IS TONAL UNITY A MYTH?
For some time now I've wanted to explore the possibility that tonal unity - the idea that a composition gains coherence by virtue of starting and ending in the same key - is a myth. I admit this contradicts common sense, since almost all works from the common practice period end, in fact, in the keys with which they begin. But is this unity of key something we hear, or is it something we see? Is it possible that the growth of a literate musical tradition over the last several centuries has led to a confusion (shared as much by composers as by performers and listeners) of notation and sound?
To address this possibility and to answer these questions I devised an experiment. I selected a group of listeners that I see as fitting into three categories. The first category consists of musical amateurs and musicians with a background in popular music. The second category is comprised of professional musicians (and students of music) with perfect pitch - the ability to distinguish precise frequencies. The third category- the largest group and the one for whom the study is primarily designed - is made of professional musicians (and music students) without perfect pitch, but with acute relative pitch - the ability to discern relations without knowledge of key.
I asked these people to listen to a pair of works: a sonata by Domenico Scarlatti (K 518 in F major) and a song by Hugo Wolf ( In der Frühe) - a selection that spans the gamut of the common practice period, that period which lays claim to the efficacy of tonal unity. None of the listeners was well acquainted with either work.
Each piece was performed three times. One performance of each piece was faithful to the original notation and exhibited tonal unity. The other versions were altered so that the ending key, in each case, was different from that of the beginning. The listeners were asked, in each case, which performance exhibited tonal unity? If a large majority answered correctly, that would seem to prove that tonal unity is no myth, but an aurally recognizable phenomenon. If a majority answered incorrectly that would indicate guess- work, and suggest that the presence - or absence - of tonal unity is of negligible significance in our perception. The musical examples, though highly contrasting in style, share a richness of chromaticism: the frequent and distant changes of key in both works render the prospect of an ultimate return to the tonic either supremely dramatic and effective or completely arbitrary and useless.
What's at stake here, of course, is not merely the question of whether or not tonal unity is perceptible at a conscious level, but whether its presence enhances (or its absence detracts from) the coherence of a work. While that question has relevance for all the categories of listeners, it's probably most difficult for the perfect pitch people to address, since it's hard to separate an objective knowledge of key relations from a subjective judgment of aesthetic values.
Indeed that's the circumstance I find myself in as a musician possessed of perfect pitch.
I am intrigued by the question of the significance of tonal unity at the same time that I am unable reliably to form an opinion of its merits, prejudiced as I am by the cultural suppositions that lurk behind the ordered musical notation. I can identify the opening key of a piece and recognize its final return, but I can't say for sure, after all that's transpired between these events, whether it matters.
The questions I am raising here go beyond those asked in scientific studies on the perception of pitch. Such work, though highly illuminating, tends to avoid confronting the artistic repercussions of its own findings. I should also state that I am aware of the formidable body of scholarship performed in the name of Schenkerian analysis that bears on the topic of tonal unity. But it seems to me that Schenkerian work, by its nature, assumes the efficacy and perceptibility of tonal unity. This paper questions that fundamental presupposition.
Before proceeding to an examination of the pieces chosen, I should acknowledge that there do exist works from the 18th and 19th centuries which end in keys other than those in which they begin. One famous example is the Crucifixus movement form J. S. Bach's B minor Mass. But the scarcity of such instances compels us to seek reasons for such exceptional behavior and, in the case of the Crucifixus, explanations are not hard to find. The movement is a Passacaglia with twelve repetitions of a bass pattern in the key of E minor. Tonal unity (symbolizing the brotherhood of the Apostles) is betrayed by a modulation to the relative key of G in the thirteenth and final variation (representing the treachery of Judas, the "false disciple"). Ironically, this exception proves the rule: Bach clearly intended the unusual ending to provide his listeners with a disconcerting impression that audibly contradicts the expectation of closure and wholeness he evidently believed arises from his customary employment of tonal unity.
