Ultra-Low Frequency ‘Pulse’ / ‘Hypermeter’ in Dinnerstein’s Bach

I    wanted it to have a feeling of spaciousness, and of ‘breath’ ... I was influenced by Marie-Claire Alain’s [interpretation of Bach’s ‘Goldbergs’] in Paris, who played a Bach recital... an incredible sense of rhythm, almost an organic sense of rhythm ... [to] these large rhythmic structures. But the smaller beats [in Alain’s interpretation] were very free. [The overall effect of Alain’s approach was such that] it had [qualitatively, an astrophysical] feeling—almost like the turning of the Earth [on its axis] ... that there was an inevitability to the way the pulse was going, but within it there was this kind of feeling of ‘give-and-take’ in the rhythm. And I think that [by contrast to Alain,] a lot of the approach to rhythm has [for other pianists] been very ‘motoric’, and influenced by having a very strong feeling of a ‘small’ pulse. And I wanted to experiment with freeing myself of the small pulse and feeling a larger pulse.”
  —  Simone Dinnerstein interviewed by Sarah Dallas of www.moreintelligentlife.com, commenting on rhythmic freedom, breathing, phrasing, and why the silences in Bach, are as important as the notes, 2007.

S imone Dinnerstein catapulted to fame on the merits of her recording of Bach’s Goldberg Variations worldwide in August 2007. Her Berlin recording has also been very well-received, and she has a very busy touring schedule. Dinnerstein is a graduate of The Juilliard School where she was a student of Peter Serkin. Last night she performed in Kansas City in the Friends of Chamber Music’s piano series.

H er interpretation of Bach is highly unusual, as some reviews and the blockquote above attest. Despite the written time signatures, Bach’s ‘French Suite’ No. 5 gives the impression of a compound meter. The groupings into hierarchies of nested two-, four-, six-, eight-, 10-, 12-, 16-, 20-, 24-, and 32-bar structures contribute to this.

A rtists’ interpretations of these are widely varied, and the variations are especially pronounced where the hypermeter or polymeter structures change—for example, become more accentuated or obvious, or become less obvious, or become more or less competitive or conflictual. Some artists affirm or cooperate with the hypermetric and polymetric structures; other artists fight the imposition of a hypermeter by regularizing the rhythms and defeating the agogic and rubato cues that are in the score.

S imone Dinnerstein engages in a style of interpretation that alternately cooperates with and, at times, opposes Bach’s cues for improvisational and rubato freedom. At times, she also liberally expands upon the cues that are in the musical text. Characteristically in her playing she sheds light on longer-range, larger-scale hypermeter structures than might have been perceptible to us before. As a result of her emphases and rhythmic decisions, we hear what we might imagine to be the Earth spinning on its axis, one revolution every 24 hours. Maybe more accurately, we imagine the Earth’s axis precessing, one cycle every 26 thousand years. We hear celestial mechanics operating in timeless, wheels-within-wheels majesty. Music of the spheres...

P  robably the most beautiful written-out rubatos in all keyboard music are those in the Andante of [Bach’s] Italian Concerto, BWV 971. With the aid of rhythmic notation of unparalleled subtlety, Bach wrote down the free rhythms that a contemporary singer or instrumentalist schooled in the Italian style might have improvised in performance... To be sure, even Bach’s notation cannot wholly render the infinite subtleties which characterize great artistry in performance. A sensitive harpsichordist will emphasize the B-flat here by playing it just a shade early in order to be able to sustain it slightly longer. This rhythmic flexibility enables good harpsichordists to overcome the relatively inflexible dynamics of their instrument and still play cantabile.”
  —  Paul Badura-Skoda, p. 66.

M ost studies of agogicity and rubato address small temporal deviations with regard to the beat, as defined by the prevailing time signature as-written—they address the ‘shimmering’ effect on a timescale of tens of milliseconds up to several seconds, usually. But hypermeter also has a pulse—it’s just not an explicitly written one, and not readily apprehended on the timescales of our usual attention-span. There can be agogic and rubato effects that arise on the very long timescales of hypermetric patterns—what I might only half in jest call an astrophysical, nebula-esque shimmering on a timescale of tens of seconds to hundreds of seconds: eons, musically speaking. Here are the longest hypermetric timescales that occur in Dinnerstein’s account of BWV 816.

