Aleatory Quiz

John Cage and Karlheinz Stockhausen, c. 1958

John Cage and Karlheinz Stockhausen, c. 1958

It’s Aleatory Week in my Music Theory IV class, and I always give a fun aleatory quiz for the occasion. Aleatory (derived from the Latin alea, meaning “dice”) is “a term applied to music whose composition and/or performance is, to a greater or lesser extent, undetermined by the composer.” (Grove Music) Aleatory is thus synonymous with the term indeterminacy. Two broad types of aleatory music can be distinguished: music in which elements of the compositional construction are determined by chance (resulting in fixed compositions), and music in which elements of the performance are undetermined by the composer and must be determined by the performer(s) (e.g. through the use of graphic notation or “mobile form”). Certainly it is possible for these two types to be combined in a single work.

The below quiz contains six excerpts from the following three piano works: Pierre Boulez’s Piano Sonata No.2 (1947-48), Karlheinz Stockhausen’s Klavierstückeset 1 (Nos.1-4) (1952), and John Cage’s Music of Changes (1951). Only the Cage work is aleatory. It is a composition in which each element was determined by the use of chance procedures. “Each detail of his score was determined by the toss of three coins six times, which directed him to a specific number in I Ching (the Oriental “Book of Changes”); this in turn sent him to a numbered position on one of twenty-six charts he had devised. Thus a single pitch was determined. The procedure was then repeated in the determination of duration, timbre, and other parameters.” (Watkins, Soundings, p.560) Cage’s Music of Changes is then aleatory of the first type described above – that is, chance operations were used in constructing its fixed, carefully notated score.

The quiz, then, essentially requires the listener to aurally identify Cage’s chance music from among the other two highly-controlled works. Each of the three works listed above are represented at least once on the quiz. If you are up for a real challenge, try to distinguish the Boulez excerpts from the Stockhausen excerpts as well. (No fair cheating with your Shazam app!) Answers are posted at the bottom of the page.

THE QUIZ
Number 1
Number 2
Number 3
Number 4
Number 5
Number 6

The obvious point of this quiz is the ironic fact that aleatory of the kind represented by Cage’s Music of Changes often produced results that are strikingly similar to works of composers in the modernist avant-garde, composers that came to loathe Cage’s aleatory. Boulez, who initially recognized an aesthetic affinity between Cage and himself, eventually attacked Cage mercilessly (without naming him) stating that the adoption of chance procedures only “conceal[s] a fundamental weakness in compositional technique… It is an artificial paradise, comfortably arranged, whose dreams are, I suspect, never very miraculous: a narcotic which protects against the needle-prick of invention.” (Boulez, “Alea” 1957, tr. Stephen Walsh)

# Answers (highlight boxes below to reveal answers)
1 Cage, Music of Changes
2 Boulez, Piano Sonata No. 2, mvmt 4
3 Stockhausen, Klavierstück II
4 Boulez, Piano Sonata No. 2, mvmt 4
5 Cage, Music of Changes
6 Stockhausen, Klavierstück I

 

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Glenn Gould’s Singing Transcribed – Bach Sinfonia 4

So, what to make of Glenn Gould’s incessant singing and muttering while performing? Some find it intolerable. Others find it charming. Some of us may even have favorite Gould vocalized passages. (One of mine is the 17th measure of the 14th Goldberg Variation from the 1981 recording.) Personally, I find Gould’s singing in no way distracting. I am no longer the big fan of Gould’s pianism that I once was, but that has nothing to do with his eccentric vocalizations. Most of the time, I even forget they’re there. (The subconscious mind must be at work here distinguishing the intentionality of musical tone from the non-intentionality of extraneous sounds.) If anything, Gould’s singing authenticates and humanizes his performances. It reveals a performer so entirely absorbed in the music’s moment and reminds us that this is a performance, even if within the confines of a recording studio. Gould’s mutterings distinguish his recordings from those countless note-perfect recordings available today that take on a fabricated, sterile, and even robotic quality. (Is perfection ever very interesting?)

What I find a bit more off-putting than Gould’s vocal eccentricities are the middle-register hiccups that emanate from Gould’s beloved “CD 318” Steinway piano on a couple of his recordings. The hiccups are perhaps most pronounced on Gould’s 1964 recording of Bach’s Inventions and Sinfonias (the first recording project following his well-known withdrawal from the concert stage) and are apparently the result of Gould’s constant tinkering with CD 318 in order to achieve as harpsichord-like a quality as possible. Gould found the hiccup effect charming enough not to abandon his dear CD318, which traveled with him throughout his concertizing career. (In the early 1970s, CD 318 suffered irreparable damage in a moving accident, which devastated Gould.)

Below is a transcription of Glenn Gould playing and singing the fourth Sinfonia in D minor. The score reflects exactly what Gould played and not necessarily what Bach notated (i.e. embellishments are written out), exactly what Gould sang (notated to the best of my ability), and the hiccups that ring from CD 318 (notated with boxed noteheads). Gould’s notated sung part is obviously an approximation in certain passages given his use of vibrato, frequent portamenti (some before the beat, some after), and occasional intonational imprecision. Whatever you make of Gould’s singing, at least now you can follow along. (By the way, is that Gould himself in the final measures or a passing bus?)

Listen here. (Headphones are an obvious advantage.)

Click to embiggen

Click to embiggen

The difficulty of transcribing Gould’s singing depends on several factors such as how fast and loud the piano is, how vocal and loud Gould is, whether the lower piano part falls in Gould’s baritone singing range, etc. (This fourth Sinfonia then is an ideal piece to transcribe as it is a slow work that lies above Gould’s singing range much of the time.) What makes transcribing Gould even possible, however, is that he truly does sing, as opposed to, say, the loud, guttural, untranscribable noises that Keith Jarrett makes while performing. (I am a big Jarrett fan and have learned to ignore all of his noises as well (though jazz improvisation is admittedly a different animal than playing Bach). To me, Jarret’s physical gyrations, which were worse in his younger years, are more distracting than his vocalizations, but perhaps that’s only because I don’t often watch him play.)