Let's examine the Scarlatti sonata first. Like almost all the composer's hundreds of sonatas, this one is in binary form, but here the tonal plan is unusual. Beginning in F major, the first section cadences, not on the expected dominant, but on the mediant, A minor. The second part commences in the parallel key, A major, and, through a series of chromatic sequences, returns, with Scarlatti's characteristic unobtrusiveness, to the tonic, which receives an expansive diatonic treatment to balance the earlier instability
In my first alteration of K 518 I rewrote the last portion of the first section and all of the second section. The change I make is simplicity itself: in ms. 39 of the original, Scarlatti arrives in the distant of G sharp minor - and so do I. But whereas, from 39 to 48, he embarks on a complicated transition to arrive in A minor, I simply omit those measures and cut directly to 48 where I resume his music but still in G sharp minor, a half step lower than the original.
Thus my revised first section ends in that key, and my second section begins one measure later in its parallel major, enharmonically A flat major. Having made my move, I simply stick with it, transposing the whole second part of the sonata down a half step so that the piece ends in E major.
Some might argue that, in performance, if the repeats are taken, the move from G sharp minor back to F major might seem jarring. And so I've devised an alternative, second alteration, in which the changes occur after the first double bar. In this case the rewriting starts at ms. 85 where I heighten the suspense by employing a deceptive cadence in the key of A minor. I then construct a six-bar phrase utilizing the jumping octave motive found in the previous two phrases, along with what I hope is a convincingly Scarlattian progression that leads to F sharp major in ms. 90. In the original this marks the return of the tonic, F major, but in this version, from here to the end, all is a half step higher.
Now let’s look at the Wolf song (In der Frühe). The tonal plan is common in Romantic music: a murky opening in D minor is redeemed, after much and dissonant wandering, in the parallel major. (The scheme is found not only in miniatures such as this, but in larger works ranging from Beethoven's 9th symphony to Schoenberg's Verklaerte Nacht.)
But this is not a fair example! one might exclaim: D minor is not the same as D major - though the tonic is not changed, the alterations in harmonic quality, along with changes of register, texture and melodic style, conspire to make the apprehension of tonal unity problematic!
Ah, but a look at the score would seem to reassure us. That glorious final key change with its two sharps cries out in a kind of tonal affirmation of the text: morning is here, nighttime phantoms are dispersed, all is well again in this same place!
Wolf's scheme in the second part of the song - a rising chain of mediants - signifies the brightening dawn. Especially felicitous is the ending: after a series of minor thirds - from E to G to B flat - one might expect yet another, which would place us in D flat, condemned to the kind of quasi-octatonic circularity in which tonal hierarchies dissolve into predictable symmetries. But the composer breaks this cycle: ascending a major rather than a minor third, and (to our delight) placing us in the tonic key of D.
Yet, this paper asks, after so much tonal wandering, is this delight in return a visual or an aural experience, is it something we read in the notes or something we hear in the tones?
My first rewriting of this song puts that question to the test. On the second page of the score I retain Wolf's first three keys, E, G and B flat. But I alter the quality of the chord on the last beat of ms. 17 so that B flat becomes a dominant. The last phrase I place in E flat, a key, according to the rationale of the circle of fifths, considered distant from the tonic (as were the keys of E and F sharp in comparison with the tonic F in the Scarlatti examples) - but a key, in terms of absolute pitch, that's right next door to the original tonic of D, a half step above. Is it possible that listeners will find my solution provides a more convincing sense of closure, as, for the only time in the song, a conventional V - I resolution is heard?
I also composed an alternative rewriting of this piece. Again my changes commence on the last beat of ms. 17 where I transform B flat from tonic to dominant. But in this case a deceptive resolution to flat VI ensues, and this flat VI (enharmonically B major) persists, attempting to usurp the position of tonic by mere, blithe obstinacy. This is the kind of game Haydn made famous in his recapitulations - except, of course, that in such cases the preparation for the returning tonic was calculatedly "wrong" so that the deceptive resolution emerged "by surprise" as the "right key.” My quotation marks betray my skepticism about such procedures, while this version provides a challenge to their efficacy.
