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Program Notes: Filippo Gorini

Johann Sebastian Bach
The Art of Fugue  BWV 1080

By the 1740s Bach had largely withdrawn from composing new church music for Leipzig’s Thomaskirche, devoting his creative energies instead to a series of large-scale projects that responded more directly to his own personal and professional interests. These monumental works were encyclopedic in scope, systematic in design, and concentrated in focus.

That focus was the practice of canon and fugue, the two most intellectually challenging musical genres of his time.

The year 1744, for example, saw the publication of the second book of Bach’s Well-Tempered Clavier, a companion to the first book of 1722, both sets of which made the case for equal temperament in keyboard tuning by providing a collection of 24 preludes and fugues in all the major and minor keys. Each of the 48 individual fugues in this two-volume work was composed with its own individual fugue subject, demonstrating, as Bach surely intended, the wide variety of theme types to which fugal procedure could be applied.

Most of the other major works from this decade take the inverse approach, showing the variety of contrapuntal techniques that can be applied to a single theme or motive.  These ‘monothematic’ works include the Goldberg Variations (1741), the Musical Offering (1747) and the Canonic Variations on ‘Von Himmel hoch da komm’ ich her’ (1747).

But crowning this series of learned essays is Die Kunst der Fuge, a collection of 14 fugues and 4 canons that illustrate the range and variety of contrapuntal techniques available to the serious composer, from the elementary to the arcane. In the manuscript each fugue is labelled contrapunctus, in Latin, to enhance the magisterial authority of the project. The work was largely complete by 1742 but Bach continued to revise it and add movements throughout the decade, leaving it, at his death in 1750, with its final massive fugue incomplete. The manuscript was edited by his sons and published in 1751.


The Motto Theme

Running through The Art of Fugue is a theme of Bach’s own invention that acts as a kind of ‘motto’ for the work as a whole. The unique inner architecture of this theme is specifically designed to maximize the potential for ‘motivic echoes’ in whatever texture it appears.

Its triadic opening, affirming D minor as its stable tonal centre, sounds almost fanfare-like, enabling the theme to stand out in a multi-voice texture by virtue of its easily recognizable intervals: a rising 5th and two falling 3rds.

The remaining portion, however, presents the exact opposite, moving in scalar fashion, by step, to outline an unstable interval: the diminished 4th C#-F. This implied dissonance requires a resolution on the tonic (D) that arrives in the 5th bar.

In support of this harmonic resolution is an accelerating rhythmic pattern as the theme moves along – from half notes to quarter notes to 8th notes – providing a slingshot-like release of momentum driving the theme home to its conclusion.

Bach’s theme is a miniature masterpiece all on its own, but what he manages to do with it in The Art of Fugue is nothing less than miraculous.


The Simple Fugues:  I to IV

The Art of Fugue is organized so that the fugues presented illustrate fugal procedure in increasing order of intellectual and compositional complexity: from the simplest to the most intricate. The ‘simple’ fugues present the theme — called the subject in fugue parlance – in a texturally clear manner that allows it to stand out at every appearance. In the simple fugues there is a clean division between single entries of the theme and background contrapuntal detail, so that the ear is never confused as to what to listen for.

Contrapunctus I seems to emerge from the depths of time, its key of D minor evoking the austere severity of a work in the Dorian mode from centuries past. A persistent 8th-note rhythm soon comes to dominate its onward progress with lively interchanges between the voices in sequential repetition occurring frequently in the episodes, i.e., the sections in which the fugue subject is not sounding in the texture.

Contrapunctus II takes a stylistic turn towards France by adding a dotted rhythm to the subject, a clear reference to the French preference for instrumental pieces with a jaunty, dance-like character.

In Contrapunctus III the fugue subject appears in both its inverted and right-side-up forms. But the emotional character of this fugue is dominated by the slip-slide-y nature of its highly chromatic countersubject, the term for a secondary theme that accompanies the subject virtually every time it appears.

