Higher-Order Virtuosity: Richard Goode and Chopin’s Ballade No. 3

I  n everything Chopin wrote, no matter how complex and virtuosic, that powerful simplicity is there at the core. Although he wrote some very difficult and impressive stuff, the ultimate effect of his music, I feel, should never really be to ‘impress’. But that’s exactly what the pianists we usually hear are striving to do: impress the contest judges, the critics, the public. The world we classical performers live in gives us very little room not to play big ‘show’ pieces, or make everything we play into one... Chopin’s third ballade suffers particularly from this problem. The ballades are all difficult, but No. 3 is the easiest of them—sort of like the shortest Himalaya. It seems as though all the star performers I’ve heard end up trying to make it as hard as the others, plowing through it with virtuosic flare, and thus trivializing it. [And how wonderful it is when, instead, someone like Richard Goode plays this piece with selfless transparency. –DSM]”
  — Paul Cantrell blog, In the Hands, 02-MAR-2005..

M y favorite part of Richard Goode’s performance last night in Kansas City [a program that included Mozart, Beethoven, Schumann, and Chopin] was the Chopin Ballad No. 3, Op. 47. This 9-minute piece is maybe the strangest of Chopin’s four ballades, on account of its unrelenting optimism. Goode’s expressive dexterity handles the staggering complexity with seeming ease and imparts a vigor suffused with warmth... perfect for this sweet, cheerful work.

G entle A-flat 6/8-meter dolce, evoking donkeys Chopin observed in the hills of Majorca? Donkeys with jobs, but happy jobs that they enjoyed doing.

T  he technique [of musical gesture] is perhaps a musical version of what is referred to as a ‘suture’ in film theory: placing the camera in such a way that it functions as the eye of the protagonist of the film, thereby drawing us, as unwitting spectators, to become the subject of the film ourselves, since we share the same visual field and same [Majorcan] point of view.”
  —  Patrick McCreless, in Almén & Pearsall, p. 13.

W hat a narrative trajectory! What storytelling! Social media of 1841! Our minds engage, imagination runs free, and we ‘friend’ or ‘follow’ this peripatetic, vacationing Chopin voice from the beginning to the end. The feeling is physical, not just emotional; it coheres—for Goode, and for us in the audience—throughout the piece, all the way to the satisfying, happy ending. For example, the motion from C (mm. 230, 232) down to the E-flat (mm. 231, 233) suggests the subsequent plunges to the low A-flat at the end. Energy flows! We “feel” the path that we are on, anticipate things along the way, anticipate them accurately. And this experience of uncanny accuracy is part of what is pleasant and thrilling for us: in material that is this complex and unpredictable, we don’t usually experience ourselves as being so graceful or right as this. We love being unexpectedly better than we are!

U ltimately, our minds and bodies gladly go everywhere Chopin’s and Goode’s narrative aims to take us. Theirs is a higher-order virtuosity that doesn’t strive to impress. It strives only to reveal what’s True, to tell this true story. But it’s not just ‘telling’, not just a musical ‘text’. The human body is involved—fingers, arms, flesh, nerves, mortal gifts, physical mass. The higher-order virtuosity inhabiting the body averts its gaze and embodies Laws of Physics in action—beauty incarnate; a kind of transcendence—something for which we surely hadn’t planned on our Friday night out, and something for which we feel thrilled and grateful. Bravo!

V  iewed as a sign, ‘formative repetition’ refers to what is repeated: it is usually a marker of segmentation, a grammatical feature. When a figure is repeated more than once, the attention begins to be attracted by the repetition itself; instead of focusing on the repeated material only, we focus on the act of repetition as an activity signifier per se and seek a symbolic interpretation of it. It is then a sign, not of segmentation or grammar, but of connotative meaning. It evokes extra-musical associations of... emphatically [re-]emphasized speech, dancing, laughing, etc.”
  — Raymond Monelle, p. 88, quoting Lidov.

• Richard Goode page at Frank Salomon Assoc
  
• Richard Goode page at Nonesuch.com
  
• Chopin F. Ballade No. 3, Op. 47 score at IMSLP.org
  
• Agawu K. Music as Discourse: Semiotic Adventures in Romantic Music. Oxford Univ, 2008.
  
• Almén B. A Theory of Musical Narrative. Indiana Univ, 2008.
  
• Almén B, Pearsall E, eds. Approaches to Meaning in Music. Indiana Univ, 2006.
  
• DSM. Richard Goode's emergent Chopin. CMT blog, 02-OCT-2011.
  
• Hatten R. Interpreting Musical Gestures, Topics, and Tropes: Mozart, Beethoven, Schubert. Indiana Univ, 2004.
  
• Huron D. Sweet Anticipation: Music and the Psychology of Expectation. Bradford, 2008.
  
• Monelle R. Linguistics and Semiotics in Music. Routledge, 1992.
  
• Nattiez J-J. Music and Discourse. Princeton Univ, 1990.
  