Now on to the very important research made possible by this project. Which part does Gould prefer to sing? Outer voices? Inner voice? And how often does Gould provide an added part as has been claimed? Well, Gould sings the top voice 23.1% of the time, the middle voice 24.5% of the time, and the lower voice 51.4% of the time. The fact that the lower voice falls nearest his voice range may be the most logical explanation for this preference. Only 2.2% of the time (for a total of 2 beats in mm. 13 & 14) does Gould sing an added part, and even these moments are more added notes that true parts.

So there you have it.

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Review – Bach: Music in the Castle of Heaven by John Eliot Gardiner

ImageBach, the epitome of a musician who strove all life long and finally acquired the ‘Habit of Perfection,’ was a thoroughly imperfect human being – something we don’t usually tolerate in one of our heroes.” (p. 525) These words open the fourteenth and final chapter of John Eliot Gardiner’s new book, Bach: Music in the Castle of Heaven. In the thirteen chapters prior, Gardiner, founder and director of the Monteverdi Choir & English Baroque Soloists and newly appointed president of the Bach Archive in Leipzig, provides a refreshing and entertaining account of a thoroughly human musician who gave us heavenly music.

What distinguishes Gardiner’s account as a unique contribution to the mound of existing Bach scholarship is Gardiner’s perspective as performer and conductor, as one of the leading interpreters of Bach’s choral oeuvre. “I seek to convey what it is like to approach Bach from the position of a performer and conductor standing in front of a vocal and instrumental ensemble, just as [Bach] himself habitually did.” (p.xxxi) This performer’s perspective is manifest throughout the entire book in a variety of ways, from practical solutions in performance (“Success in [the “Laudamus” of the B minor Mass] depends on the two solo performers keeping the essential ‘bones’ of the folk-melody always to the fore, on making adequate provisions for breath between the phrases and on gliding effortlessly through Bach’s thicket of embellishments.” p.492), to descriptions of Gardiner’s rehearsal techniques (rehearsals during his ensemble’s 2000 “Pilgrimage” cantatas tour being described on pp. 239ff), to considerations of instruments and performance materials. (“[T]hose of us who have learnt to play or direct period instruments and listened to what they can tell us feel that we stand a rather better chance of re-entering and inhabiting Bach’s sound world than was possible when we set out thirty-five or so years ago. An ensemble of period instruments played by expert virtuosi… carries with it a colossal element of excitement and zing. The performance becomes a communal rite…” p.522)

But it is for the rich insights he provides into the music, insights that will undoubtedly enhance the listening experience, that the reader will likely be most grateful. Gardiner delves into nearly one hundred of the cantatas to varying levels of degree, with individual chapters being devoted to the two passions and to the B minor Mass. (As expected, the choral works receive the most of Gardiner’s attention, though infrequent mention is made of instrumental works). Gardiner’s comprehensive knowledge of every aspect of the cantatas – historical context, original manuscripts, structure of the music, etc. – is brought to bear in his rich descriptions. Ideally, the reader is best served by listening to the musical excerpts as Gardiner discusses them, but even if this be impossible, Gardiner’s reflections will enrich future listening experiences and serve as a valuable reference. I personally wrote the word, “Listen!” in the margins at least a dozen times, most emphatically during descriptions of BWVs 6 (pp.334-5), 25 (p.249), 101 (p.321), 106 (pp.149-52), 159 (p.335), 179 (p.199), and of the two passions. A pre-existing knowledge of this musical repertory brings significant advantage to the reader, especially since Knopf has disappointingly provided very few musical examples.

Middle and late chapters are devoted to these enlightening descriptions of the music – 9 to the Leipzig cantata cycles, 10 to the John Passion, 11 to the Matthew Passion, 12 to Bach’s text-setting idiosyncrasies and the motets, 13 to the B minor Mass. The earlier part of the book (following an opening chapter in which Gardiner gives an account of own background, of the establishment of his Monteverdi Choir, and of his personal enthusiasm for Bach) is devoted to constructing an image of Bach, adding human flesh to one of our music elusive musical “heroes.” Chapter 2 (“Germany on the Brink of Enlightenment”) serves to set the historical and contextual stage onto which Bach appears. Gardiner’s thoroughly researched account includes details of Bach’s Lutheran heritage and childhood education, the regional geographical terrain, the effects of war, and of the general quality of life. In Chapter 3 (“The Bach Gene”), Gardiner places Sebastian within the Bach lineage, describing how Sebastian’s musical training allowed him to emerge from among other gifted Bachs. If chapter 3 places Sebastian among his kin, chapter 4 (“The Class of ‘85”) places him among his peers as the lives and careers of Scarlatti, Handel, Rameau, Mattheson and Telemann are contrasted with those of Bach. Gardiner’s comparative tack here is quite effective in showing just how different Bach’s life might have been were circumstances, decisions (Sebastian’s, his peers’, and his [potential] employers’), and personal temperament slightly different. Bach’s uncertain relationship with opera receives attention here as well. Gardiner turns his attention to the role that the Lutheran faith had on Bach and his music in Chapter 5 (“Mechanics of Faith”), using three early Mühlhausen cantatas (BWVs 4 “Christ lag in Todesbanden”, 131 “Aus tiefer Not schrei ich zu dir”, and 106 the “Actus tragicus” funeral cantata) as mini-case studies. The beautifully rich description of these works whets the reader’s appetite for later chapters devoted more exclusively to the music. Chapter 6 (“The Incorrigible Cantor”) delves further into Bach’s temperament showing how his personality affected his often-tumultuous relationship with employers. Gardiner turns in Chapter 7 (“Bach at his Workbench”) to a fascinating account of Bach’s compositional practice, providing illuminating and vivid descriptions of his working relationship with librettists, of his work with copyists in creating scores and parts, of what those manuscripts tell us about his working methods, and of the process of working with musicians to bringing his works to life. Chapter 8 (“Cantatas or Coffee?”) includes descriptions of Bach’s secular cantatas and of his workings with the university collegium during his later Leipzig years. The book’s rather meandering concluding chapter (“’Old Bach’”) both gives an account of various activities of the elderly Bach and also serves as a kind of final assessment of Bach’s legacy, once again situating Bach among his “Class of ‘85” German contemporaries.