Contrapunctus IV uses the inverted form of the subject, combining it a constant stream of motivic chatter that merrily repeats two fragments of the original right-side-up version. The first comes from the four descending 8th notes at the tag-end of the original theme, the second from the falling 3rds of its opening triad – which in their sequential repetition many scholars have thought sound like cuckoo calls.


Canon alla ottava

Four two-voice canons are found in Bach’s The Art of Fugue, each based on some variation of the motto theme. Filippo Gorini has judiciously placed these canons on his program as ‘boundary markers’ to set off the five principal groupings of fugues in the work.

A canon, for those unfamiliar with the term, is simply a round. Its answering voice, however, need not enter on precisely the same pitch as the leading voice, as it does in such round songs as “Frère Jacques” or “Row, row, row your boat.” Canons take their full technical name from the interval at which their answering voice does enter. “Frère Jacques” or “Row, row, row your boat,” then, would be referred to as all’ unisono (at the unison).

The first round in this work is alla ottava (at the octave) and it uses an elaborated version of the motto theme in which many single melody notes are transformed into triple 16ths while others are shortened into staccato 8ths. The resulting dance-like rhythm is almost gigue-like.


The Stretto Fugues: V to VII

In his second grouping of fugues Bach ups the intellectual ante a notch by introducing procedures that significantly increase the density of motivic reference in the fugal texture. He does this in two ways.

First, he introduces stretto, which is to say the close overlap of different voices singing out the same melody. The effect is like that of hearing a marching band playing a tune that echoes back from nearby buildings a beat or two later.

Second, he presents the fugue subject not just upside-down, i.e., inversion, as in previous fugues, but in augmentation (double note values) and diminution (half note values) as well. Being able to follow these various versions of the fugue subject presented at different time scales – often addressing the ear simultaneously – requires a degree of eyebrow-knitting concentration that not all listeners are born to achieve. Give yourself extra points if you notice how the opening statement of the subject in all three of these fugues is inverted in the answer.

Contrapunctus V uses a dotted-rhythm version of the motto theme with passing notes filling in many of its intervals. With all this passing motion the texture becomes creamy smooth but intensity builds up as the distance between overlapping entries in stretto is gradually reduced to a single beat.

Contrapunctus VI is another fugue in the French style, but not the French dance style. The abundance of heavily dotted rhythms, rushing 16th-note figures and ringing trills suggests more the pompous stop-and-go character of a classic Lullyan French overture. The same filled-in version of the subject is used as in the previous fugue, in both upright and inverted forms, both regularly paced and in diminution.

Contrapunctus VII is denser still in its tossed salad of motivic references, with the fugue subject working its way in plodding augmented note values from the bass all the way up to the soprano, in both right-side-up and inverted versions. There are virtually no episodes in this fugue since almost every bar is frothing, churning or gently burbling with some version of the subject.


Canon per augmentationem et in contrario motu

This canon sounds almost modern with its jagged melodic lines, ecstatic leaps and sudden chromatic detours. The contours of its two voices in canon are derived from the principal notes of the motto theme, but the answering voice is the inversion of the leading voice – in augmentation (!). This has the effect of making it sound like a ‘walking bass’ to the jazzy-sounding meanderings above.

Then, just to make things interesting, the two voices switch roles halfway through, the ‘walking bass’ becoming the ‘walking treble’ and the former soprano line going squirrelly in the nether regions of the keyboard.


The Multiple-Theme Fugues:  VIII to XI

Bach’s next step up in complexity is to write fugues with more than one principal theme, each theme getting its own exposition (the term for the opening section of a fugue in which all voices present the fugue subject in turn).

Contrapunctus VIII is a triple fugue, i.e., a fugue with three separate thematic subjects. The opening theme is full of open intervals, wandering chromatically to outline the melodic descent of an octave. The second, coming after a resolute cadence, is a whinging lament in continuous 8th notes clearly audible in the texture by virtue of its insistent rap-tap-tap of repeated notes. Finally a third subject, a segmented descendant of the motto theme, exhales into the texture like laboured breathing, three quarter notes at a time, with a rest on the first beat of each bar. These three subjects are introduced in successive expositions, after which they constantly bump into each other until, mirabile dictu (wondrous to report), they all get combined together at a final gathering of the clan to create a climactic ending.