• Pearsall E. The structure of conflict: Dialectics and the play of personae in Chopin’s Op. 27, No. 2. Indiana Theory Rev 2003;24:107-27.

Richard Goode’s Emergent Chopin

I    have a hard time with music I can’t hear and construe tonally. I suppose it’s a habit of ear.”
  —  Richard Goode, interview with Cheryl North, 2002.

R ichard Goode performed in Rockport today…

• Schumann: Kinderszenen, Op. 16
  
• Schumann: Kreisleriana, Op. 16
  
• Chopin: Nocturne in E-flat No. 2, Op. 55
  
• Chopin: Scherzo No. 3 in c-sharp minor, Op. 39
  
• Chopin: Waltz in A-flat No.3, Op. 64
  
• Chopin: Waltz in C-sharp minor No. 2, Op. 64
  
• Chopin: Waltz in F Major No. 3, Op. 34
  
• Chopin: Ballade No. 3 in A-flat Major, Op. 47

T he performance reminds me that the delicacy of Chopin involves not only the delicacy of touch but also delicateness of the mind. The Scherzo Op. 39, especially, illustrates this. The C# minor tonality is latent, deferred for a long time, 24 bars or so, depending on how you interpret some of the bars. This was composed during one of the periods when Chopin’s tuberculosis was exacerbated—a time when we naturally imagine his uncertainty about his health and what would come next was also exacerbated.

T   uberculosis was never confirmed, and the Chopin autopsy report has never been found. Both cystic fibrosis and alpha-1-antitrypsin deficiency are possible differential diagnoses that can explain his symptoms.”
  —  Ulf Kongsgaard, University Hospital, Oslo, 2011.

T he tension abates a bit when the original pattern is overcome by C# sonorities that are more persuasive both metrically/cadentially and tonally. The stable major harmonies that began the composition are transformed into contrapuntal chords, ones that evoke passing tones—naturals, flats, double-sharps—on the path toward a less-complex C#. The meaning of what’s gone before gradually emerges as the complexity recedes. The essayist’s/composer’s/performer’s ideas are not expounded so much as they’re ‘discovered’. (The Op. 39 Chopin descending D-flat major ‘sparkle’ figures in the upper register presage Ray Lynch’s celestial electronica by more than 100 years.)

I n other words, these ‘character pieces’ reveal the composer-as-discoverer or composer-as-kluger/tinkerer/experimenter, and stand in stark contrast to the usual notion of composer-as-omniscient-designer/architect.

G oode gazed out the windows at various moments during the Schumann, looking at the large waves crashing outside on the rocks. How could this scene not influence his next move? How could the liveliness of the waves not have an impact on the ‘Sehr lebhaft’! How could the excitement of the wheeling gulls not impart something extra to the ‘Sehr aufgeregt’!

O ne or two attendees asked whether the screen could be drawn, to darken the hall and “Could you please put a spotlight on Mr. Goode’s face?” David Deveau, MIT Senior Lecturer and founder and Artistic Director of Rockport Music, replied after the intermission that, no, no changes would be made: the lighting and the open view of the sea were precisely as Mr. Goode had requested. Goode finds the late afternoon light of the Atlantic stretching off to the northeast a fine and rewarding view to contemplate while performing these particular works.

I n summary, it was a performance that was intensely enjoyable, warmly recommended, with even more of the spontaneity and essayistic qualities for which Goode is so well known. Perfect for this complex, chilly, drizzly Sunday in October. The F-minor Chopin waltz and Bach’s Sarabande from the B-flat partita were Goode’s parting encore gifts to us all. We went away satisfied and grateful.

T he new Shalin Liu Performance Hall is very nice, by the way—acoustically as well as visually. The irregularities of the dry-laid stone walls on the main floor are enough to prevent any notable resonances or dead zones. And the multi-glazed windows and reception hall on the third floor provide excellent acoustic isolation. There was a 25-knot breeze blowing outside and 1-meter chop in Sandy Bay, none of which was audible inside the Shalin Liu hall. Delightful.

P .S.—Cystic fibrosis was only recognized as such in the 1930s [Andersen D. Cystic fibrosis. Am J Dis Child 1938;56:344-99] and alpha-1-antitrypsin deficiency was only discovered some 30 years after that. So the fact that Chopin’s death was attributed to “tuberculosis” is not surprising, given the minimal medical knowledge at the time.

I   have a photo of Richard Goode in my office. I have known Richard for 25, no, 30 years. When my son was small, he asked ‘Dad, is that picture Beethoven?’ And I laughed and replied, ‘No, but almost. As good as if it were Beethoven. He plays almost as if he were Beethoven.’ ”
  —  David Deveau, pre-concert remarks.

• Goode page at Frank Salomon Associates website
  
• Goode bio at Jay K. Hoffman Associates website
  
• Bedau M, Humphreys P, eds. Emergence: Contemporary Readings in Philosophy and Science. MIT, 2008.
  