• Allemande, 4/4, two 12-bar repeats: 104 sec
  
• Courante, 3/4, two 16-bar repeats: 48 sec
  
• Sarabande, 3/4, 16-bar repeat and 24-bar repeat: 130 sec and 196 sec
  
• Gavotte, 2/2, 8-bar repeat and 16-bar repeat: 19 sec and 38 sec
  
• Bourée, 2/2, 10-bar (4:6) repeat and 20-bar (8:12) repeat: 52 sec and 104 sec
  
• Louré, 6/4 (2), two 8-bar repeats: 34 sec
  
• Gigue, 12/16 (2), 24-bar repeat and 32-bar repeat: 86 sec and 116 sec

    [30-sec clip, Simone Dinnerstein, Bach, ‘French Suite No. 5, BWV 816, Saraband’, 1.2MB MP3]


    [30-sec clip, Simone Dinnerstein, Bach, ‘French Suite No. 5, BWV 816, Courante’, 1.2MB MP3]

A    century before Bach, Heinrich Schütz had perceived regular time to be ‘as it were, the soul of music’ [preface to ‘Auferstehungs-historia’, Dresden, 1628] ... It is revealing to compare the ‘slow beat’ mentioned here with the remarks about Bach’s conducting... Between the firm ‘pillars’ of the beats there was a large degree of freedom. With the exception of pieces in perpetuum mobile style, there were all kinds of rubato, breathing pauses, breaks, and thematic dovetailing running counter to the beat.”
  —  Paul Badura-Skoda, pp. 16-17.

I f you were a listener who had never seen the BWV 816 score and you did not know that the dances that are “in 2” are separate movements, or that the dances with meters that are “in 3” are separate movements I suppose you might impute even longer-scale hypermetric patterns in French Suite No. 5—ones that transcend inter-movement boundaries.

G lenn Gould, Andras Schiff, Angela Hewitt, Piotr Anderszewski, Constance Keene, Edward Aldwell, and others—almost devoid of these hypermetrical effects and tremendously different from Simone Dinnerstein in myriad other ways.

T he spontaneity and greater temporal elasticity of, for example, Dinnerstein’s Sarabande—reduce our attention to the longer-scale structure. But the more motoric dances draw our attention to longer-scale hypermetric structure and the rubber-banding that Simone is doing with time and meter.

W e take a look at how this works quantitatively, using the mathematical/statistical formalism of ‘copulas’. Copulas are functions that link univariate (single-variable) marginal values to their statistical variations with multiple other variables—to their joint multivariate distributions. Copulas are useful because they allow us to discover concurrent or joint multivariable correlations with any set of univariate marginal distributions that may happen to exist. Each ‘voice’ in the left-hand part(s) and the right-hand part(s) in ‘French Suite’ No. 5 has its own rhythmic marginal distribution (of inter-beat time intervals, quantized to 4 millisecond time-resolution or better). Figuring out how Simone Dinnerstein makes this thing ‘breathe’ the way she does is possible by computing the copulas, and comparing them to, say, Aldwell’s or Goode’s or Gould’s.



C opulas are a way of quantitatively characterizing the dependence structures of vectors of multiple random variables. Although copulas were first studied more than 50 years ago, they were not extensively applied. Interest in copulas has been renewed recently in biostatistics, reliability engineering, and financial engineering, and other fields. Within the past 10 years in finance, copulas have become a standard analytical technique for multi-asset basket pricing (especially CDOs and other credit derivatives), equities portfolio modeling, risk management, etc.


A nja Volk, in her paper at the 2004 ICMPC meeting, considers all metric pulses arising from equally spaced notes’ onsets (the so called local meters). All external information (bar lines and time signature) was ignored. Only the internal relations of the actual as-composed notes were analyzed. Anja modeled the inner metric structure of music mathematically, and contrasted it with the outer metric structure given by the accent hierarchy of the as-written time signature. The inner metric weight for each note is calculated on the basis of the meters m_s,d,k it participates in and which have a minimum length that is not smaller than a fixed value l. The variable s denotes the starting point, d denotes the period (the duration between consecutive onsets of the local meter) and k the length of the local meter. The contribution of each local meter to the metric weight depends solely on its length k, not on its starting point s nor its period d. She denotes m_s,d,k= m(k) and gain for each note’s onset o the metric weight w_l,p as the weighted sum of the length k of the corresponding local meters:


whereas the minimum length l and the weighting parameter p can be varied. The calculation of the inner metric weight of a musical piece (or a passage, a part, a passage from a part) can be easily understood from figure below.


