees of musical phenomena." (Review of Salzer's Structural Hearing, reprinted in The Collected Essays of Milton Babbitt.)

In other words, the kind of psychology that Schenker is doing is first-person, not third-person. (There is also a normative component beyond the merely empirical, but that's a separate distinction.)

ThumMeister said...

An article in the forthcoming Winter 2007 Computer Music Journal describes the notion of tuning invariance, which -- when combined with Sethares' notion of aligning the partials of a given tone with the notes of a given tuning -- may have the potential to extend tonal harmony beyond the harmonic series to a wide set of pseudo-harmonic tunings & related timbres.

But you would be better able to comment on this than I. A draft of the paper can be found at http://www.thummer.com/blog/2007/06/isomorphic-controllers-and-dynamic.html.

Regarding the perception of tone, there is some evidence -- albeit exceedingly scant -- that the brain recognizes intervals in a tuning-invariant manner, as described here: http://www.thummer.com/blog/2007/06/bob-duke-first-contact.html

If true, then this could help extend the theory of tonal harmony to embrace the music of non-Western cultures, with the differences disappearing at a sufficiently high level of abstraction. http://www.thummer.com/blog/2007/06/non-western-cultures.html

All of this is grossly speculative at present; your feedback welcome.