• Blum D. Quintet: Five Journeys toward Musical Fulfillment. Cornell Univ, 1999. [Ch. 4 ‘Going to the Core’, pp. 112-151]
  
• Bunge M. Emergence and Convergence: Qualitative Novelty and the Unity of Knowledge. Univ Toronto, 2003.
  
• Corradini A, O’Connor T, eds. Emergence in Science and Philosophy. Routledge, 2010.
  
• Feltz B, et al., eds. Self-organization and Emergence in Life Sciences. Springer, 2006.
  
• Herer B. Tuberculosis and music: A case report and review of clinical, epidemiologic, and cultural factors. Med Prob Perf Artists 2005;20(3):131-8.
  
• Hoeckner B. Programming the Absolute: Nineteenth-Century German Music and the Hermeneutics of the Moment. Princeton Univ, 2002.
  
• Kongsgaard U. Frédéric Chopin and his suffering. Tidsskr Nor Laegeforen. 2011;131:707-10.
  
• Montecucco L, ed. Complexity and Emergence. World Scientific, 2003.
  
• Chopin Scherzo No. 3, Op. 39, score at IMSLP
  
• Rockport Chambermusic Festival website
  
• Society for Complexity in Acute Illness (SCAI)
  
• Performing Arts Medicine Association (PAMA)

Autocorrelation and Agogicity: Measuring Goode’s Bach

W    hat one remembers most from Goode’s playing is not its beauty—exceptional as it is—but his way of coming to grips with the composer’s central thought, so that a work tends to make sense beyond one’s previous perception of it... The spontaneous formulating process of the creator [becomes] tangible in the concert hall.”
  —  David Blum, New Yorker, 29-JUN-1992.

To say exactly why we like or dislike a particular artist’s interpretation of a piece of music is difficult. And to compare and contrast two different artists’ interpretations in a way that can be objectively assessed and broadly agreed upon is also hard. The language of analysis and criticism readily devolves into nebulous descriptions or into abstruse technical terms that get in the way of conversation and real understanding. But the superb performance last night by Richard Goode in Kansas City in a Bach-Chopin program that was part of the Friends of Chamber Music’s ‘Master Pianists Series’ prompted me to take a whack at remedying this.

I thoroughly enjoy everything Richard Goode does, always. But in this recital I especially liked his accounts of Bach’s Sinfonias (BWV 791-801) and Preludes and Fugues from Das Wohltemperirte Clavier, Book II (BWV 870, 878, 885, 889). And I very much admire his accounts of Bach’s Partitas... one of Richard’s encore pieces was the Sarabande from the D major Partita No. 4 (BWV 828). How to describe it? His interpretation is not as ‘dry’ as others’ Bach interpretations; it is optimistic and expansive—and it projects a distinctive, quintessentially ‘American’ attitude of curiosity and humor about life.

I confess I always feel that flowery, subjective descriptions are less than satisfying though. When I tell you why I like Richard’s interpretations, I want instead to be able to give you something that you can independently and reliably and objectively assess for yourself. I want to compare what Richard does quantitatively to, say, Glenn Gould’s and others’ interpretations—and calculate how they differ in various passages, and why those differences cause us to perceive and respond to the interpretations in such varied ways. How shall we do that?

One way to do it is to take digital recordings of the performances and perform a number of signal-processing measurements on them; examine the timings within critical phrases or across longer expressive spans; calculate various time-domain metrics from the digitized music; perform statistical tests on the metrics, to see whether and how they differ; and so on. I regularly do that, as a hobby—not just with baroque music but with other things, too, when I’m trying to understand why I am feeling a certain way about a piece. (Somewhat weird hobby, I admit, but it’s just in my engineer’s nature to want to take things apart and figure out what makes them ‘tick’.) Usually I use MATLAB or MAPLE or MATHEMATICA other fancy math software to do this. But it’s actually possible to do a number of interesting and useful analyses with something as simple as Microsoft Excel. Here goes!

Think, for example, about the difference between Goode and Gould when playing Bach. Actually, to make a clean ‘apples-to-apples’ comparison, let’s think about just Bach’s 6 Partitas and, within those, let’s think about just one of the movement forms that has a consistent time-signature—for example, the Allemandes.

As an historical dance usually in 4/4 time, an Allemande can have a tempo ranging from largo almost up to presto. Gould’s tempi are quite fast; Goode’s are generally more leisurely, at least ‘New Yorker leisurely’. But just noting the large-scale differences in tempi is too crude—it doesn’t explain very much about why their interpretations are so different. The ‘pulse’ is a function of time, operating and varying on a multi-dimensional, fractal time scale: rubato—small-scale, intra- and inter-beat and inter-measure variations; and larger-scale accelerando/ritardando decisions.