A n algorithm calculates all local meters (i.e. arithmetic sequences) within the set of onsets under consideration (there are five such local meters in the short example). The metrical weight encodes the incidences of different meters, i.e. the metric weight of an onset is determined by the set of all local meters passing through it.

M    aintenance of the metre depends on the basic rhythmic character of a work. An arioso allows greater rhetorical freedom—more rubato, that is—than, for example, a gavotte or a minuet. The greatest agogic freedom is permissible in freely structured forms such as the stylus phantasiticus of the toccata and the fantasia. Works of this kind had their origins in instrumental improvisation, such as the free invention of preludes.”
  —  Paul Badura-Skoda, p. 18.

H ave a listen to Dinnerstein, remarking on her intentions with regard to Bach’s ‘Goldberg Variations’ (YouTube):



I n my day-job, among other things I perform signal-processing and mathematical modeling of time-series. Sometimes the timeseries are physiologic monitoring variables related to health and survival in critical care units; other timeseries I have modeled include financial trading timeseries and geophysics/seismic timeseries. I think that the spectral analysis software and mathematical tools that are used in those areas have broad applicability to quantifying what is going on in music, including helping to account for what is so unusual about Simone Dinnerstein’s Bach interpretations and rhythmic/metrical decisions.

S o-called ‘adaptive filters’ offer advantages over Wiener filters for time-varying processes. They are used for mathematical ‘deconvolution’ of seismic data which exhibit non-stationary, time-varying behavior, much like Dinnerstein’s ‘waves’ of slowly altering meter. Different algorithms for adaptive filtering exist. The least-mean-squares (LMS) algorithm, because of its simplicity, has been widely applied to data from different fields that fall outside geophysics. And that is what I have used, on my measurements of Dinnerstein’s Berlin recording—I bought her CD, ripped ‘French Suite No. 5’ tracks’ MP3s from it, and performed Fourier transform and Wavelet transform calculations on those digital audio files, annotating each bar against my pdfs of the score.

T he ‘stacking velocities’ I used to model the time-varying alterations of meter do not need to be known very accurately because—just as in deep-reflection seismography—the residual deviations (‘move-outs’) are small on a beat-to-beat basis and have only a minor influence on the results of the adaptive time-slicing.


W hat I discover is what amounts to a very low frequency (VLF = 0.01 to 0.1 Hz) ambient ‘seismic’ hypermetric architecture of Bach’s French Suite No. 5, something I think is heretofore unreported. Maybe it’s just Simone; maybe it’s really there; we will have to measure other elite performers’ interpretations and see if we can find (less pronounced) evidence of it. That such a thing should seem novel is particularly likely in recent years, as the trend has been toward highly ‘motoric’ species of virtuosity, especially with Bach interpretations.

B ut here in Dinnerstein we have ‘ocean waves’ that “couple” into ‘seismic waves’ through (what appears to be, from my measurements and analysis thus far—) a quadratic nonlinearity of the metrical surface boundary condition. The quadratic nonlinearity may be entirely under the artists’ conscious control; or maybe it is not, or at least not entirely. The nonlinearity couples pairs of slowly propagating metrical ocean-like waves of similar frequency to a high metrical phase-velocity component that has approximately double the frequency. These “approximately 2f” relationships are easy to discern in the FFT spectra of French Suite No. 5, with its hierarchical organization of phrases and repeats.

B esides seismology, gravitational wave physics also offers some useful tools and analytical methods for investigating metrical and hypermetrical phenomena in music. Waves familiar from other areas of physics such as water waves, sound waves, and electromagnetic waves are able to carry energy, momentum, and angular momentum. By carrying these away from a source, waves are able to dissipate energy and ‘rob’ that source of its energy and linear or angular momentum. Gravitational waves do the same thing in space. For example, a binary star-pair loses angular momentum as the two orbiting stars spiral towards each other: the angular momentum of the mutually-orbiting pair is radiated away by gravitational waves.