Gardiner truly excels in his descriptions of this heavenly music, which he obviously loves dearly. It is in his humanizing account of Bach the man that some readers may have qualms, depending largely on the expectations the reader brings to the book. Such misgivings will surely not be due to any lack of knowledge on Gardiner’s part. His thorough familiarity not only of the current Bach scholarship but also of the original manuscripts is evidence in every chapter. Copious citations and footnotes leave us confident in Gardiner’s expertise. But where gaps in our knowledge occur – gaps left by a general paucity of biographical information, by a lack of correspondence and first hand accounts, and by a less than trustworthy obituary (Nekrolog) self-servingly and hastily published by his C.P.E. Bach  and pupil Agricola –  JEG all too happy to offer missing details, often in ways that are remarkably imaginative. JEG, the consummate interpreter, gives us an interpretation of Bach that is admittedly personal (“What is presented here is very much one person’s vision.” p.xxxii). JEG, the performer, gives a stunning performance filled with imaginative conjecture that is not always supported by evidence. Several such examples are worth pointing out.

One gets the sense that some of Gardiner’s more fanciful reconstructions stem from a desire to provide a fresh take on commonly accepted views. Take for instance his questioning of the traditionally accepted reasons for Bach’s poor school attendance, namely illnesses within the Bach family, family gatherings, and an apprenticeship with his father. Gardiner finds these reasons “not altogether convincing” without ever provided any basis for doubting. “[T]here could be alternate, more disquieting explanations,” he states flatly. (p.46) Gardiner develops a habit of seeing things he wishes to see.

In Chapter 4, Gardiner proposes the idea that Bach may have visited the Hamburg opera during his trip to that city, even while acknowledging a lack of evidence and, at the same time, challenging such an eminent Bach scholar as Christoph Wolff:

“Just because the writers of his obituary do not mention the Hamburg opera or any contact with its leading light, Reinhard Keiser, does not mean that Bach ‘at the time had no particular interest in opera,’ (citing Wolff, Bach; The Learned Musician, p.65) […] Either of these men (Hamburg opera conductor Keiser or Reincken, organist and board of directors member) could easily have accompanied Bach, given him letters of introduction to attend Keiser’s theatre or even arranged for him to participate in any of the twelve operas Keiser composed for Hamburg between 1700 and 1702. We can surmise that his natural musical curiosity drew Bach as a listener into its orbit, even if, once in, what early biographers identified as an innate shyness held him back from the networking needed for success in a pressurized world whose purpose was to satisfy ‘the vanity of [its] individual executants’.” (pp.99-100)

This is quite a remarkable conclusion built on a mere assumption that “natural curiosity” would have led Bach to the opera. Being willing to venture ideas on such scanty evidence at times leads Gardiner to conclusions that are less than convincing.

ImageOr take JEG’s curious exercise of analyzing painted portraits in order to glean character traits. Scanning a portrait of Sebastian’s father reveals to Gardiner that Ambrosius “gazes out of his portrait like a prosperous brass-player – fat-chinned, full-nosed, lazy-eyed, stubborn and evidently fond of drink.” (p.61) Fondness of food and drink is also “evident” in Sebastian’s portrait which is thoroughly read by Gardiner in the concluding fourteenth chapter (pp.545-50) as if a fortune-teller reading a palm.

JEG takes the same kind of fanciful approach when looking at manuscripts. An ink blot on a title page penned by Kuhnau, one of Bach’s best copyists, is, in this sport of conjecture, attributed to an abusive outburst on the part of Bach due to a misspelling of his name in the bottom corner: “[Kuhnau] misspells the composer’s name and writes Bacch. Clearly not amused, Bach must have given his errant copyist a sharp smack: a black smudge appears right across the page – Kuhnau’s pen following the trajectory of the chastising biff.” (232)

Or the imaginative scene Gardiner paints when describing Wilhelm Friedemann’s “jittery” copying of BWV 127 under his father’s watchful eye: “[Wilhelm] gets the first note wrong […] but after the initial blip he corrects himself. The same happens with the viola part. […] Meanwhile Bach decides to take over copying the continuo part for the bass arioso himself. He is now really pressed for time. […] Caught up in the creative frenzy and elation of the moment, Bach has to rush to finish. He cannot risk the snail’s pace of his son’s progress. Perhaps the orchestra is tuning up.” (234-35) This is great drama. And apparently the “thick pen-strokes” on the manuscript of BWV 101 in the composer’s hand “by their pressure reveal his urgent intent as much as they do his failing eyesight” (323), and raindrops on the score of young Bach’s Buxtehude transcription rather bizarrely indicates to Gardiner that “it may have travelled in his rucksack.” (82)

In addition to using portraits and manuscripts to fill gaps of biographical information, Gardiner also turns to the music itself. In fact, the endeavor is central to the enterprise of the entire book, as he himself claims in its concluding chapter. Gardiner’s aim includes “scrutinizing the music and looking out for instances when his personality seems to penetrate the fabric of his notation.” (p.550) When it is that Bach’s true character emerges is up to Gardiner himself. The soprano aria from BWV 84 whose primary message is contentment with whatever lot one is given “helps us to find out how [Bach] dealt with [the] extremes” of “doing his job conscientiously and to the utmost of his abilities, on the one hand, […] and on the other, the bother of having to put up with ‘almost continual vexation, envy and persecution’.” (p. 198) BWV 178, on the other hand “exhibits such sustained defiance that one asks whether there is a submerged story here – of Bach operating in a hostile environment… How much more satisfying, then, for him to channel all that frustration and vituperative energy into the music, and then to watch as it rained down from the choir loft on to his chosen targets below.” (p.199) And the bass aria of BWV 135 is “superb, angry music executed with a palpable fury, with Bach fuming at delinquent malefactors. One can picture the city elders, sitting in the best pews, …starting to feel increasingly uncomfortable as these shockingly direct words – and Bach’s still more strident and abrasive music – hit home.” (p.200) (So this aria isn’t about Jesus giving consolation to us in our tears caused by evildoers?) And of BWV 81, “one wonders whether there is a pinch of dramatic realism here, of yawn-induced rebuke (the repetition of warum?) or even of mild satire – one of those occasions when Bach may be poking fun at one of his Leipzig theological task-masters.” (p.310) At least Gardiner wonders.