But the differences arise from more even than that. The durations that particular notes are held are also distinctively different. ‘Agogic’ is the fancy music-theory word that means varying a note’s (or beat’s) emphasis by varying its duration. A dry, flat, highly ‘motoric’ performance like Gould’s doesn’t have much agogic variation. A more romantic performance like Goode’s has many places where lots of agogic emphasis is used.

A    •gog•ic [uh-goj-ik]
(noun) the theory that accents within a musical phrase can be produced by modifying the duration of certain notes rather than by increasing dynamic stress.
(adj) stressed or accented through a variably prolonged duration.”

So, gee, you can take an MP3 and use a cheap digital audio editor software app; you drag the cursor over the beginning of a note and then rubber-band-drag the cursor to the end of the note; you measure how many milliseconds that time-interval is. You can do that for all of the notes in 4 or 6 or 8 bars of a passage that contains what, for you, is emblematic of the interpretive difference you’re interested in. Do that for one artist’s recording, and then do the same thing for the same bars in another artist’s recording. You put the information into a spreadsheet or database. You then quantitatively calculate the ‘agocity’ of the two artists’ performances/interpretations.

W hich is what I did, after being stimulated by Richard’s wonderful performance last night. I just had to figure out why it is that I like his Bach so much while I simultaneously like various other artists’ Bach interpretations very much, too. And I wanted to be able to say objectively how their characteristic personal rhythmic decisions differ in crucial passages. I wanted to put together a little ‘tool’ that I could share with you, which would enable all of us to conveniently figure these things out in the future—not just for Bach but for anything. That way we won’t be frustrated by nebulous words that don’t really say very much or that have hopelessly imprecise meanings.

Autocorrelation (of beat-to-beat time-intervals; or of note-to-note durations) is a statistical function that measures repeating patterns, such as the presence of a periodic signal which is (partly) obscured by variability.

It’s used frequently in signal processing for analyzing series of values, so-called time-domain signals or time-series. Mathematically, it represents the quantitative similarity between observations as a function of the time separation between them. The time-domain is divided up into units—in this case, my measurements were in milliseconds for note/beat durations over passages over various lengths (up to 6 bars at a time in the portions of the Partitas that interested me). Then I ‘normalized’ those values to the average milliseconds per beat across the number of measures in the passages I compared, and I set the normalized tempo for Goode to 100% and the normalized tempo for Gould to 100%. Next, to take into account that Gould plays almost everything substantially faster than Goode, I calculated the ‘within-performer-within-phrase’ autocorrelations from the percentage deviations from those by-performer normalized 100%-meter values. The autocorrelation can be expressed as an equation involving the covariance and variance of these time-series from time i to time t as a function of the beats in between (lag k):


The results of this little experiment are in this Excel spreadsheet. You can click on the screenshot below to open the file or download a copy of it. If you like, you can use the spreadsheet to make your own measurements of selected bars of pairs of performances you’d like to compare.


To me, the significance is that I now understand much better what it is about Goode’s Bach that pleases me so much: it is this particular autocorrelation pattern—a characteristic species of agogicity that the autocorrelogram graphically shows. There are long-range, high, positive autocorrelations at various inter-beat distances that line up more or less on the first-beat-of-measure boundaries [and also the phrase and hyper-meter boundaries], and those autocorrelation peaks taper off quite slowly the further apart any two notes are (the more ‘lag’ units there are between them in the sequence of notes or beats). By contrast, Gould (and other ‘drier’ Bach interpreters) has a high autocorrelation for adjacent notes (at Lag = 1), which damps out pretty quickly the further apart any two notes are.

W hat the autocorrelation analysis tells us is that Goode’s playing manifests a high degree of ‘associativity’ of time intervals over longer time-scales—and this is equally true for intervals that he compresses to be shorter than the nominal meter, and for intervals that he agogically prolongs and stresses. The peaks in the autocorrelogram amount to a sort of ‘polymeter’ that is distinctively Goode’s.

By contrast, Gould’s playing manifests a ‘memory-lessness’—nearly devoid of associativity of rhythms and durations on long time-scales for non-adjacent notes. Both Goode and Gould perform these motoric Bach dance suite movements with motoric rhythmicity. But their motor-like rhythms are remarkably and measurably different—the differences in our cognitive and emotional perceptions when we hear these disparate interpretations arise from their deliberately different, highly personal and unmistakeably different autocorrelations. Here we have quantitatively different ‘agogicity’ as a measure of interpretive style.

I    fixed the action in some of the instruments I play on — and the piano I use for all recordings is now so fixed — so that it is a shallower and more responsive action than the standard. It ... is rather like an automobile without power steering: you are in control and not it; it doesn’t drive you, you drive it. This is the secret of doing Bach on the piano at all. You must have that immediacy of response, that control over fine definitions of things.”
  —  Glenn Gould.

