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Introduction to Schenker for Freshmen
Allen Gimbel

Lawrence University, April 1995

The following lecture was given at Lawrence University's Conservatory of Music, Appleton, WI, April, 1995, in order to introduce third term freshmen to Schenker's ideas. The analyses of the Haydn (the St. Anthony Chorale, used by Brahms in his 'Variations on a Theme by Haydn') and the theme of Mozart's A Major Piano Sonata first movement variations are taken from Allen Forte and Steven Gilbert's textbook, 'Introduction to Schenkerian Analysis', but presented here with some freedom of expression. I would like to thank Professor Lorna Peters, then at Lawrence and now professor of harpsichord and piano at Sacramento State University, for assisting me as pianist in this lecture. It is hoped that the musical examples will be attached at a later date, but I think they may be deduced from the text and/or the aforementioned textbook.

*****

[Play St. Anthony Chorale, Masur]

"... I hear present a new concept, one inherent in the works of the great masters; indeed, it is the very secret and source of their being: the concept of organic coherence." (FC p.xxi)

This quotation is not from Payne/Kostka; think of how unlikely it is that such a passionate, assured statement would be found in a contemporary American textbook (in any field!) Its source is the introduction to Heinrich Schenker's "Free Composition" (Der Freie Satz), the third (and final) volume of his vast treatise entitled "New Musical Theories and Fantasies", written sporadically between 1906 and 1935 (the year of his death). Schenker sought to transform the way we think about "common practice" tonal music in reaction to 1) atrociously dull, lifeless, and unmusical theory teaching and 2) the wave of modernism that he saw as causing the death of great musical art as he understood it. The first volume is entitled "Harmony", the second "Counterpoint" (itself in 2 volumes), and the final installment "Free Composition" (Der Freie Satz). Like any great work (and let me assure you this is a very great and imposing work), one could spend several careers involving oneself in its interpretation and application (not to mention its attempted refutation, as well as its expansions and refinements): it is, in other words, a model of what Thomas Kuhn would call a "paradigm".

Schenker was not the equivalent of what we in America know as a "Professional Academic". He was the product of the kind of education a promising student with a musical and philosophical bent would get in late 19th century Vienna. He received his terminal degree at the University of Vienna in music, and that meant philosophy -- the two departments were one and the same. Schenker was a fine pianist, and spent most of his life as a local piano teacher (Greta Kraus, one of his students, still teaches at the University of Toronto and is a close friend of your Dean, Robert Dodson). He was also active as a critic; in fact, one rather well-known composer went so far as to refer to him as "our only critic" (his name was Johannes Brahms). Not only could he theorize you under the table, but by all accounts play you under it as well. So it must be remembered that Schenker's theories were written not only for the purpose of articulating a beautiful and profound poetic vision (as if there were something suspicious or pretentious about that) but also to have an effect on performance. (It certainly did -- the great conductor Wilhelm Furtwängler used Schenker as a consultant throughout his career, and that is only one example.)

My talk today is intended to give you an introduction to Schenker's theory of organic coherence in music. The search for unity -- organicism -- was of fundamental importance for intellectuals at this time, perhaps because the world around them was so obviously falling apart. (This might also explain the intense interest in Schenker's work in our time.) At the same time, challenges to such a conception were making themselves felt, as they continue to be today. It is a remarkable fact that Schenker appealed to Einstein (of all people) for help in securing publication for this book, which is so contrary to any relativistic conception. But Schenker clung to the idea of functional tonality as an ideal, flawless system, one that could serve as a playground for the musical fantasies of those who most reasonable musicians consider to be the greatest musical geniuses of all time.

Schenker sought to discover how the musical genius's mind worked. His strategy was to poetically invoke what he termed the "composing-out" process, in order to trace, step-by-step, the path from the nature-given acoustical entity -- the triad -- to, say, the St. Anthony Chorale. In other words, this is a Generative theory: it explains how the chorale is literally generated through a number of definable, yet probably intuitive, processes. This is the subject of "Der Freie Satz". Let's trace this process in the St. Anthony Chorale, beginning with its A section.