There is little question that Bach may have written his feelings into the music he composed, but using such arbitrary selection as to when his true character emerges from the notation can lead one to erect a Bach of any kind, so wide is the expression of his music. At least Gardiner acknowledges how dubious this tack is, though not until the book’s final chapter. “[O]n several occasions in the course of this book I have pointed to times when Bach allows the mask to slip and his personality to come through in his music, times when we sense his many moods: his intense grieving, his passionate beliefs, but also his tussles with faith, his bursts of anger, his rebellious subversive streak, his delight in nature or his unbridled joy in God’s creation. … These are tantalizing areas, arising from a world of subjective feeling and ultimately unprovable. Yet, treated cautiously, they provide us with a bridge – spanning the traces of Bach’s personality we think we can detect embedded in the music and such historical truths as we can establish about the nature of his character.” (pp.542-43) An extremely shaky bridge it is.

Gardiner’s episodes of conjecture sometimes result in contradiction. The story of young Sebastian’s unauthorized copying of manuscripts by candlelight during his years under the tutelage of his elder brother Christoph at once “smacks of legend” to Gardiner, being “a story heavily embroidered in the remembering and rehearsing of it” (p. 79). And yet it is taken for granted as true later when Gardiner traces Sebastian’s poor eyesight “back to the strain of that illicit nocturnal copying in his brother’s house” (p.546 footnote). The story is seemingly taken to be true merely because it served the immediate train of Gardiner’s narrative thought.

And just how sincere was Bach’s devotion to his Lutheran Christian faith? At some points, Gardiner casts doubt based on evidence that is hardly convincing. Of the transition passage between the Confiteor and the Et expecto in the B minor Mass, Gardiner “detect(s) traces of Bach’s own struggles – with tonality, counterpoint and harmony – but perhaps even with belief.” (p.482) “To what degree was he truly convinced by Christian dogma, especially the kind that emphasized personal faith and the rewards of salvation? asks Gardiner. “These are questions to which no very convincing answers can be found in the archives,” he flatly answers. (146) Yet many answers are indeed provided by Gardiner throughout the book, from descriptions of Bach’s extensive theological library, which according Robin Leaver “many a pastor in Bach’s day would have been proud to have owned” (155), to frequent reference to marginalia written in Bach’s own copy of Calov’s Bible commentary, to numerous characterizations of musical numbers in his choral works as deep expressions of a sincere faith, to simply stated affirmations that his “Lutheran zeal was sincere (and there are no grounds to believe that it wasn’t).” (p.453) One gets the sense that Gardiner’s flair for the dramatic and propensity for stating ideas that serve the immediate train of thought regardless of their credibility or the extent to which he believes them perpetually guides his prose.

If Gardiner’s historical methodologies are at times dubious, his jaded attitude toward analysis is simply curious. From the outset, Gardiner tells us that analysis will not get us very far. “The techniques we habitually use to analyse music when it is joined to verbal expression are of little use. We need a different tool-kit.” (xxxiii) This is exceedingly strange since Gardiner uses analysis throughout the entire book when describing Bach’s music. (In fact, several reviewers have lamented the amount of music theoretical verbiage Gardiner employs as off-putting to the average reader.) In my opinion, Gardiner uses analysis remarkably well, for instance, when discussing the Trauer-Ode, BWV 198, intended to commemorate the death of Queen Christiane Eberhardine, Electress of Saxony.

“First he builds up the sonic profile by introducing each of the eleven upper lines one by one, each evoking a bell of a different size – from the smallest via the tap-tap chiming of the flutes, to a sustained tolling of middle-sized bells in the oboes and a haze of plucked strings, to the deep, sonorous booming of the larger bells in the gambas and continuo that clang ominously in regular fourths and fifths. By now we have moved from D with a flat seventh in the oboe via a diminished seventh to C minor, a minor ninth on E. Then, below the third inversion of the dominant seventh on C#, comes an abrupt (and by the standards of the day, impermissible) rocking back and forth from E# to A in the bass, before the bells peter out one by one in the same order as they began. What this tonal analysis seems to be telling us is that, as a result of the queen’s death, time has stopped working with its normal God-appointed regularity – that with her demise the natural world is out of kilter.” (p. 221)

Just as with Gardiner’s historical methodologies, the extent to which such theoretical description is off-putting will largely depend upon the reader’s expectations and background. But for those who are willing (and able) to follow these analytical threads, their understanding and experience of the music can be enhanced. The number of asides in which Gardiner sets up a dichotomy between analysis and performance is unfortunate, as Gardiner himself demonstrates that the one can (and should) assist the other in tandem.

Given all these considerations, readers should modify expectations accordingly (if necessary). When done, the rewards from Gardiner’s book will far exceed any shortcomings. Gardiner’s account of Bach is one that indeed humanizes. If the exercises in imaginative conjecture sometimes run wild, the more legitimate historical exercise of counterfactuals (the “what if?” game) serve the purpose of bringing the composer to life. (cf. p.527) What if Bach had accepted the offered position in Halle? What if Bach did not receive the Leipzig appointment? What if Bach had turned to opera? These are very legitimate questions that further show just how different things might have been had Bach’s circumstances and temperament been even slightly different. If anything, musings such as these leave the reader eternally grateful that circumstances of Bach’s life led him to compose such a rich repository of masterpieces in the cantatas, passions, motets, and the “great catholic Mass.”

Gardiner, the consummate performer, has given a tour de force performance in this book. It is consistently engaging, elegantly written, and extremely informative with numerous extra-musical sources and ideas (from painting, to psychology, to science, to architecture) to assist and vivify the reading experience. Chiefly, it is imaginative, both a prerequisite and byproduct of being a superb interpreter of music. And perhaps it is exactly this quality that distinguishes this book from other Bach accounts. We have Gardiner to thank for a valuable reference for all future hearings of Bach chorale works and for a vividly refreshing image of one of the great heroes of our Western tradition.