Saying that Gould’s Allemande playing is relatively ‘memory-less’ or anti-agogic is not to say that his playing was ‘mechanical’ or automatic or that his vision of these Allemandes was ‘microscopic’ and eschewed a macro-scale rhythmic architecture. By no means! Goode has and Gould had—each of them—comprehensive conceptions of each of these Allemandes—of each of the Partitas’ and Suites’ movements. But the metric organization and fractal scales that they each use to build their interpretations’ rhythmic structure are dramatically different—in ways that, as you see above, can be measured and compared numerically and displayed graphically. By autocorrelation analysis, we find out exactly how Goode paints with a ‘broader’ somewhat impressionistic brush (Rembrandt?) and Gould with a magnifying glass and a ‘finer’ one (Vermeer?). Both are highly detailed and narrative in their delivery of the Partitas and Suites; both are illusionistic.

So here we have one good, objective way to measure and say how they do what they do, and how it works. Leigh Smith and other music theoreticians have examined things in similar ways in years past [see links below], not for Bach and not with quite the same purpose as what we’re doing here. They have used wavelet transforms and other frequency-domain methods, not just autocorrelation and time-domain methods. Smith in particular discusses the difference between measuring the actual timing (from waveform or other performance data) versus capturing the musician’s intention (from MIDI keystrokes datastream or other empirical data that precede the music being made audible). In my own experimentation to prepare this CMT blog post, I have (obviously) only the features in the waveforms digitized in the (audible) MP3 files to work with and have spent only a few hours working on it. This post and its Excel attachment are meant only as a quick demonstration that these things work and that they are useful to help us understand the music better. Enjoy!


    [50-sec clip, Richard Goode, Bach, Partita No. 1, BWV 825, Allemande, 1.2MB MP3]

    [40-sec clip, Glenn Gould, Bach, Partita No. 1, BWV 825, Allemande, 1.2MB MP3]


    [50-sec clip, Richard Goode, Bach, Partita No. 2, BWV 826, Allemande, 1.2MB MP3]

    [45-sec clip, Glenn Gould, Bach, Partita No. 2, BWV 826, Allemande, 1.2MB MP3]


    [50-sec clip, Richard Goode, Bach, Partita No. 3, BWV 827, Allemande, 1.2MB MP3]

    [45-sec clip, Glenn Gould, Bach, Partita No. 3, BWV 827, Allemande, 1.2MB MP3]


    [50-sec clip, Richard Goode, Bach, Partita No. 4, BWV 828, Allemande, 1.2MB MP3]

    [45-sec clip, Glenn Gould, Bach, Partita No. 4, BWV 828, Allemande, 1.2MB MP3]


    [50-sec clip, Richard Goode, Bach, Partita No. 5, BWV 829, Allemande, 1.2MB MP3]

    [35-sec clip, Glenn Gould, Bach, Partita No. 5, BWV 829, Allemande, 1.2MB MP3]


    [50-sec clip, Richard Goode, Bach, Partita No. 6, BWV 830, Allemande, 1.2MB MP3]

    [40-sec clip, Glenn Gould, Bach, Partita No. 6, BWV 830, Allemande, 1.2MB MP3]

In Goode’s Bach I hear a sort of Walt Whitman-esque, America-flavored ‘agogic freedom’—Goode’s rhythm and emphases and playing style represent to me a sort of ‘democracy trope’. I hear in him an enthusiasm for discovery; an ever-renewing openness for life’s ambiguities and ‘matters-arising’.

Goode’s affect or vision involves more rhetorical freedom than Gould’s concept of Bach, I think, in part because of the sentinel differences in their autocorrelation patterns and ‘agogic polymeter’. Oh, there is of course a difference between rubato (freedom ‘between’ the beats) and agogics (freedom ‘of’ the beats—in where the beats fall). Agogics are often applied at harmonic-pivot points. That’s just where they naturally and logically tend to go.

But Goode’s autocorrelated ‘agogic polymeter’ (or whatever you’d prefer to call it) I think ‘subverts’ or calls into question what we perceive the meter to be—by injecting variable, conflicting metrical structure and by modestly shifting the phase of the metrical accents. This is why it has the strong, friendly effect on me that it does. The initial events of each of these Allemandes provide evidence sufficient for us to establish contexts and referential schematics—mental ‘models’ for what we imagine will follow. The acoustic cues fit into the schematic or framework around which our subsequent anticipation is formed. Deferring or subverting the established meter, as Goode does, forces us listeners to attend to the present moment and continually revise and re-form our expectations. By contrast, with Gould, most of what we anticipate promptly materializes. Gould’s epistemological and perceptual effect and the impact on our cognition and emotions are quite different from Goode’s.

Cognitively, we subconsciously keep track of and group the conflicts and uncertainties/ambiguities that are caused by Goode’s mounting ‘phenomenal agogic accents’. Maintaining these multiple concurrent and conflicting suppositions in our heads as we listen to Goode play—asks that we put a considerable and peculiar sort of effort into it. It is a different sort of attention, I would say, than the attention that Gould’s playing asks of us. Goode’s agogically autocorrelated playing requires our listening strategy to allocate attention and memory toward establishing groupings and processing long timescale expectations. Goode engages us in a distinctive and different sort of conversation/meditation. And the autocorrelation analysis just helps to reveal a quantitative pattern that explains how it’s different.


