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 this group to listen to a pair of works: a sonata by Domenico Scarlatti and a song
by Hugo Wolf - 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 (ex. 1A) 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.






Ex. 1B is my rewriting of 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, Ex. 1C, 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 (Ex. 2A).  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?

Ex. 2B is a rewriting of this song which 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?


Ex. 2C offers 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 Ex. 2C 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 that 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 first
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
pitch 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 they began in?  

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 an 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?)