H ere’s what I think: a prevailing musical pulse and meter manifests a particular musical metrical ‘mass’ that exerts a quasi-gravitational force on the space-time continuum through which it passes and which we occupy. If the performer suddenly alters the pulse, it is as though a gravitational wave is created, which propagates forward and may make space-time seem to either dilate or contract, compared to the previous regime. If the performer imparts a hypermetric periodicity, that can be detected or sensed, via neurophysiological monitoring and analytics not too dissimilar from methods to detect gravitational waves.

T he transmission of hypermetrical ‘waves’ is not only through the ‘physical’ medium (sound through the air) but also through ‘cognitive’/’neurophysiological’ media. The latter media have an ‘impedance’ and transfer-function, with rate-dependent,time-dependent, remanent properties—almost like thixotropic or rheopectic non-Newtonian liquids and gels, or like non-Newtonian star-stuff in space. So the transmission of hypermeter waves is imperfect—the waves suffer delays and phase-lags; depending on its spectral properties, the waves experience more or less attenuation and dissipation as they propagates; they undergo refraction at ‘apertures’ (phrase boundaries; movement boundaries) and interferometric interaction with other hypermeters that exist concurrently in the same space-time.

W hen the musical polyphony is ‘shallow’, the hypermeter waves undergo wavefront-steepening and the wave amplitude increases like tsunami waves; and so on. This would seem to me to be a rich space for cross-disciplinary study in the future. To my knowledge, cross-pollination between music theory and physics has not explored these possibilities to-date. Maybe you will be intrigued enough to pick up this line of analysis and give it a ‘go’.

I   t can be seen in accompanied recitatives that tempo and metre must be frequently changed in order to rouse and still the rapidly alternating affections. The metric signature is in many such cases more a convention of notation than a binding factor in performance.”
  — C.P.E. Bach, ‘Versuch über die wahre Art, das Clavier zu spielen’, Leipzig, 1753, p. 153 (trans, W. Mitchell, ‘Essay on the True Art of Playing Keyboard’, 1949).

• Simone Dinnerstein website
  
• Simone Dinnerstein concert in Kansas City, 14-FEB-2009
  
• Dinnerstein S. The Berlin Concert. (Telarc, 2008.)
  
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Latent Meaning: Performances as Authorship, Transcriptions as Intrepid Exploring

C    an Bach’s famous keyboard variations actually be improved? . . . it depends what you mean by ‘improved’. If ‘given a fresh new perspective’ qualifies, then the answer, according to this CD, is a resounding ‘Yes’! Hearing three distinct voices instead of one truly enhances the experience of listening to this classic. So how did Dmitry Sitkovetsky transcribe it? Violin & viola for the right hand, cello for the left? It would be nice if it were that simple. Sometimes the treble line involves the viola and violin, sometimes just the violin. In the case of Variation 19, Sitkovetsky does something quite impish. He sneaks pizzicato figures into the counterpoint mixture, so that when the violin and viola are conversing, the cello provides background plucking. But wait! That’s not all! A few bars later, the pizzicato is traded back and forth among the instruments, only to fade in and out of prominence. And it all happens in less than two minutes. Other dazzling feats occur in this performance. The centerpiece is the haunting Variation 25, the longest (7:39) adagio in the piece. Harpsichordist Wanda Landowska called it ‘The Black Pearl’, perhaps for its deeply affecting, melancholic beauty. The trioists inject it with an impressive array of dramatic techniques, like deft shifts from pianissimo to mezzo-forte and slight shadings in tempo. It almost sounds like a string trio piece from the late classical period. Why does this arrangement of the Goldberg Variations succeed so well? … the structure of the piece lends itself to three instruments, not one. When played on keyboard instruments, the two upper voices are virtually indistinguishable [but in string trio the voices are each more distinct].”
  —  Peter Bates, review of Rachlin et al., AudiophileAudition, 11-JAN-2008.

I f you haven’t previously heard Dimitry Sitkovetsky’s transcription of Bach’s ‘Goldberg Variations’ (BWV 988) for string trio [see links below], you will, I think, be pleasantly surprised. I particularly like the Deutsche Grammophon recording of the performance of it by Julian Rachlin (violin), Mischa Maisky (cello), and Nobuko Imai (viola).