Compared to Goode’s interpretations, Gould’s Bach has—I go out on a limb here—an ‘anti-expressionist’ aesthetic. From Gould (and others) we get unrelenting introspection, plus transcendent but psychologically ‘dissociative’ experiences, almost PTSD-like experiences.

To me, the ideal affect with Bach also involves a certain amount of rhetorical surprise as well as angst. Agogic accents—a ‘sung’ or ‘danced’ rhythm that either personalizes or depersonalizes—orients or disorients—can make the expression seem as though it were uttered by a particular and known ‘self’ (e.g., Goode; or Bach) or, alternatively, by an ambivalent or profoundly unknowable entity—(e.g, Gould; or God/TheDivine/TheCosmos).

So these Bach suites—and these Allemandes—are no mere dances. Goode ‘dances’ mostly ‘out’; Gould—and others—dance them in a mostly ‘inward’ way. The depth and the originality in the ways that Goode and other artists ‘dance’ them, while they are surely very diverse, never cease to delight and inspire and propel us to take hold of life and figure things out.

The two-hour program last night also included a wonderful collection of Chopin Mazurkas (Op. 6 No. 3 in E major; Op. 7 No. 2 in A minor; Op. 7 No. 4 in A-flat major; Op. 56 No. 2 in C major; Op. 56 No. 3 in C minor), Nocturnes (Op. 15. No. 2 in F-sharp major; Op. 27. No. 2 in D-flat major), and Waltzes (Op. 34 No. 3 in F major; Op 64. No. 2 in C-sharp minor; Op. 64 No. 3 in A-flat major)—24 pieces in all. Both the Op. 39 No. 3 Scherzo in C-sharp minor just before the interval and the Op. 61 Polonaise-Fantasie at the end of the program brought the appreciative audience to its feet. Bravo!

M    aking a break from the first and second notes of a melody is to be recommended where the tempo changes from slow to fast. In passing from the Andante to the Allegro in the Sinfonia of Partita No. 2, for example, it is advisable to retain the slow tempo on the final G major chord and not to embark on the faster tempo until the two semiquavers which follow... A relative degree of independence of the beat also applies in the case of recitative.”
  —  WWPBSD? [What Would Paul Badura-Skoda Do?], p. 18.

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• Richard Goode at Friends of Chamber Music Master Pianists Series, 18-OCT-2008.
  
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• Smith L, Honig H. Time-frequency representation of musical rhythm by continuous wavelets. J Math Music 2008. [1MB pdf]
  
• Smith L. Modeling rhythm perception by continuous time-frequency analysis. Proc Intl Computer Music Conf, 1996. [1MB pdf]
  
• Stout M. The Myth of Sanity: Divided Consciousness and the Promise of Awareness. Penguin, 2002.
  
• Toiviainen P, Snyder J. Tapping to Bach: Resonance-based modeling of pulse. Music Perception 2003; 21:43-80.
  
• Tomita Y. The six partitas. Queen’s University Belfast, 2002.
  
• Troeger R. Playing Bach on the Keyboard: A Practical Guide. Amadeus, 2003.
  

Goode: Whitman-esque Voyager-Prophet of the Universal ‘Want’

I  considered how best to describe to you Richard Goode’s unique accomplishment; how best to characterize that quality which makes his a distinctly American voice. And it occurred to me that he is, in many ways, the musical equivalent of Walt Whitman. Richard Goode is, among pianists, the epitome of a Whitman-like ‘voyager ego’—someone who is able to take the specifics of one individual’s feeling and experience and, through his playing, make them universal. In doing so, he transforms us . . . ”

  —  Cynthia Siebert

CMT: The human brain, according to Nussbaum, is a living record of its evolutionary history. Relatively recent cognitive developments derive from older representational functions, about which the science is all less than forty years old and of which we are hardly aware. But consideration of music performance can shed light on ancient cognitive functions that underlie modern human cognition. The biology, psychology, and philosophy of musical representation have much to tell us about what we are, and what, as a species, we have been.

DSM: It isn’t just music that offers us revelations like this. ‘Poets Thinking’, one of Helen Vendler’s books, argues that poetry is a mode of thinking that reveals not just our aesthetic values but also our psychology. Vendler is a wonderful elucidator of individual poems. Nobody writes more insightfully about a poem’s stylistic structure, and the emotional and intellectual purposes that the structure serves. And by examining the distinctive strategies of thinking in the work of such radically different poets as Pope, Whitman, Dickinson, and Yeats, Vendler makes visible aspects of style and language that other critics simply haven’t seen.