[Play A section]

All tonal works begin with the concept of the triad. A triad may be voiced in three ways: with the third on top, with the fifth on top, or with the octave on top. The composer begins by choosing a voicing. Here Haydn (for whatever reason) chooses to write in B-flat major, and senses a work that emanates from the voicing with the third on top.

[Play Bb major triad with 3]

A vertical sonority does not take up that much time, however, and the artist must find a way to turn this vertical sonority into a horizontal entity: in other words, he must "unfold the primal sonority in time." In order to move smoothly from the third of the chord to the Bb, we insert a passing tone c. We now have taken 3 times the amount of time it took to simply play a B-flat major chord! To clarify this motion, we counterpoint (or harmonize) these tones with a bass line related to our originary triad (Bb, F, and Bb): we have created a simple I V I progression.

[Play ex. a]

This simple tonality-defining structure may be interpreted as "what it means to be IN Bb major, specifically when we begin with scale degree three in the soprano."

"But it's all over too fast " (says Haydn). "I need to PROLONG the structure further -- after all, I'm trying to write a piece of music! What if I INTERRUPT the progress of these three chords by inserting a V chord after the initial (melodic) d, and then retrace my steps and resolve the structure, like this.

[Play level b]

This is now five times longer than my initial triad! I think I'm starting to get the idea. I think I need to prolong this structure, too. But how? Let me examine my musical materials and see if anything suggests itself. There sure is a lot of d, c, Bb in this piece. What if I prolong ALL the ds with d c Bb? I think I have a MOTIVE, and it's really beautifully integrated, ja? And I just had another really delectable idea, since using the same chords to harmonize these notes might get boring -- I could give the first two Bbs a deceptive vi chord rather than a I.

[Play level c]

So I've created (procreated) two baby d c Bbs out of the big (though interrupted) d c Bb. Is everybody following me? [Pause for questions] I think it's time for a little contrast. What if I prolong the prolongations? Let me think of my catalog of usable DIMINUTIONS in tonal music. I've already used passing tones, filling in portions of my original triad (FILLED IN CONSONANT SKIPS). How about decorating my ds with a nice E-flat neighbor note?

[Play d eb d neighbor figure]

Since I decorated the d, I should probably decorate the c, right? (that is, the first c of the interruption -- the first beamed c in ex.c). I just introduced this new note (eb) as a neighbor note -- what if I used the same note to get to the c, and insert a passing tone d to get to the c? This is another 3-LINE (eb d c), which not only relates by transposition to my CONTROLLING 3-LINE (d c Bb), but incorporates the same pitch class (eb) as my new neighbor note diminution (d eb d d). (Note the bracket on the graph (ex. d) which shows the MOTIVIC PARALLELISM between the two 3-lines, d c Bb and eb d c).

But wait. The cadences in each part of the INTERRUPTION are different -- the first is a half-cadence (c over F), the last is a PAC (B-flat over B-flat). (I am at the cadences of both phrases.) The functions of the Cs are thus different. The final C could take another three-line, descending into the inner voice a (see the bracket on the example), and by so doing I have created a third motivic parallelism: d c Bb, eb d c, and now c B-flat a. And note that all of these GROW from the simple cadential premise exposed way back in ex. a.

Now to harmonize these motivic units. Let's look at my neighbor note figure: d-eb-d. How about I-IV-I! And IV is an Eb MAJOR CHORD!!! Perfect. What should I harmonize the diminutions around C with? Eb-d-c could be harmonized with a ii6, which also has an Eb in the bass! These pitch class correspondences (the omnipresent ebs) could provide me with more material for later on, even though we are only talking about an innocent sounding single note. Can a single note be motivic?

Let's see how it sounds.

[Play level d]

Where have I heard this before? It sounds like Brahms (no, that's impossible, he hasn't been born yet.) Anyway, I think I'll try to imagine what this might sound like orchestrated.