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Gerard Manley Hopkins and Molto Adagio Thoughts on Music

hopkinsLiterary critic F.R. Leavis, who is significantly responsible for the posthumous acclaim Victorian Jesuit poet Gerard Manley Hopkins has enjoyed, once said of his poetry, “Hopkins is really difficult, and the difficulty is essential. If we could deceive ourselves into believing that we were reading easily his purpose would be defeated; for every word in one of his important poems is doing a great deal more work than almost any word in a poem of Robert Bridges.” (Leavis, New Bearings in English Poetry, 164-65) Switch “reading” to “listening,” “word” to “note”, and “poem(s)” to “composition(s)” and the passage above would fittingly describe any number of composers within the last 100 years. Each note of a Webern or Boulez piece does a great deal more work than each note of a Phillip Glass piece. (This idea, of course, easily applies to other historical periods as well. Each note of a Bach fugue does a great deal more work than each note of a Telemann concerto.)

In a letter to Robert Bridges, Hopkins acknowledged the difficulty of his own poetry by suggesting that it “must be read molto adagio.” This idea of reading poetry molto adagio is intriguing and perhaps offers a new way of characterizing the difficulty of listening to complex music. Can it be said that frustration that many people experience when listening to modern works stems from the fact that their complexity requires a molto adagio hearing when such is an impossibility (or when such does unjust damage to the character of the work)?  Poetry can be read molto adagio. Paintings and sculptures can be viewed molto adagio. But only music whose tempo is molto adagio can be properly heard molto adagio.

Performers of such complex works have the obvious advantage of practicing and rehearsing at slower tempi. They develop a deeper understanding of such works that only comes through repeated slow practice. Listeners, however, are not usually provided such a luxury, but are often faced with a daunting task when listening to a complex work for the first time. If they are unfamiliar with the language of a given style or composer, the listening experience becomes all the more challenging. Listening—that is, listening well—is indeed a skill that must be honed through intentional practice.

Despite the risk of losing a reader or two, let me try a sports analogy. (Sport and art have striking parallels, though I would guess that the percentage of artists that engage in sport (and vice versa) is not high.) When describing a player who has reached a level of skill beyond the players around him—a point guard running a basketball offense; a football quarterback looking over the opposing defense—some will say that “the game slows down” for them. They are able to see things happening before they happen, to see all contingencies in a developing play. For the listener who is armed with a listening skill that has been honed through years of careful study and practice, a work of great complexity can in a similar way “slow down.” Such a listener is able to hear and take in more aspects of the music than others, is able to imagine contingencies as the music unfolds.

AN EXPERIMENT

BoulezLet’s try an experiment with one of my favorite short passages of music from Pierre Boulez’s formidable Derive 2 for 11 instruments—an experiment that approximates the reading of poetry molto adagio. (This passage occurs at Rehearsal 225, toward the end of the piece.) The goal of this short exercise is to develop a deeper understanding of the passage through repeated hearings and, more to the point of the blog post at hand, through slowing the passage down.

Two audio clips are linked below: the first contains five repetitions of the passage at tempo. The second contains three repetitions of the passage at half speed. The (transposed) score is also below.

If I were doing this experiment with my students, I would ask them to report first on what they heard after one hearing and then on what they heard after multiple hearings both at tempo and at half speed. I would suggest several strategies such as listening first to just the winds, then to just strings, then to percussion, or listening first for the “bass line” of the passage, then the upper register. Etc. What changes through the process of familiarization? After listening several times at half speed, were you able to hear a lot more clearly and with a higher level of comprehension once returning to full speed? Did your perception of the character of the passage change between the first hearing and the last?

AUDIO #1 (at tempo)

AUDIO #2 (half speed)

Click to embiggen.

Click to embiggen.

Boulez’s passage is so rich in its layered complexity that experiencing this music the first time certainly gives even the most experienced listener a sense of information overload. But the comprehensibility level elevates with each hearing. By the end of this experiment, I personally hear a lyricism in this music that I had not initially heard. The lyricism is corporate as the entire ensemble partakes as a unified whole, as a web in which instruments pull on and move with each other as if following some melodic compulsion that transcends themselves. (Heterophony pervades this work from beginning to end.) In Boulez’s texture of constantly revolving timbral colors, every note belongs, doing its assigned work. This efficiency of expression in this music, certainly unappreciated on my first hearing, connects Boulez with his forebears, particularly of the 18th century. In my mind, Derive 2 is in essence a Baroque piece of music, and I’m convinced that J.S. Bach would be proud.

And now let’s end with a poem by Hopkins appropriately on the subject of patience. Read it molto adagio.

‘Patience, hard thing’

Patience, hard thing! the hard thing but to pray,
But bid for, patience is! Patience who asks
Wants war, wants wounds; weary his times, his tasks;
To do without, take tosses, and obey.

Rare patience roots in these, and, these away,
No-where. Natural heart’s-ivy Patience masks
Our ruins of wrecked past purpose. There she basks
Purple eyes and seas of liquid leaves all day.

We hear our hearts grate on themselves: it kills
To bruise them dearer. Yet the rebellious wills
Of us wé do bid God bend to him even so.

And where is he who more and more distills
Delicious kindness?–He is patient. Patience fills
His crisp combs, and that comes those way we know.

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Goldberg Tempo Variations

I like charts. And I like Bach’s Goldberg Variations. Here is a chart of tempos taken from six prominent recordings of the Goldberg: Glenn Gould’s landmark 1955 recording, Gould’s 1959 live recording, Gould’s 1982 recording, Murray Perahia’s 2000 recording, András Schiff’s 2001 recording, and Angela Hewitt’s 2000 recording.

Click to embiggen

Click to embiggen

The detailed data is given in the table below. Naturally, performance tempos are rarely maintained with any kind of precision throughout an entire movement. These tempo readings, therefore, reflect simply the first steady tempo established in each movement, the tempo that is generally maintained through a good portion of its opening. For those movements which are too slow to effectively determine a tempo and/or which are played with enough rubato to make calculation difficult, tempo readings were determined by dividing the number of beats played by the track’s duration. Asterisks (*) in the chart below mark tempos derived in such a way. Tempos in bold indicate the quickest pace for each movement; markings in italics, the broadest. For the bipartite 16th variation, the Overture, two tempo markings were registered.