    [50-sec clip, Julian Rachlin et al, Sitkovetsky transcription of Bach’s Goldberg Variations for String Trio, ‘Aria’, 1.2MB MP3]

It is amazing how well-suited the variations turn out to be for strings. Sitkovetsky’s transcription is an expecially thoughtful and innovative one, which teases out new expressive elements that previously have been only ‘latent’ and never realized when played on a harpsichord or a piano.

New meanings that have lurked in Bach’s text for almost 270 years become apparent, even obvious. New kinds of tension—melodic, harmonic, textural, and metrical—that contribute to the music’s overall effect begin to take hold of us.

Dmitry Sitkovetsky was born in Baku, Azerbaijan in 1954 and is a Russian violinist and conductor. He grew up in Moscow, studying at the Moscow Conservatory. When he wanted to leave the Soviet Union in 1977, he feigned mentally illness, was granted permission to emigrate to the U.S. and studied at Juilliard. In 1979 he won first prize in the Kreisler Competition in Vienna. From then on he has appeared as soloist with renowned orchestras around the world. He was the Principal Conductor and Artistic Advisor of the Ulster Orchestra from 1996 to 2001 and was Conductor Laureate of the orchestra during 2002. Since 2003, he is Music Director of the Greensboro Symphony Orchestra and Principal Guest Conductor of the Russian State Symphony in Moscow.


Each of the trio parts avails the player the opportunity for an expansive response to the text, as well as challenges to maintain a good blend and ensemble. Rachlin sounds especially intense and personal here, which is what one always wants from a performer. The prodigious insight of Sitkovetsky’s compositional decisions is ample justification for what might otherwise have been thought to be an ‘unnecessary’ transcription of ‘Goldberg’. Once you have it, you realize that you needed it all along...

Bach’s two- and three-part keyboard writing for most of the ‘Goldberg’, so double-stops might be thought to be the natural approach to a string trio transcription that would render the harmonies in the original text. But there is far more here than that. Sitkovetsky emphasizes the dialogues in the counterpoint by exquisitely leveraging the timbral differences between the instruments. Rachlin, Maisky, and Imai are genuinely inspired by the ideas that Sitkovetsky has provided, as you will readily hear in their superb Deutsche Grammophon recording.

Variation 18 ending


    [50-sec clip, Julian Rachlin et al, Sitkovetsky transcription of Bach’s Goldberg Variations for String Trio, ‘Variation 18’, 1.2MB MP3]

Variation 19 opening

Variation 19 ending


    [50-sec clip, Julian Rachlin et al, Sitkovetsky transcription of Bach’s Goldberg Variations for String Trio, ‘Variation 19’, 1.2MB MP3]

Variation 20 opening


    [50-sec clip, Julian Rachlin et al, Sitkovetsky transcription of Bach’s Goldberg Variations for String Trio, ‘Variation 20’, 1.2MB MP3]

In trying to understand why the Sitkovetsky string trio transcription of the ‘Goldberg’—and the Rachlin et al. performance of it—are so novel and genuinely illuminating, I recall that Peter Kivy once noted that “the quality that persists through [Landowska’s] various performances of the ‘Goldberg Variations’: performance is to be valued not as process but for the interpretation it embodies.” Kivy argued that performances are full-fledged ‘versions’ of works in precisely the same sense as arrangements are—performance becomes a vicarious act of composing. It is that full-fledged creativity that we hear here.

S    o in the case of the Goldberg, there is in fact one pulse, which—with a few very minor modifications—mostly modifications which I think take their cue from ritards at the end of the preceding variation, something like that—one pulse that runs all the way throughout.”
  —  Glenn Gould, interview with Tim Page, 1982.

Rachlin plays the opening aria with what feels to me to be just the ‘right amount’ of circumspection. The introspective sensitivity and exquisite variety of touch that Maisky and Imai achieve are a joy to hear as well. The transitions between Variations are well thought-out and deliver a perfectly coherent, consistent sense of ‘pulse’ from one Variation to the next—consummately Bach-like. The rhythmic alignments, Variation-to-Variation, amount to a kind of [64-bar] hypermeter that threads its way throughout the aria, the 30 variations in all their diverse 2-beat and 3-beat and 4-beat meters, and the da capo restatement of the aria. Click on the image below to open an Excel spreadsheet showing color-coded alignments of the tempi between Variations, as they are rendered in the Rachlin et al. recording of the Sitkovetsky transcription for string trio.