[Play Masur recording of "a" section]

Very nice. But it's not long enough. I'll repeat it, but I need a contrasting middle section. Since I think this is going to be a rounded binary form, it would make sense to prolong the dominant while using material I have already presented. Now, let's see if I remember my Freshman Theory. How do you spell a V chord in B-flat major? F-I-V-E -- no, wait, -- F A C. But the tune is going to return, which means it's going to begin on a D. If I prolong a V7 chord --F A C Eb, using the Eb as a goal, -- I can create a very large-scale version of my neighbor note motive, d eb d -- an immense version of THE FIRST THREE NOTES OF THE PIECE!!! The head note of each phrase in the a section is D (D c, D c Bb). Now the goal tone of my b section would be Eb, and the headnote of the recap would, of course, be D. I would have another one of my motives existing on MORE THAN ONE STRUCTURAL LEVEL!

Now, what should I use to prolong this V7 chord? A simple way would be just to move from its lowest voice (F) stepwise to Eb, and then descend stepwise, maybe to the inner voice a.

[Play "b" section, ex. e ]

Not too interesting melodically, but it has a nice beat and you can dance to it. I think I'll prolong the prolongations -- how about with my neighbor motive?

[Play "b", ex. f]

Too many neighbors. When I get to the Bb, it seems that I need to stop the neighbor notes. I'll just eliminate the rest of them and keep on going, and then resume them when I begin the descent from Eb. So the "un-neighbored" notes would be Bb, c, and D. Something sounds familiar and I know why! It's my d c Bb motive backwards! But I can counterpoint it with a VOICE EXCHANGE to bring back my ORIGINAL motive (now in the bass), and produce a phrase which contains all of my main materials (the neighbor motive, the filled in interval of a third, and even my Eb), all at closely interacting but differing structural levels. All that remains is to harmonize the remaining pitches tastefully, and my b section is complete.

. To finish off my little piece, I'll just bring back the consequent of "a", and improvise a little coda. Since I'm a genius, I won't have to think too hard about it, but can YOU tell me what the coda is all about?

[Play b section with a' and coda]

And that is a generative analysis of the St. Anthony Chorale. It has shown us that the piece is built on two motives: a three-line, and a complete upper neighbor figure. Every gesture in the music is intimately related to the interaction of these two motives, and in fact this interaction extends beyond the realm of melody into elements of larger scale, such as choices of harmony (remember the b sections' V7 chord) and elements of form. But most importantly it illustrates Schenker's idea that the most complex surfaces originate from events of the utmost simplicity.

The interaction of these simple events even affects rhythmic choices, an aspect which Schenkerian analysis is often accused of ignoring. You will eventually learn (if you haven't already) that the 4-bar phrase is considered to be the norm in common practice tonal music. Schenker puts it this way:

"Since the principle of systole and diastole is inherent in our very being, metric ordering based on two and its multiples is the most natural to us." (p. 119)

Note again that the metaphor employed is a biological one.

Keeping this in mind, note that the two phrases of the St. Anthony Chorale's "a" section are actually FIVE-BAR phrases. Which is the extra bar? A little experimentation will reveal that the chorale sounds utterly normal (and banal) if one eliminates bar 3 (and 8).

[Demonstrate]

What does the extra bar contain? It contains, of course, a closing off of a statement of our 3-line -- naked (un-prolonged), but demanding continuation because of the deceptive cadence --, and thus our first encounter with this crucial motive.

How crucial is it? We have already seen it in various manifestations, but let me alert you to yet one more. The work begins with D (over Bb), and closure is achieved at mm. 22-23 with a final statement of C (over F) and Bb (over Bb -- the fact that D is covering this final Bb makes it no less final, but this situation would lead us to far afield for right now). This means that the ENTIRE WORK is framed (or "controlled") by one large statement of D, C, and Bb. That is, it's not "merely" in B-flat major, but is IN the B-flat major with scale degree 3 on top, closing through a harmonized passing tone (C over F) and onwards to its root, Bb over Bb. And this D C Bb is, of course, motivic.

We are speaking here of STRUCTURAL LEVELS (or as Schenker puts it, TRANSFORMATION LEVELS). Our D C Bb which controls the whole piece is referred to as the BACKGROUND level; the D c Bb which occurs between measures 1 and 3, a prolongation which is itself prolonged, is referred to as a level of MIDDLEGROUND, and the d c Bb which occurs as the bass of the voice exchange in m. 14 would be considered FOREGROUND, because it contains no deeper level expansions.