Movement Gould 1955 Gould 1957 Gould 1982 Perahia 2000 Schiff 2001 Hewitt 2000
Aria 50* 53* 31* 48* 54* 47*
Var. 1 137 121 83 104 103 114
Var. 2 111 95 79 81 96 79
Var. 3 (Canon 1) 72 60 63 68 66 57
Var. 4 69 61 58 59 62 62
Var. 5 173 154 166 144 131 129
Var. 6 (Canon 2) 67 73 73 48 50 38
Var. 7 63 59 55 75 86 64
Var. 8 140 124 111 109 118 105
Var. 9 (Canon 3) 104 96 97 60 89 71
Var. 10 (Fughetta) 99 99 94 86 91 85
Var. 11 77 67 74 78 67 63
Var. 12 (Canon 4) 115 105 92 90 104 77
Var. 13 52 55 42 42 46* 43*
Var. 14 110 99 96 92 103 93
Var. 15 (Canon 5) 29* 26* 19* 30* 34* 30*
Var. 16 (Part 1) 33 34 26 40 37* 28
Var. 16 (Part 2) 93 82 69 76 72 71
Var. 17 118 111 109 121 92 90
Var. 18 (Canon 6) 92 96 94 96 104 94
Var. 19 146 130 90 130 150 122
Var. 20 141 118 118 107 117 109
Var. 21 (Canon 7) 43 49 47 52 71 50
Var. 22 102 96 93 90 85 94
Var. 23 111 103 103 105 94 95
Var. 24 (Canon 8) 108 103 89 82 90 68
Var. 25 15* 23* 16* 26* 28* 25*
Var. 26 114 111 112 99 94 97
Var. 27 (Canon 9) 85 75 73 80 86 68
Var. 28 94 98 92 93 68* 87
Var. 29 102 103 94 86 108* 85*
Var. 30 (Quodlibet) 91 80 73 82 108 70
Aria 45* 48* 26* 44* 54* 41*

In 13 of the 33 movements (counting Variation 16 as two separate movements), Angela Hewitt provided the broadest tempo among the six performances. Eliminate Gould ’82 from the chart and that number rises to 18. In fact, Hewitt’s rendition as a whole is easily broader than Gould’s notoriously broad ’82 recording. Averaging out all the tempo readings in Hewitt produces an overall average of 74.3 bpm compared to a 77.5 bpm average in the Gould.

It may come as little surprise to those who know Gould’s ’55 recording that it represents the briskest recording of the six with an average of 90.6 bpm, registering the quickest tempo in 16 of the 33 movements. (Hewitt provided the briskest tempo in none of the movements.) What I did find a bit surprising is that while I expected Gould to provide the most metronomic performances (and thus the easiest to do a tempo calculation), this was not at all the case. Easily the most metronomic of these performances is by Hewitt. One almost gets the sense that she practices hours on end with metronome on. Natural as it may be that András Schiff’s ultra-dynamic pianism made tempo calculation in his performances most difficult, I was still surprised at just how elastic his tempi can be.

Calculating tempo averages from quickest to broadest puts Gould ’59 just under Gould ’55 at 85.1 bpm followed by Schiff at 83.6 bpm, Perahia at 79.5, Gould ’85 and Hewitt.

I could go into further mundane details about the chart, but I will refrain and let the reader explore those details. Readers interested in hearing more about tempo choices in Gould’s 1982 recording might want to listen to the pianist’s (entirely scripted) interview with Tim Page conducted at the time of the recording’s release. The interview took place just months before Gould’s death.

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Goldberg Variation 5, Measure 17 and Dead Kittens

I absolutely love the Goldberg Variations. I even took the time (a lot of time!) to arrange a version of them myself. But something has always bothered me about measure 17 in the fifth variation of Bach’s Goldberg Variations. Below are measures 17-18, the first being from the first edition of the score, the second from the Bach-Gesellschaft Ausgabe:

GoldbergVar5m17 FirstEdition GoldbergVar5m17 Gesellshaft

It’s been said that every time someone writes or plays parallel fifths, Bach kills a kitten. Good luck playing the beat 3 ornament in measure 17 without killing at least one cat. You may even kill a couple. If you want to find them yourself before reading on, think about how that ornament might be rendered. (Keep in mind that this variation is invariably played at a faster tempo.)

The ornament figure contains three elements: a “prefix” (the scoop at its beginning), a trill and a mordant or “termination.” Below, in J. S. Bach’s handwriting, is a preface to Klavierbüchlein für Wilhelm Friedemann Bach. A clearer version of this chart in modern notation is found here. 800px-Bach-ornamentguide

According to this chart, the 17th measure of the 5th Goldberg Variation should be rendered as follows:

ImageRenderingByBachPreface

Rendered in such a way, no objectionably part-writing parallels occur. In reality, however, such a realization of this figure would be far too rapid to be executed given the quick tempo at which this variation is invariably taken. More realistically, the figure could be taken at half speed. But in doing so, parallels suddenly occur on the fourth 16th of beat three: F#—E over B—A.

ImageSimplifiedRealization

However, this particular ornament is more commonly rendered in performance as a 6-note sextuplet figure that neglects the opening prefix: G—F#—G—F#—E—F#. If played precisely, not one but two sets of parallels emerge, one on third 16th of beat three (G—F# over C—B) and the other near the fourth 16th of beat three, only slightly misaligned.

ImageUsualRendering

Again, this is the most common, that is, the usual rendering of this measure, producing three consecutive P5s in a row!  And it really bothers me.

FURTHER RESEARCH

Then I got curious. Taking the nine recordings of the Goldberg sitting on my CD shelf altogether, just how many kittens are killed in total? Let’s get to the bottom of this important matter and analyze them one by one.

GOULD 1957 & 1981

Many people know of the two studio recordings Gould made of the Goldberg, recordings that bookend his all-too-short career. Less well known is the 1957 live Salzburg & Moscow recording. For our present research, I take this 1957 together with the 1981 recording because Gould takes the same interpretation in both—he simply plays the F# as a quarter note, without ornamentation.