Before getting to the results of the experiment, I shall attend to certain objections that could legitimately be raised. Purists of Baroque performance practice might point out that Scarlatti played and heard his sonatas on a variety of keyboard instruments (though not a pianoforte) and that these instruments might have employed a number of temperaments (but not the absolutely equal temperament with which the modern musician is familiar). The small but perceptible differences in the size of the half steps that existed even in the well-tempered system advocated by Bach endowed each tonality with a subtle individuality so that, beyond mere differences in frequency, keys such and F and F sharp were distinguishable by character. It seems to me this is an important issue - one that might be explored through an experiment like ours. Indeed, I would say that, if tonal unity is more appreciable in the older methods of temperament (and if its absence proves more disconcerting), then maybe the current practice of tuning in the performance of Baroque music should be reconsidered.
It might also be objected that tonalities are easier to distinguish from one another on certain instruments. Mahler's 9th symphony starts in D but ends in D flat - a very rare exception to the symphonic practice of tonal unity - and the ethereal quality of the coda seems bound up with the muted string sonorities unique to the latter key. I would acknowledge the significance and effectiveness of the composer's choice; at the same time, I would wonder whether anyone in the audience, after all the time that's elapsed, has any recollection of the first movement's key to compare with that of the last movement.
RESULTS
Our first group of listeners, non-literate musicians and amateurs, acknowledged overwhelmingly that they had no idea which versions were "correct," either by recognizing the return of the original key or through a general sense of coherence.
The second group, musicians with perfect pitch, had no difficulty (as one would expect) in choosing correctly, but asserted almost unanimously that the altered versions were no less satisfying or complete than the originals.
Literate musicians without perfect pitch but with keen relative pitch (the core group for whom the study was designed) chose correctly in most cases. But the reasons given render their verdicts problematic. For most listeners in this category, the determination was made, not through a feeling that the original key was recognized at the end, but by a sense, expressed in various ways, that the other versions did something weird. These listeners heard certain passages - either highly chromatic or unusually dissonant ones - as evidence of my tampering. But each such listener located the aberration in a different passage from those chosen by the others, and, in almost all such cases, the passages in question belong to the authentic version.
A number of listeners in this last category confessed to having attempted to follow the key changes so as to keep track of the tonal scheme, but all such attempts led to confusion, as the music outstripped the ability to calculate. One listener heard small but significant changes in timbre from one key to another and used this difference to distinguish between black and white keys. (This is close to my own type of perfect pitch, most reliable on the piano where, since childhood, I have associated each key with certain vowel sounds.)
To summarize: non-literate musicians and amateurs can't tell, musicians with perfect can but feel it doesn't matter, and literate musicians with good relative pitch mostly choose correctly but for the wrong reasons.
Is tonal unity, then, a myth? The ambiguous nature of my findings leads me to believe that this question was posed naively. People attend to music with varying degrees of perspicacity, and even among the perspicacious, people listen with various focuses and emphases.
Acknowledging all that, it's safe to conclude, in a general way, that tonal unity is not a myth, but that, while it's a perceptible phenomenon, it tends to be overrated. We hear it, but its impact on the coherence of a work seems negligible. The prestige that has accrued to this practice (evidenced by its virtual universality) is, I believe, accountable in some degree to the literate tradition which it exemplifies: it looks more important than it sounds. Notation has seduced centuries of musicians into confusing what they notice with their eyes and what they perceive with their ears. A literate tradition emerged in western music with the purpose of preserving that most ephemeral art, and wound up transforming it in unexpected ways.
But really, has any harm been done? Has music from the last three hundred years suffered from this delusion? Would these works have profited from eschewing tonal unity, scrupulously ending in keys other than those in which they began?
Certainly not. The music would not have been better - but neither would it have been worse. And that being so, we are compelled to ask why. Why doesn't tonal unity matter? I would propose two main reasons: 1) Equal temperament makes all keys sound the same. 2) Individual pitches performed on instruments with pure timbres lack character.
Let's first examine equal temperament. A modulation is a kind of promise - that we will be transported, taken somewhere new, shown something different from what we know. Equal temperament generously offers to take us anywhere we might wish - but only by sacrificing the individual characters of the keys, with the result that the promise is unfulfilled. We get on a train, we feel the thrill of movement beneath our feet, we gaze with expectation out the window at a landscape blurred by rapid motion. But when we arrive at our destination and the door opens, we find ourselves in another place that is exactly like the place we were before. No deliverance, no transcendence, no breakthrough.