Schenker only presents 3 possible backgrounds in tonal music, because there are only 3 possible voicings of the triad. These are presented for you on your handout. The concept of background is very abstract, and causes problems for some people. But all it really is is a definition of the term "functional tonality", and thus is only of concern to those who shy away from attempts at precision. We have already seen how profound this concept can be in its less abstract manifestations, that is, when it appears at transformation levels closer to the surface of the music. Can awareness of such concepts have any bearing on musical performance?

Let's compare 2 performances of the St. Anthony Chorale. I should warn you that the first performance (the one we've been hearing) is on a recent glitzy CD, and the second is an LP from the early 1950s with an oboist whose sound might not be appealing to some of you. But listen and see if you can see the point I'm trying to make.

[Play Masur "a" section, then Knappertsbusch]

The first performance, by the New York Philharmonic under Kurt Masur, PLAYS the work, with fine intonation and balances. The second performance, by the Vienna Philharmonic under the great Wagner conductor Hans Knappertsbusch, SHAPES the work, bringing out the interplay of structural levels through the use of dynamic shading. More specifically, the oboist is attempting to bring out the linear progressions of a third, that is, our crucial d c Bb motive. Schenker puts it this way:

"The player who is aware of the (organic) coherence of a work will find interpretative means which will allow the coherence to be heard. He who performs in this way will take care not to destroy the linear progressions; such destruction would paralyze our participation." (p. 8)

[Play Knappertsbusch again]

No such shaping exists in the Masur recording -- its character is more that of a professional run-through, which I am quite sure it is. And although I have no evidence or this, I would be quite astonished if Knappertsbusch was unfamiliar with Schenker's work, given its circulation in German-speaking countries before the war (incidentally, Schenker's works were suppressed during the Second World War by the Nazis, since Schenker was Jewish.)

You may be wondering how one generates a generative analysis. It is a fatal mistake to begin analysis generatively. Instead, one proceeds REDUCTIVELY from the surface of the existing music in order to reach the background's FUNDAMENTAL STRUCTURE, the combination of the upper voice line (the FUNDAMENTAL LINE) and the counterpointing BASS ARPEGGIATION. As Schenker puts it: "I did not invent the fundamental line: I observed it."

Let's pretend you were playing Mozart's Piano Sonata in A Major, K. 331 and wanted to know what was going on in it. Let's listen to the opening of the first movement's theme, and proceed to construct a REDUCTIVE, rather than generative, analysis.

[Play theme, A section]

Now THIS is what they do in Dr. Gimbel's mysterious theory class! (And it's not ALL they do!) We begin by locating the HIGHEST ACTIVE HARMONICALLY-SUPPORTED VOICE. This is a bunch of highly loaded and supremely significant requirements, and Schenkerian analysis is utterly dependent upon them. They are loaded because they contain two crucial Schenkerian axioms: 1) that tonal music is controlled by the counterpoint of the OUTER VOICES (not by "chords"), and 2) that tonal music "moves" through time linearly, and LINE is defined as STEPWISE MOTION. A voice is active if there is a linear connection to it, and this is the kicker: if there is a linear connection to it AT SOME LEVEL.

A further axiom involves the notion of HARMONIC SUPPORT. In your study of harmony, it becomes all too easy to get the idea that, being American, all vertical sonorities are created equal. But in tonal music this is clearly not the case. As Allen Forte and Steven Gilbert put it so concisely in their textbook "Introduction to Schenkerian Analysis" (pp. 105-6):

"The basic large-scale harmonic progressions (in tonal music) are two in number: I-V and V-I."

We therefore look for tonics and dominants to support linear elements, which are being PROLONGED by ornamentation in the form of passing tones, neighbor notes, consonant skips, and most crucially, imaginative combinations of the above. It is through these ornaments, or DIMINUTIONS, that motives are created, and thus the individual content of each work of tonal musical art.

Looking at the Mozart example, and keeping the above comments in mind, we see that the highest active voice in this section is a motion from E to d to c# to b, at which point the second phrase begins, initiated by a return to E, which retraces its steps until it cadences on A in m.8. Are these notes harmonically supported? The E is supported by a I chord, the d by a vii (or, better, and incomplete V 6/5), the c# by I, and the b by V. The motion is INTERRUPTED, and then retraced until the cadence on a over I in m.8. (This is a "period with interrupted harmonic movement" -- as was the Haydn "a" section -- according to my analysis teacher, Douglass Green: now you know where he got the term from.)