AUDIO

That’s one way to avoid the parallels! With the potential for two parallels in each recording, four kittens’ lives are saved. (I say four instead of eight because Gould elects not to repeat the second half of this variation in both recordings. Most pianists, of course, repeat the second half.)

TOTAL KITTEN BODY COUNT: 0

GOULD 1955

In his 1955 debut recording of the Goldberg, Gould does elect to add the ornament. The audio below presents the passage at full speed, then at half speed, then at one-quarter speed. While the slowed version is rather grainy, Gould appears to render the figure straightforwardly as the “usual” sextuplet figure notated above.

AUDIO

The graininess of this early recording does make it difficult to assess, but even with the second F# in the figure not projecting well, I would venture to say that two kittens died in this rendering.

TOTAL KITTEN BODY COUNT: 2

SCHIFF 1982

Andras Schiff recorded the Goldberg multiple times. In this 1982 release, Schiff’s rendering is, as always, quite nuanced. In the audio excerpt below, you will hear Schiff’s first pass at the passage (at the three different speeds) followed by his second pass.

AUDIO

ImageSchiff1982first  ImageSchiff1982second

In the first pass, the second of the two potential parallels is averted. Kitten saved! The first, however, is a judgment call. Is the F# in the right hand offset from the B in the left to the extent necessary to save a kitten? Unfortunately, it is my opinion that this is not the case. Kitten croaked.

In the second pass, the F# definitely aligns with the B to do the damage. Another kitten dead. I believe, though, that the E arrives early enough in front of the A to prevent feline death.

TOTAL KITTEN BODY COUNT: 4

SCHIFF 2001

Here is a live recording by Schiff from 2001.

AUDIO

ImageSchiff2001first  ImageSchiff2001second

Schiff exercises some fancy maneuvering in his first pass, preventing kitten carcasses altogether. In the second pass, the second potential parallel is clearly averted. As for the first, we have once again a judgment call. Does a 64th note’s worth of misalignment prevent kitten death? I suggest that the answer is no. A dotted 64th note’s worth of misalignment? Maybe. But not here. Kitten dead. Still, you have to applaud Schiff for his finesse in doing as little damage as possible!

TOTAL KITTEN BODY COUNT: 5

PERAHIA 2000

Perahia’s recording is sublime. But does it kill cats?

AUDIO

ImagePerahiafirst  ImagePerahiasecond

On first pass, the E locks in with the A dead on. Here is a parallel fifth if there ever was one. No pulse in this kitten! As for the first potential parallel, the F# arrives just after the B. This is a close call! But I suggest that the kitten just did escape. On the second pass, two certain deaths! The F# arrives with the B, and the A in the left hand seems to arrive early, lining up with the E. Three feline deaths. Way to go Murray!

TOTAL KITTEN BODY COUNT: 8

HEWITT 2000

In Angela Hewitt’s recording, only the first pass has enough definition for clear assessment (though the second pass can still be heard in the audio).

AUDIO

ImageHewittfirst

In that first pass, the F# clearly aligns with the B. Kitten killed. The E does not align with the A, however, so no harm done. From the limited evidence available on this recording, it appears that no kitten deaths occur in the second pass.

TOTAL KITTEN BODY COUNT: 9

TIPO 1986

The pianist Maria Tipo elects, like Gould, not to repeat the second half of the variations. So only two kitten lives are at stake here.

AUDIO

It seems to me that Tipo plays the figure as a rather straight sextuplet figure that has been fractionally delayed. It begins a hair late, and this cuts slightly short the final note of the sextuplet figure. As a result, I would suggest that the first parallel is averted with the F# being delayed, but the figure’s delay brings the second P5 into closer alignment. One kitten dead.

TOTAL KITTEN BODY COUNT: 10

ROSEN 1969

The great Charles Rosen (R.I.P.) was a brilliant scholar. A brilliantly executed measure 17 of Goldberg Variation 5 this is not. Listen:

AUDIO

ImageRosenFirst ImageRosensecond

Umm. As far as I can tell from this mumbo jumbo, four kittens died here.

TOTAL KITTEN BODY COUNT: 14

So there we have it. Taking my nine recordings of the Goldberg Variations altogether, 14 kittens died. That’s 1.56 kittens per recording.

So now you see my dilemma. What to do the next time reading through this variation? Skip the measure? Forget the ornament ala Gould, ignoring Bach’s score indication? Or go ahead and kill as many kittens as possible? Quite the conundrum.

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Detecting Errors in Benward & Kolosick’s Ear Training

ImageEver since Bruce Benward & Tim Kolosick’s aural skills textbook Ear Training has been packaged with the music theory textbook I currently adopt, I’ve made use of it in aural skills labs. It serves as a convenient source of aural exercises and dictation material. And what I find particularly useful are the error detection exercises, error detection being an absolutely essential skill required of young musicians and one that is often, in my experience, under-emphasized in aural skills courses.

Fortunately for students, they are given plenty of extra opportunities to detect errors in the harmonic dictations provided in the ET Teacher’s Manual. Unfortunately, I don’t believe this was the authors’ intention. Being so annoyed by questionable part-writing in these harmonic dictation exercises is likely something of an over-reaction, a byproduct of having spent years grading music theory assignments. Yet here I am, greatly annoyed.

And it’s not just one or two mistakes. They’re everywhere! In fact, the frequency with which they appear provoked me to do some research to see if I had in fact been grading my students too harshly all this time. (More on such research later.)