Contrapunctus IX, by contrast, is a peppy double fugue with an opening fugue subject that begins with an octave leap, making it instantly recognizable in the texture. This is eventually paired with an augmented version of the motto theme to create a merry-go-round of toe-tapping excitement so infectious, that this fugue has even been recorded by the Swingle Singers.

A mood of calm reflection returns in the double fugue of Contrapunctus X, which opens with a theme in sighing three-note cells, as in Contrapunctus VIII, and which later encounter a dotted version of the motto theme with filled-in passing notes. A small number of motives is presented in a seemingly endless variety of guises, unfolding in a constant flow of varied melodic lines.

The mighty triple fugue of Contrapunctus XI uses the same three subjects as animated Contrapunctus VIII, presenting them first in their inverted form and then in their original upright versions. But the emotional character of this fugue is much different, more profoundly searching in its advanced chromaticism, a chromaticism that seems to be reaching out to the furthest edges of the sound world.


Canon alla duodecima, in contrapunto alla quinta

This canon bubbles over with ear-tickling rhythmic effervescence, presenting an elaborated version of the original motto theme  constructed out of roiling sextuplets that alternate with duple-value 8ths. The interval of a falling diminished 7th adds rhetorical drama to the melodic line.


The Mirror Fugues

Not content to have merely created two separate fugues in Contrapunctus VIII and Contrapunctus XI from the original and inverted forms of the same fugue subjects, Bach sets himself the challenge of writing pairs of single-subject fugues in which not just the fugue subjects but all the individual voices, and the textures as a whole, are exact mirror images of each other.

So the bass line in the first fugue of each pair become the soprano line of the matching second fugue, but with its intervals inverted, and similarly with the tenor and alto lines.  The vocal lines and the textures they embody perform this switch in the middle of each so-called “mirror” fugue.

Contrapunctus XII preserves the melodic shape of the original fugue subject exactly, but puts it in triple meter to create a gently lilting rhythmic feel in both fugues of the pair.

Contrapunctus XIII alters the theme considerably with filled-in triplet 8th notes and a perky octave leap, that combined with this fugue’s pervasive dotted rhythms makes you actually forget what a dazzling intellectual feat is unfolding in your ear.


Canon alla decima, in contrapunto alla terza

The appeal of this utterly charming canon lies in its simplicity and easy-to-follow melodic lines, which mix long notes with innocently swaying triplet 8ths. Bach seems to depart from his austere pose as the learned composer of intellectually rigorous textures by offering the performer a bit of freedom at the final cadence with the indication cadenza – an invitation for the performer to improvise a bit of fancy fingerwork of his own to end the piece in style.


The Last Fugue

Bach’s final fugue in this series remained unfinished at his death in 1750 and the specifics of its overall architecture have been the subject of debate amongst Bach scholars. Given the systematic increase in intellectual complexity and contrapuntal skill demonstrated in successive groups of fugues as the work progresses, it is reasonable to assume that this 14th fugue was meant to crown the set by displaying Bach’s absolute mastery of the form in some way.  But how?

The answer seems to lie in the three themes that Bach chose for this multiple-subject fugue, themes that sum up in one final work the different styles of melody presented so far and the emotional characters they evoke.

The first subject is a near relative of the motto theme, concentrating in long note values on the principal tones of the D minor triad. Proceeding at an even quarter-note pace, it recalls the austere mood of Contrapunctus I.

The second subject presents another kind of melody, ornamenting the motto theme in a continuous stream of 8th notes that twist and wind in a pattern that contrasts with the placid calm of the opening section.