To Kivy, music is never dominated by the text in front of us; music is performance and is therefore irreducibly ‘social’. It involves a direct and private communication from composer/transcriber to listener. The intelligibility of the piece is negotiated in real-time—none of the social participants has ‘omniscience’, or a privileged perspective of meaning and intelligibility.

How, after all, could we know would we know what Bach intended? All sorts of evidence, sure—some of it fragmentary, some flawed. So the musical text is under-determined with regard to performance practice, and performance interpretation can never be a matter of absolute ‘correctness’ but rather one of rigorous ‘coherence’ and thoroughgoing ‘genuineness’.

W hich is what we get here, in the Sitkovetsky played by Rachlin et al. Performers-as-composers/improvisers. Performers and transcribers as explorers, discovering new [historically informed] territory as they go.

This wonderful string trio transcription of ‘Goldberg’ convinces us that a piece of music is better considered as a ‘script’ rather than a ‘text’. We must not be relentlessly clinical or obsessively literal, focusing on the text as the ultimate source of truth and aesthetic value. To do that would be ruthlessly sterile and anti-musical, as Glenn Gould once said. This Sitkovetsky strikes me as one of the most ‘genuine’ transcriptions of anything, ever. Absolutely wonderful, and a fine ‘tool’ by means of which it’s possible to discover yet more meanings in a work that we might previously’ve thought we pretty thoroughly understood…

• Julian Rachlin—Born in 1974 in Vilnius, Lithuania, his parents emmigrated in 1978 to Austria. In 1983, he entered the Konservatorium Wien and studied with Boris Kuschnir and Pinchas Zukerman. In 2005, Rachlin made his Carnegie Hall debut when he performed with the New York Philharmonic under Maazel. Rachlin also performs chamber music with such artists as Martha Argerich, Itamar Golan, Natalia Gutman, Gidon Kremer, and used to perform with Mstislav Rostropovich. In 2000, he joined Rostropovich and Yuri Bashmet, among others, in the premiere of Krzysztof Penderecki’s Sextet. The same year, Rachlin also founded his own music festival in Dubrovnik, ‘Julian Rachlin and Friends’. In 2000, he was rewarded with the prestigious International Prize of the Accademia Musicale Chigiana of Siena. Julian Rachlin plays the 1741 ‘ex Carrodus’ Guarnerius del Gesù violin.
  
• Mischa Maisky—Born in 1948 in Riga, Latvia, Mischa Maisky began his musical training at Riga’s Music School and Conservatory. In 1962 he enters the Leningrad Conservatory. In 1966 he won first prize at the International Tchaikovsky Competition in Moscow and began his studies with Rostropovich at the Moscow Conservatory. He was imprisoned by USSR authorities for 18 months and emigrated to Israel in 1973. He has maintained a busy and illustrious performing and recording career ever since.
  
• Nobuko Imai—Born in 1943 in Tokyo, Imai began her training at Tokyo’s Toho Gakuen School of Music and soon after came to the United States where she studied at the Juilliard School and Yale University. She won first prize at both the Geneva International Music Competition and ARD International Music Competition at Munich. She taught as a Professor at the Detmold Academy of Music from 1983 to 2003, and currently teaches at the Conservatories of Amsterdam and Geneva, and at Conservatoire Supérieur et Académie de Musique Tibor Varga in Sion.

• JulianRachlin.com
  
• MischaMaisky.com
  
• Nobuko Imai page
  
• Sitkovetsky page at Nonesuch
  
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• Trio Accord. Goldberg Variations, Arr. String Trio (Sitkovetsky). (Skylark, 2008.)
  
• Trio Echnaton. Goldberg Variations, Arr. String Trio (Sitkovetsky). (Coviello Classics, 2008.)
  
• Trio Zilliacus-Persson-Raitinen. Goldberg Variations, Arr. String Trio (Sitkovetsky). (Caprice, 2007.)
  
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Shadows Over Grandeur: Bach’s Partita No. 2 in D Minor, Chaconne

O  n one stave, for a small instrument, the man writes a whole world of the deepest thoughts and most powerful feelings. If I imagined that I could have created, even conceived the piece, I am quite certain that the excess of excitement and earth-shattering experience would have driven me out of my mind.”
  —  Johannes Brahms, letter to Clara Schumann.