CMT: This is what Cynthia Siebert was hinting at in her introduction of Richard Goode. Music, like poetry, has often been considered an irrational genre, more expressive than logical, more meditative than given to coherent argument. And yet, in each of the four very different composers Richard Goode performed last night, he reveals a style of thinking in operation. Although they may prefer different means, he argues, all composers of any value are thinkers. He convincingly traces a trajectory from Bach’s Partitas, through late Mozart, through Brahms, to Debussy. Admittedly, Goode’s Bach is a more romantic account than is usual. But it’s a very plausible interpretation.

DSM: Whitman was writing as a poet of repetitive insistence—someone for whom thinking must be followed by rethinking. Goode shows us Brahms thinking in images, using montage in lieu of argument. He shows us Debussy as a satiric miniaturizer, remaking in verse the form of the essay. He shows us Mozart experimenting with plot to characterize life’s unfolding. The repetitions that Goode localizes in each of these composers’ works become, in his mind and hands, coherent arguments—ones that are set forth, defended, critically turned over, reiterated after deliberation and reflection. This is part of what makes Goode so ‘new’.

C   ome, said my soul, such verses
for my Body let us write, (for we are one,)
That should I after return,
Or, long, long hence, in other spheres,
There to some group of mates the chants resuming,
(Tallying Earth’s soil, trees, winds, tumultuous waves,)
Ever with pleas’d smile I may keep on,
Ever and ever yet the verses owning
 —as, first, I here and now
Signing for Soul and Body, set to them my name . . .
The untold want by life and land ne’er granted,
Now, voyager, sail thou forth to seek and find.”

  —  Walt Whitman, Leaves of Grass

CMT: It’s also, I think, what makes his playing so universal, so meaningful to each person, and fresh for each person upon repeated listenings. With his characteristic lucidity and spirit, Goode traces through these composers’ expressions to find evidence of thought in lyric; the silent stylistic measures representing changes of mind; the condensed power of poetic thinking. His work argues against the reduction of performance to well-worn and long-since elucidated themes and demonstrates, instead, that there is, ideally, in music a serious process of thinking, a deliberated style—however ancient the theme may be—and one that is powerful and original, fresh and new.

DSM: Whitman seeks the redemption of America through the reconstruction of individual subjects in conversion. Would Cynthia Siebert say that Goode seeks to redeem us by inducing ecstatic, regenerating experiences in his audiences?

CMT: Yes. That is the consequence of her opening remarks—consummate presenter that she is. She gives us not merely an introduction, but a capsulized lesson. There are the de rigeur honorifics, of course. But then she invariably gives the audience a ‘pearl,’ some unique bit of insight, a provocation, even. She cautions us that Goode is about to spin an emotional tale. You know a well-known “rule system” has been developed at the Royal Institute of Technology in Stockholm (Sundberg et al., 1983), for characterizing emotional content in music performances. The KTH model consists of a set of performance rules that predict or prescribe aspects of timing, dynamics, and articulation, based on local musical context. The rules refer to a limited class of musical situations and theoretical concepts (simple duration ratios between successive notes, ascending lines, melodic leaps, melodic and harmonic charge, phrase structure, etc.). Most of the rules operate at a low level and look only at very local contexts and affecting individual notes. But there are also rules that refer to entire phrases, much apropos of Richard Goode’s expressive playing. The rules are parameterized with a varying number of parameters. Originally, the KTH model was developed using the so-called “analysis-by-synthesis approach” that involves a professional musician directly evaluating each tentative rule brought forward by the researcher. Musician and researcher engage in constant feedback to iteratively find the best formulation and parameter settings for each rule. This method has the advantage of modeling a kind of performer–listener interaction, but it falls short by placing high demands on the evaluating expert musicians and by not permitting reliable evaluations due to the small number of judgments.

DSM: Thinking of the performance that Richard Goode just gave last night, consider just one particular rule: DURATION CONTRAST. This rule modifies the ratio between successive note durations in order to enhance and make more easily perceivable the differences in duration. Most commonly it changes the durations of a long and a short one so that the longer becomes a bit longer, and the shorter becomes shorter. As for every rule, there is a quantity control parameter (k) to be set by the analyst. This parameter is designed so as to give a fairly good result when its value is around 1. With a k value of 0, a particular rule is effectively switched off; when k is set to a negative value, the rules are inverted (in DURATION CONTRAST, it would blur the rhythmic contrasts)—which, by the way, can produce unmusical results. I can show you on my DAW synthesizer-sequencer if you like. An important aspect of the model is that it’s additive. For instance, there are several rules that influence the duration of a note, and the effects of the individual rules are added cumulatively to give the final duration. Sundberg and colleagues examined how well the KTH model can be fitted to a particular performance of a slow Mozart sonata movement (K.332, first 20 bars of the Adagio) manually, by trial and error. They focused exclusively on expressive timing of the melody (in terms of deviations from the score) and determined similarity between the performance and the model with the correlation coefficient. The PHRASE ARCH rule (shaping phrases on different structural levels) seemed to dominate the performance, although they could not find one single k parameter for these initial bars. Therefore, they tested k values for each phrase individually. Here it was mostly the PHRASE ARCH rule that got the highest correlations, as well as HARMONIC CHARGE and negative DURATION CONTRAST. The KTH model has also been used to model certain emotional colourings that might not be immediately inherent in the music structure. For example, the DURATION CONTRAST rule was found to especially distinguish between a sad and a happy performance. Some specifically selected subsets of rules and k parameter settings (“emotional rule palettes”, see Bresin & Friberg, 2000) were derived from measured performances in order to model emotional coloring of performances.