We are like that character from the children's book, Fuzzy Fogtop who, believing he has been taken from one city to another on a train that never departs, exclaims, "Minsk is exactly like Pinsk!"
"...But completely different," he adds, and I would agree: Modulation is not wholly an exercise in futility. It really does impart an audible sense of movement, and music tends to convey a greater sense of drama in proportion to its tonal restlessness. But this feeling is located in the modulations themselves, those transitional areas filled with dissonance and expectation, those magical moments when we seem to slip through a trap door (or, to use a more fashionable comparison, through a wormhole). The letdown comes upon arrival, when we recognize a redundant landscape as the price of ubiquitous key change.
The second explanation I would offer as to why tonal unity seems not to matter is that the instruments most prominent in the stylistic period we are examining possess relatively pure timbres, producing clear and clean pitches which lack the character necessary to be remembered. Of course, this purity, this clarity of pitch, allows for the virtually endless combinations of these pitches, but it renders them neutral as individual sonic events. They are in some ways akin to the letters of modern alphabets - small, simple, individually meaningless elements which, thanks to their simplicity and brevity, can be strung together to form meaningful aggregates - memorable tunes and colorful chords. And that, of course, is what we could all agree we do recognize in musical listening: the return of a theme or the transformation from a minor to a major key harmonization.
In such music the pitches function as building blocks, and so our attention naturally focuses not on their frequencies but on the larger, highly distinguished gestures they combine to produce. Thus, while only some musicians possess perfect pitch, all good listeners, by definition, have relative pitch, which we may define as the ability to perceive relationships among pitches without an awareness of what their individual frequencies are.
Now we can summarize:
1. Tonal unity is a not a mere myth: most literate musicians, even without perfect pitch, can distinguish it. But it seems that neither does its presence enhance, nor its absence detract, from the coherence of a piece of music.
2. The mystique (if not the myth) of tonal unity arises from the confusion of notation with sound: listeners, composers and performers cherish ideas about music based on visual rather than aural perceptions.
3. The reasons why tonal unity, recognized or not, makes little contribution to a work's coherence are:
A) In equal temperament all keys sound the same, and
B) Mere pitches lack the requisite character to attain memorability.
Since I have suggested that our faith in tonal unity is connected to our dependence on
the visual cues of notation, it is logical to ask whether, in non-literate practices of music- making, where no written score exists, tonal unity is any less conspicuous.
In addressing this question I shall leave aside consideration of all non-western and ancient music as transcending the limits of our present inquiry - though of course, in a diatonic system lacking in modulatory procedures, tonal unity will exist of necessity. Within the realm of the common practice period there exist certain genres - Fantasias, Toccatas and the like - which point beyond their own historical period to a tradition of improvisation. It is remarkable that, as a rule, such works display a bewildering restlessness of key. One wonders if, in these latter-day "notated records" of improvisation, as they are sometimes characterized, the composer has imposed an artificial tonal unity on the piece, whereas - who knows? - the original performer on whose improvisation the score is based, ending the piece when he needed to (or when circumstances required him to) might not even, at that moment, have remembered the key he began in, contenting himself with the momentary satisfaction of authentic cadence.
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I'd like to end with the reminder that, just as there are things in notation that can't be heard, there are things in performance that can't be written down. Together - along with the tactile dimension of understanding that comes from playing - they constitute the full meaning of music in a literate tradition. From this vantage tonal unity emerges as a kind of idealized dream of order, the contemplation of which requires us not only to listen but to listen while reading along. I am not advocating bringing your score to a concert (though as an enthusiastic undergraduate I did, even to the opera house, to the dismay of my neighbors). But a complete appreciation of this kind of music, like a complete appreciation of much literature, is possible only with recourse to its written form. The myth of tonal unity, like all myths, is meaningful, and its effects are enjoyed, not in the mundane world of what merely is and sounds, but in the rarefied realm of ideas. (Have I ended on different note from the one on which I began? Did you notice? Does it matter?)