The third subject increases the musical tension significantly, moving chromatically within a small range around the notes B-flat, A, C and B natural – not coincidentally the German musical spelling of the composer’s own name: B-A-C-H. And it is just at the point when Bach begins to combine all three subjects together that the manuscript suddenly ends, leaving us breathlessly bereft of what contrapuntal marvels might have come in the bars to follow.


*                      *                      *


But is it ‘music’?

The extraordinary feats of contrapuntal skill displayed by Bach in his Art of the Fugue have given rise to bewildered push-back amongst astonished commentators, prompting them to ask: Is this really music? The mere act of posing such a provocative question implies an answer in the negative and is motivated by two distinct lines of thought.

The first sees the work as purely didactic, as Augenmusik (music for the eyes) intended merely for silent study by aspiring contrapuntists rather than as a work intended for the enjoyment of audiences in live performance. This, however, is a false dichotomy, as the artistic merit of Chopin’s Études, Bartók’s Mikrokosmos and Bach’s own Klavierbüchlein für Wilhelm Friedemann Bach amply prove.

A second, more serious objection to the work’s suitability as concert music is a reproach often levelled at 12-tone serial compositions: that the essential structuring elements of these works is beyond the capacity of human perception to appreciate. And admittedly, the likelihood that even the most alert listener – with perfect pitch and a fresh injection of espresso – might remember the initial scoring of one of Bach’s mirror fugues well enough to notice its complete textural inversion halfway through is remote indeed.

And yet, as the saying goes in software development: this is not a bug, it’s a feature.

In the worldview of early-18th-century religious thought, which Bach shared, God was immanent in all Creation. All things on earth were imbued with the presence of the Divine, and manifested that presence in all its astonishing variety of forms and its underlying unity of purpose. To be bewildered by this astonishing variety and unity of purpose was to engage in an act of worship.

Bach, whose many manuscripts are marked with inscriptions betokening deference to the greater glory of God, conceived of his creative musical output as a sonic parallel to the variety and orderliness of the created world, a world that must inevitably surpass all human understanding.

So every fractal echo in his fugal textures of motives from the original motto theme – every rising 5th, every falling 3rd and every melodic phrase in stepwise motion – is a theological statement, standing proxy to echoes of the Divine in the natural world. In this regard, experiencing bewilderment at the dazzling complexity of Bach’s fugal textures is as natural as feeling overwhelmed with awe when contemplating the patterns of the stars in the night sky.

By ESA/Hubble, CC BY 4.0,


Donald G. Gíslason 2022



Ludwig van Beethoven
Sonata A flat major Op. 110

Beethoven’s penultimate piano sonata is remarkable for the utter simplicity of its musical ideas and the directness with which they are expressed. The most obvious late-period features of this work are an extremely wide keyboard range and a melding of slow movement and finale into a continuous musico-dramatic unit.

The first movement, marked con amabilità (likably), opens with a tune one could well imagine accompanying a thoughtful walk in the forest. Simple as it is, it moves to become simpler still, passing into a songful melody-and-accompaniment texture before evaporating into a delicate pattern of harmonic lacework luxuriantly caressing the keyboard over a space of four octaves. It is this gracious pattern of figuration, almost Romantic in its warmth of tone and celebration of keyboard colouring, that most attracts the ear in this movement. Its complete absence from the central development section is amply compensated for when it rises richly up from the bass to inaugurate the return of the main theme in the recapitulation.

The second movement is one of Beethoven’s most jocular scherzi. Its main section is based on two popular tunes of the time: the feline nativity ode Unsa Kätz häd Katz’ln g’habt (Our cat has had kittens) and the anti-hygienic anthem Ich bin liederlich, du bist liederlich (I’m so slovenly, you’re so slovenly). Inspired thus in equal measure by the reproductive capacity of household pets and the haphazard grooming habits of the Austrian male, Beethoven lards his first section with rhythmic irregularities, dynamic surprizes, dramatic pauses and other raw signifiers of loutish humour. The central section continues the mayhem with a series of tumble-down passages high in the register, rudely poked from time to time by off-beat accents.