CMT: This extension to emotionality has led recently to more comprehensive computational models of expressive performances. These models include, besides the generative KTH model and the emotional models, also random variability within certain bounds, and analogies to physical motion. Recently, it was proposed to extend it with a factor of “stylistic unexpectedness” (see Juslin). To date, there is plenty of evidence that the KTH rule model is a viable representation language for describing expressive performance. To what extent it can account for the observed variations in large collections of performances of truly complex music is still an open issue. These other more recent quantitative models with more complexity and more degrees of freedom may ultimately capture more of the expressive range . . .

DSM: One of those recent models based mainly on mathematical considerations is the “Mazzola model”. The Swiss mathematician and Jazz pianist Guerino Mazzola developed his mathematical music theory and performance model beginning in the 1980s. His most recent book (Mazzola, 2002) extends over more than 1,300 pages and gives a comprehensive survey of the theoretical background as well as its computational implementation.

CMT: The Mazzola model builds on Mazzola’s mathematical music theory that includes various aspects of music theory and analysis and involves philosophical, semiotic, and aesthetic considerations as well. Every step is explained in specifically mathematical terms. He invents special terminology that is greatly different from what is commonly used in performance research, so musicologists do seem to hold it somewhat in abeyance. Engineers and mathematicians, like Bill Sethares at Wisconsin, seem to have greater receptiveness to Mazzola’s ideas . . .

DSM: The Mazzola model basically consists of an analysis part and a performance part. The analysis part involves computer-aided analysis tools for various aspects of the music structure as, e.g., meter, melody, or harmony. Each of these is implemented in particular plugins, the so-called “rubettes”, that assign particular “weights” to each note in a symbolic score. The performance part that transforms structural features into a synthesized performance is theoretically anchored in the so-called “Stemma Theory” and “Operator Theory” (a sort of additive rule-based structure-to-performance mapping). It iteratively modifies the “performance vector fields”, each of which controls a single expressive parameter of a synthesized performance. I’ve been playing around with that over the past couple of weeks on my old Ensoniq equipment . . .

CMT: What about quantification of individual style? Predictive models like the KTH or the Mazzola models generally focus on fundamental, common performance principles—that is, on those aspects that most performances have in common. Of course, there have also been attempts at measuring, quantifying, and describing stylistic performance differences. Statistical analysis can reveal a number of characteristic and distinctive phrasing behaviors, some of which could be associated (in a statistical sense) with a particular pianist. Can we do that with Goode?

DSM: Well, yes. After the concert last night, I extracted some tracks off Goode CDs that we own. We can examine visualization performance trajectories from those mp3s. Basically, the detailed performance data – beat-level tempo and dynamics curves – can be represented in an integrated way as trajectories in a two-dimensional “tempo–loudness” space that show the joint development of tempo and dynamics over time (see Langner & Goebl, 2003). This plot shows a trajectory from Richard Goode’s recording of a performance of the Mozart Rondo in A minor (K. 511) that we heard last night at the Folly Theater in Kansas City.


CMT: The line is produced by interpolating between the measured tempo and dynamics points that you captured off the CD, and smoothing the result with a moving-window Gaussian to make the trends visible. The degree of smoothing controls the amount of local variation in the plot. This is similar to Dixon’s “Performance Worm” (Dixon, 2002) that computes and visualizes performance trajectories. But the trajectory representation here also provides the basis for more detailed quantitative analysis, with data analysis (data mining) methods. So for Goode’s ‘voyager ego,’ as Cynthia Siebert called it, we should be able to map his (or other artists’ – ) expressive voyages after the fact, catalogue them, compare them.

• Goode R. Mozart. (Nonesuch, 2005.)
  
• Goode R. Bach Partitas 1, 3 & 6. (Nonesuch, 2003.)
  
• Goode R. Bach Partitas 2, 4 & 5. (Nonesuch, 1999.)
  
• Goode R. Beethoven. (Nonesuch, 1993.)
  
• Goode R. Brahms. (Nonesuch, 1992.)
  
• Goode R. Schubert: Sonata in B-flat; Impromptu in A-flat. (Nonesuch, 1992.)
  
• Goode R. Schubert: Sonata in c; Ländler. (Nonesuch, 1992.)
  
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• KTH website, Stockholm