And it’s not as if these “mistakes” can be chalked up to those inevitable errors that invade any first edition of a newly devised manuscript. We’re dealing here with the seventh edition of this text! They’ve had 6 chances to make improvements since it first came out. So, here we go…

Parallelism Created by Figuration

By far the most common occurrence of poor part-writing involves parallelisms created by passing and neighboring tones. Here are some instances:

Page148no123fifths

Page107no3fifthsPage107no6fifthsPage305no4fifthsPage329no6fifths

The first five examples listed above involve root movement by ascending 2nd in which the root of the first chord descends via passing tone to the fifth of the second chord, the passing tone creating parallel fifths with the tenor voice. Three cheers for consistency! (Some would say (me included) that these passing tones create chordal sevenths, but B&K consistently treat such figures as NCTs, even when involving V chords.) The sixth example above (F major) also contains root movement by ascending 2nd, but the problem here involves the approach to the seventh of the ii7 chord. (More on problematic preparations of chord sevenths in a moment.) In the final example above, parallels are created by a figure that I always caution my students against–that is, by the insertion of a descending passing tone from a leading tone (or temporary leading tone in a tonicization, as is the case here) to the chord fifth of the following I chord (or of the chord being tonicized–the IV chord in this case). Such a figure draws attention to the fact that the L.T. has been “frustrated” in an inner voice.

The parallel fifths in the example below may be less problematic, but only very slightly less.

Page107no4fifthAccentedpt

The ill-effect here is slightly attenuated by the fact that the metrically accented D in the tenor is a non-chord tone while the anticipated C# is the structural tone. When the second fifth in a series of consecutive fifths involves a NCT, the ill-effect can be attenuated (to varying degrees depending on other contextual factors).

[The only consecutive perfect fifths I see in Bach chorales (excluding ones occurring between cadence endings and subsequent phrase beginnings) fall into this category of “non-structural” parallels. In a PAC with Re-Do movement in the soprano, parallel fifths can be created if the soprano’s Do is anticipated at precisely the same moment that the seventh of the V7 chord appears (Sol-Fa motion). Four instances of these cadential non-structural parallels occur in Bach’s Chorale #8 (from Cantata #40). In such a passage, the second fifth in these consecutive fifths involve not just one NCT (the soprano anticipation) but a second passing figure (even if we come to view it as a chordal 7th. Furthermore, the second fifth is metrically deemphasized. Because of these factors, the ill-effect of parallelism is highly attenuated. One does not, however, find in Bach’s chorales parallels of the kind shown above from the B&K text.]

Back to B&K. Here is even an instance of parallel octaves whose blatancy is only slightly masked by the appearance of an accented passing tone:

Page214no8octaves

The problem here is the bass’s APT. The tenor needs to get to the D at the cadential i64 but cannot easily do so without unwanted parallels, weaker chord voicing, erratic melodic shape, or rewriting of other upper voices, all because of this APT.

In the passage below, the neighbor tone does double damage: not only does it create parallels, it also essentially constitutes an improperly resolving chord seventh.

Page173no4fifthneighbor

Other Part-writing Problems

Here is an excellent example of an objectionable direct fifth. Quite literally a “textbook” example!

Page107no7directfifth

Want to see some sevenths of chords ill-prepared by descending leaps? Sure, they’ve got you covered.

Page305no123approach7th

Progression #1 above is quite a head-scratcher. Why on earth is the soprano given a G in the opening tonic chord, doubling the chord fifth? My guess is to give students a more interesting soprano line to dictate, but is that a good reason for dubious part-writing?

Progression #2 looks like an assignment from a student who has just learned of the potential part-writing pitfalls in the IV7—V progression. The very reason for the questionable approach to the chord seventh in the V7 here seems to be the prevention of parallel fifths (S/T) (which for some reason had suddenly become objectionable for these authors here??). Progression #3 is an easy fix. For the ii7 chord, keep the B in the tenor, keep the D in the alto (now the seventh is prepared), and move the soprano to G.

How about improper part-writing involving the N6? Check.

Page377no4fifthsN6Page377no6fifthsN6

Dubious Analyses

For some Harmonic Dictation sections in the ET text, they smartly(!) used actual phrases from Bach chorales. At times, however, their analyses are suspect. In the two examples below, B&K’s propensity to treat all passing figures descending from chord roots as NCTs instead of chordal sevenths leads to questionable analyses.

Page275no46analysis

Were I to provide B&K’s given analyses for these progressions, my students would likely identify the suspect “ii—I” progression (okay, some wouldn’t), and they would be right to question it. These leading-tone passing tones do more than merely “pass” through. They carry tonal reinforcement weight, and they, however fleetingly, transform the predominant chords into dominant ones resulting in a more persuasive ii-viio-I analysis.

And recently, when working with an individual student, I played the following modulating harmonic dictation. The student textbook identifies for the student the spot where B&K has marked the pivot:

Page351no1incorrectRNFB

The first problem is, as my student pointed out, viio6 doesn’t typically move to iii. What gives? Well, rather than being an incomplete iii chord (with missing chord fifth) as the answer key suggests, it is best analyzed as a I chord with missing implied root. Our ears hear the dominant function of the viio6 so strongly that we do not even need to actually hear the Bb root in order to hear the chord as Bb major. (Try it yourself by adding the fifth to the apparent iii chord—remove the beat 4 G passing tone in the alto and keep the A there—and see if the result complies with what you hear when the A is absent.)

The second problem (admittedly nitpicking here a bit) is that the pivot has been placed in the wrong location. The first indication of F major does not come until the E-natural appears. The proper place for the pivot is the ii6 chord in F major, which would be a vi6 in Bb major.

Research: Textbook Comparison

Okay, now with all pointless venting aside (I feel better now!), on to more beneficial things. I’ve been stimulated by these frustrations to do something I’ve been wanting to do for a while, and that is to compare how various part-writing concepts are treated in some of the leading music theory textbooks out there and to see to what extent those textbooks correspond to Bach’s chorale style. Such research will provide an opportunity to re-evaluate not only my grading scheme but also my choice of textbook, something I’ve been reconsidering for a while now.

Some of the concepts I want to include in this textbook comparison research, in addition to the ones mentioned in this post, are:

  • Voice crossing and overlap
  • More than an octave between adjacent upper voices?
  • Unequal fifths
  • Root position diminished triads
  • Must do go to ti in a cadential i64 resolution?
  • Are parallel fifths allowable in a Ger+6–i progression? (Is the progression allowable?)
  • Unresolved chordal seventh in V43–I6 progression
  • Using figuration to mask parallels

I’ll start (in the next blog post) with the “mistake” most frequently found in B&K’s book—the parallel fifth created by passing or neighboring tone—and go from there. We’ll see how far this takes me.

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