The sonata concludes with a wonderfully vivid piece of musical theatre, rife with dramatic contrasts and unusual turning points in the musical action. Combining the traditional lyrical slow movement and triumphant finale, it opens with an evocation of the opera stage: a lonely solo voice pleads its case in a halting recitative and then in an affecting lament of considerable intimacy over soothing & sympathetic triplet pulsations, set in the troubled key of A flat minor.

But then, like a ray of Enlightenment sunshine announcing the triumph of Reason over Emotion, a three-voice fugue steps onto the stage, replacing the little sigh motives and rhythmic hesitations of the previous section with quietly confident, evenly spaced 4ths and 3rds, the same intervals used in the opening bars of the first movement.

All this Baroque counterpoint fails, however, to ward off a relapse into pathos as the heart-rending arioso returns, even more plangently whimpering than before, until Beethoven astonishes us with the ultimate coup de théâtre. In what could only be construed as a musical representation of strengthening psychological resolve, we hear the same major chord, repeated over and over, getting louder and louder, leading back to the fugue theme, now presented in inversion. A new mood of quiet triumph and victorious liberation spills over into increasingly elaborate fugal lacework until even the fugal pretense is dropped and the sonata concludes in a glorious songful strain of rejoicing expressed over five octaves of the keyboard.

Béla Bartók
Sonata Sz. 80

In 1926 Bartók’s musical style took a ‘Bachian’ turn towards more clearly polyphonic textures. His Sonata from that year presents us with three movements in two distinct character profiles. The opening and closing movements are bold, direct and massively self-confident, characterized by driving energy and a machine-like sense of rhythm. The slow middle movement, by contrast, is unremittingly bleak, filled with dull, aching dissonances that audience members who have experienced dental surgery may find triggering.

The first movement opens with a motive comprised of a short skip and a series of hammered repeated notes, reminiscent of the striding pulse of the last of Stravinsky’s Three Scenes from Petrushka. Stravinskian, as well, is the sonic resonance ringing out clearly from the well-spaced chords that accompany this stomping, hammering pulse throughout the movement. Bartók doesn’t really present us with ‘themes’ as such, but rather short motivic cells that are continually varied, and frequently subject to hemiola effects as they shift in alignment, rhythmically, with respect to the bar line. This is a very athletic movement, with many sudden changes of register, including passages in which the right hand leaps across the left in order to punch out notes deep in the bass.

If repeating the same action over and over again and expecting a different result is the very definition of insanity, then the opening 6 bars of Bartók’s 2nd movement—featuring an A-flat-E-flat-F chord in the left hand, repeatedly set against a jarring E natural in the right—are clear cause for concern. This movement is bafflingly dissonant. Textured in uncompromisingly gritty 3-voice counterpoint that plods foreword at a relentless quarter-note pace, it offers little to orient the ear in its tangled texture of semitones and minor 9ths: only occasional reminders of the opening harmonic sound-salad and a fixation on rising scale figures. Even the abruptness of its final cadence, normally a place of emotional resolution and rhetorical disarmament, comes as a shock to the nervous system.

The monothematic final movement is by comparison a pleasant jog in the park. Its principal concern is a jaunty little folk tune of a pentatonic stamp announced at the outset. The melodic outline of this ditty—a gapped space of five tones down, then back up—gives it the air of a sea shanty, but the more it gets varied with repetition the more it starts to sound like “Good King Wenceslas”. Despite its constant changes in time signature between 3/8, 2/4 and a very Stravinskian 1/4, this movement manages nonetheless to come off as a real toe-tapper.

Karlheinz Stockhausen
Klavierstück IX

The 20th century witnessed the development of new approaches to thinking about the sounds that make up what we call ‘music’. The 12-tone system of Arnold Schoenberg spawned the serialist movement, dominated by a search to create new formal structures for music organized around ‘series’ (i.e. fixed patterns) of pitch, dynamics, timbre and other properties of sound. And then, beginning in the 1950s, sounds never heard before by human ears, artificial sounds created electronically, were admitted into the composer’s toolkit.