DSM: Christian Tetzlaff’s new CD is phenomenal! And the Partita No. 2—the Chaconne—is gorgeous. Many virtuoso violinists’ gestures aim to arouse the eye as well as the ear. The use of slight detuning of the strings or oddly difficult bow techniques can draw attention to their skill. But Bach’s sonatas and partitas are not conducive to (or tolerant of) such showiness–which tends to support the argument that Bach wrote them for his own use. Tetzlaff’s interpretation of Partita No. 2 is deeply true to the spirit of this composition—this four-bar harmonic progression with sixty-four variations.

CMT: The length of the Chaconne—about 15 minutes—is interesting in itself. Profundity requires time. The artist has to have enough space to capture the audience's attention, plant some seeds, and let them grow. Tetzlaff handles this nicely. Nothing is exaggerated or played merely for ‘effect.’ It is personal and absorbing, poetical yet natural and unadorned. Tetzlaff captures all the tireless circumnavigations around this single idea, making you wonder at Bach’s rhetoric. In Partita No. 2, Tetzlaff evokes the melancholy beneath the Bach’s tribute to his first wife, Maria Barbara. There is pliancy, grandeur, musical freedom. Tetzlaff’s playing displays no desire for ‘show’ but only the desire to engage with the musical core of this piece.

DSM: Bach’s Partita No. 2 in D minor follows a ‘da chiesa’ “church sonata” pattern, in which the slow and fast movements alternate with each other. And the Chaconne is not a short story or a novella; it is a full-blown novel! A novel has enough space to support introducing and developing a number of characters. This famous Chaconne is positively monumental in its scope and scale.

CMT: The arrival of every four-bar phrase on D is a striking aspect of the Chaconne’s beauty and poignance. It’s an emphatic eternal return, as though it were a physical “law.” The impression is one of inescapability, of inevitability. There’s also the ‘monumentality’ of the sheer variety that emanates from the solo violin as the performer progresses through the 64 variations that comprise the Chaconne. The music and the soloist become an omnipotent force. The piece evokes a transcendent ‘Other’—the Divine, if you wish.

DSM: The sheer diversity of the 64 variations compels us to acknowledge the Other. The diversity is so enormous as to boggle the listener’s mind and cause the jaw to drop. Boggling not in awe at a virtuosic human performer, but in awe at the mysteries of Life, of the Universe.

CMT: All of Bach’s compositions are, in some way or other, variations on a thoroughbass. With the first statement of the four-bar theme, the harmonies first move in halves and quarters. Then they accelerate to quarters at the cadence. Then they speed up to sixteenths.


DSM: Many of the variations occur in pairs—the second, for example, is similar to the first, but intensified. The opening eight bars comprise the theme and its first repetition, where the first three bars of the second statement are identical to the first. Then it broadens in register and introduces thirty-second-note rhythms. In terms of our cognition, Bach's 'haptic update rate' and the hypermeter of the variations’ cycling are what impart this transcendent quality to the Chaconne. Have a look at Choi and Tan paper in this month’s issue of the virtual-reality journal, Presence.

CMT: This presages the predominant dotted rhythm of the next four variations. The dotted-rhythm variations occur in pairs. The first pair is diatonic; the second pair introduces chromaticism—the descending tetrachord goes from tonic to dominant. And now this! And now this! Layer upon layer! World without end!

DSM: The texture perpetually evolves throughtout the Chaconne as well. As the velocity increases, the texture diminishes from the three- and four-voiced chords at the beginning, to single-line writing later in the piece.

CMT: As the texture becomes thinner, the chromaticism increases—the introduction of F-sharp and E-flat in the eighth statement, for example—and the registral ‘span’ increases, from the tenths in the first two statements, to about two octaves in the eighth statement and beyond.

DSM: This process—where some elements diminish while others grow—adds to the sense that the meaning intended or the theme that Bach is referencing is a commentary on life itself, on Nature, on the Cosmos.

CMT: When the next few variations featuring sixteenths evolve into an ever-expanding array of bowing patterns, wider and wider articulations, my impression is one of galaxies, of a universe that is expanding, of a supernova.

DSM: When runs of thirty-seconds first appear they are slurred (mm. 65-72), then they are separately bowed (mm. 73-76). More and more intensity. More and more and more.