So E d c# b and later a are our STRUCTURAL PITCHES, which are stemmed and, in this case, beamed to show the interruption, which controls the voice leading of the passage. What remains are consonant skips originating from the inner voices of the harmonies of each structural pitch. (See the arrows on your handout.) These inner voices are themselves prolonged by upper neighbors (on the inner voices c# and b), a passing tone (between a and c#), and a remarkable event involving the b. The b is prolonged by the notes e d and c#, and thus we see that the resultant figure (e d c# b) is a summary, at the foreground level, of the first half of the interruption controlling the voice leading at the middleground. A summary of these events may be studied (I hope) on your handout.

What happens in the B section?

[Play B section]

Following the highest active harmonically-supported voice here reveals a simple motion from E over I to f# over IV 6/4, with an immediate return to E over I. If you've followed my lecture to this point, you should be able to guess my next observation. The B section represents a middleground expansion of the upper neighbor figure we heard in the inner voice at the foreground level at the very beginning of the piece (as c#, d, c#) and it has now been "elevated", so to speak, to the upper voice (now as e, f#, e). The return of the A theme completes the resolution of the E through D, C#, B, and finally A. Unlike our St. Anthony Chorale, we may safely conclude that this is a FIVE-LINE emanating from E at the background level, and may then, if we wish, construct a speculative generative analysis filling in middleground constructions following suggestions of their content as set forth by Schenker in Der Freie Satz. We could also productively think about our analysis and its performance implications.

We've seen that the piece gradually elevates our neighbor note figure to a place of prominence, from inner voice to upper voice, and thus inevitably to the controlling melodic factor (E2) of the whole piece. How might one make this pitch grow to prominence, gradually and yet inevitably? Taking the repeats certainly gives us more time to pursue this growth process, and it should be clear that merely playing the music the same way twice does nothing to involve the listener in this remarkable little drama. How does the drama develop in the 6 variations that follow?

There is, I hope obviously, a great deal more to say about this theme, but I will leave it at this point so that we may sum up, and hopefully leave some time for questions. I hope that I have shown you why Schenkerian analysis has fascinated so many musicians in the latter half of this century, and indeed continues to do so. In our "Stop Making Sense" culture, it is often difficult to see why we should spend our time contemplating the products of genius at all, rather than letting them simply wash over us in a sensual splash of hysterical aesthetic pleasure. The student may ask: "Did these composers really think of this while they were writing? If they did, why didn't they tell us? And since they didn't, why should I care?"

Schenker answers this question right off the bat in his introduction to "Free Composition". He writes:

"This objection, intended to be a trap, only betrays a lack of education... The objection can be answered very simply: the great composers in their works have shown a mastery which evinces, both in preconception and in total recall, such a clear overall comprehension of the laws of art that they need say no more to us; of necessity, every artistic act -- indeed any action at all -- requires a preconception of inner relationships." (p. xxii)

Yet our culture bristles at such notions as "great composers", "masterwork", or "genius" -- even the term "perfection" is suspect, all because these notions are not necessarily open to the Common Man, or because these terms are so often bandied about that they have themselves become meaningless. Schenker addresses these issues in his early collection of essays, "The Masterwork in Music", and I will leave you with his comments in order to remind you that the sandbox that you are all in some sense playing in needs to be tended very carefully, since it is all too easy today for someone to jump in and burn it down:

"Perfection is true life, a true eternity: in opposition to it stands non-perfection, non-fulfillment as an incapacity for life, ultimately as stagnation and death. However energetically... the non-fulfillers may set about their toil and strife, they still do not partake of the eternal life of the idea: they withdraw from it... Merely to share in the masterwork is a truer life than to waste away in non-fulfillment. In this sense, the masterwork is the only path for those who have not had the calling (that is, to produce masterworks). Today more than ever, in the darkness of stagnation, it is the only possible way out of the chaos and confusion, the only light that points toward the future."

Heinrich Schenker
Vienna
30 August 1925

Thank you.

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