German composer Karlheinz Stockhausen was at the centre of all these developments, producing works based on the newly developed structural principles, and utilizing the new sound palettes that had been discovered. Through this work he quickly became the public face of avant-garde contemporary music—so famous, in fact, that he is featured in the crowd of faces on the cover of the Beatles’ 1967 album Sgt. Pepper’s Lonely Hearts Club Band (fifth from the left, in the back row).

The 19 works that Stockhausen composed with the title Klavierstücke (keyboard pieces) between 1954 and 2003 embody some of his most important ideas about how music can be internally organized, and the sound gestures that can form part of it. The ninth piece in this series, Klavierstücke IX completed in 1961, is one of his best-known piano works.

This work presents many challenges to the uninitiated, as the parameters of music that we are used to identifying—harmony, melody and rhythm—are not hierarchically deployed in the way that we take for granted in ‘traditional’ music. But a listener coming to this music for the first time should not be overly concerned with its ‘geometric’ dimensions—for example, with how the rhythmic proportions throughout the piece are organized by the Fibonacci series 1, 1, 2, 3, 5, 8, 13, 21 (etc.) in which each number in the series is the sum of the two preceding numbers. Nor try to count how many times the dissonant four-note chord that opens the work is played in the first (shall we say) ‘phrase’, and how many times in the second. (It’s 139 and 87, for those who like to keep track).

Analytically-oriented listeners might attempt to follow the two main ideas in the piece that alternate in dialogue: the opening four-note chord repeated at varying speeds and dynamic levels, and a slowly rising chromatic scale. But committed admirers of impressionism will want to just set their minds free, close their eyes, and imaginatively listen to the sounds emanating from the stage as if they were the soundtrack to a movie, asking themselves as they listen: what kind of movie is this?

Ludwig van Beethoven
Sonata in C minor Op. 111

Beethoven’s last sonata is surely his most poetic essay for the piano, conceived as a musical diptych expressing the contrasting states of human existence—earthly struggle and spiritual transcendence—framed in terms of the raw elemental building blocks of music itself. It comprises a fast-moving, contrapuntally active sonata-form movement in the minor mode matched with a slow-paced, harmonically stable set of variations in the corresponding major mode.

There is a skeletal starkness to the musical fabric of the first movement, its jagged leaps over harmonically aberrant intervals evoking a mood of worried restlessness, a mood only reinforced by frequent scurrying passages of fugato that seem to emphasize a disunity between the voices rather than their complementarity. Strikingly lacking in this movement is any sense of lyrical repose. The 2nd subject appears only briefly, more in the spirit of emotional exhaustion than heartfelt fulfillment. At every turn, Beethoven seems to emphasize the unusually large space that separates the voices and the hands (separating the mortal from the divine?), at one point orchestrating a climactic antiphonal exchange between treble and bass of more than six octaves.

The C major chord on which the C minor first movement ends is taken up in the second movement Arietta, marking not only a change in mode, but a fundamental change in the construction of the musical texture. Instead of angular motivic gestures we have an eloquently simple and well-rounded melody. Instead of contrapuntal conflict we have harmonic fullness and warmth. The first three variations introduce the compositional process that will guide this melody through its successive transformations: a gradually increasing animation in the figuration accompanying the variation theme. The 3rd variation arrives at degree of elation that in its syncopations prefigures the arrival of jazz, before the timbre turns dark with low murmurings underpinning melodic fragments of the theme pulsing above.

It is here that Beethoven begins to gaze up at the stars in textures that twinkle luminously in the highest register of the keyboard. As the theme becomes ever more cradled in the swaddling clothes of its enveloping figuration, it appears to glow, sonically, from within, by means of pearly chains of trills, until is transmuted, finally, into the essence of the divine.

Donald G. Gíslason 2019