CMT: The changes of mode—to the grand D major and back to D minor—are accompanied by returns to the slower rhythms that we had at the opening of the Chaconne. There is a renewal, another aspect of the eternal return.


DSM: But with each rebirth we have the beginnings again of the growing speed and chromaticism and intensity. Inescapable. Inevitable. Changes of changes. Wheels within wheels.

CMT: There’s a tension—for the performer especially, but also for the listener—between the elements of articulation, tempo, affect, bowing, fingering, and other aspects of technque. The variations call upon these in different ways—increasing the importance of one or another of them and diminishing the importance of the others. This is part of the ‘novel-esque’ character of the piece. Obviously, it's also part of why the Chaconne is such a showcase for virtuosic playing.

DSM: But it would be a mistake to dwell on technique. A technically brilliant performance of the Chaconne may be emotionally empty. Instead, the tension between these demands is the source of a cast of ‘characters’ in the composition.

CMT: These are different voices, I think—not the soliloquy of a single voice. The textures of the four strings, how Bach uses the violin's four strings, are, to me, at least four different voices in this Partita.

DSM: The developments in the Chaconne are logical and yet suprising. Its inordinate novelty—novelty begetting yet more novelty—is the source of much of the piece's profundity.

CMT: There’s an inherent urgency to the Chaconne as well. Something like the remark J. Tillman made upon hearing Josh Bell play the Chaconne in the Washington D.C. subway station last January – ‘the kind of music the ship’s band was playing on the Titanic, before the iceberg.’

DSM: In other words, the Chaconne “knows” that it must end. It is anticipating the end of the universe. In the beginning there was the Big Bang. The Chaconne is showing us the approach of the Big Crunch.

CMT: Yes, this Chaconne is not sticking to the script of Church dogma in the way that Bach’s sacred music does. This Chaconne is agnostic, or even atheist in its view. We feel the finiteness of our existence on Earth and are not exhorted to believe in any life hereafter.

T o prepare for a friend’s funeral service, I had been practicing the Chaconne every day—fussing over individual phrases, searching for better ways to string them together, and wondering about the very nature of the piece—at its core an old dance form that had been around for centuries. After the many times I had heard and played the Chaconne, I had hoped it would fall relatively easily into place by now, but it appeared to be taunting me. The more I worked, the more I saw; the more I saw, the further away it drifted from my grasp. Perhaps that is in the nature of every masterpiece. But more than that, the Chaconne seemed to exude shadows over its grandeur and artful design. Exactly what was hidden there I could not say, but I would lose myself for long stretches of time exploring the work’s repeating four-bar phrases, which rose and fell and marched solemnly forward in ever-changing patterns.”
  —  Arnold Steinhardt, Violin Dreams.

F rom the grave majesty of the beginning to the thirty-second notes which rush up and down like the very demons; from the tremulous arpeggios that hang almost motionless, like veiling clouds above a dark ravine ... to the devotional beauty of the D-major section, where the evening sun sets in a peaceful valley: the spirit of the master urges the instrument to incredible utterances. At the end of the D-major section it sounds like an organ, and sometimes a whole band of violins seems to be playing. This Chaconne is a triumph of spirit over matter such as even Bach never repeated in a more brilliant manner.”
  —  Phillip Spitta.

• Christian Tetzlaff, represented by Harrison Parrott Assoc.
  
• Big Crunch wikipedia page
  
• Josh Bell in D.C. Metro, L'Enfant station, JAN-2007. Washington Post article
  
• Video of Josh Bell in D.C. Metro, L'Enfant station, JAN-2007.
  
• Beach D. Aspects of Unity in J. S. Bach's Partitas and Suites: An Analytical Study. Univ Rochester, 2005.
  
• Choi S, Tan H. Perceived instability of virtual haptic texture: III. Effect of update rate. Presence 2007; 16:263-78.
  
• Efrati R. Bach: Interpretation of the Sonatas and Partitas for Solo Violin. Schott, 1993.
  
• Mastroianni J. Chaconne. Damian, 2005.
  
• Schröder J. Bach's Solo Violin Works: A Performer's Guide. Yale Univ, 2007.
  
• Schwenger P. The Tears of Things: Melancholy and Physical Objects. Univ Minnesota, 2006.
  
• Tetzlaff C. Sonatas and Partitas for Violin. (Hanssler, 2007.)