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The Science of Mysteries: Leave Us the Counterpoint

The views expressed are those of the author and are not necessarily those of Scientific American.


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Note: Last November, a Twitter exchange revealed that certain members of the small subset of science writers who were humanities majors (including your humble cocktail party blogger), also have a shared taste for classic murder mysteries. They thought they would co-post, on their respective blogs, various takes on the science of classical mystery writers. And they had so much fun, they decided to do so again! A full list of links can be found at the end of this post, but be sure to check out the new offerings in particular: Deborah Blum on Agatha Christie’s The Mysterious Affair at Styles, and Ann Finkbeiner on Dorothy Sayers’ The Unpleasantness at the Bellona Club.

“This kind of thing is the body and bones of music. Anybody can have the harmony, if they will leave us the counterpoint.”Peter Wimsey, Gaudy Night

Every great literary detective needs his muse, and for Dorothy L. Sayers’ creation, Lord Peter Wimsey, that muse is mystery writer Harriet Vane. They first meet in Strong Poison, when he clears her name (and saves her life) after she is tried for murdering her former lover with arsenic. It’s love at first sight — for Wimsey. Harriet, having been badly burned romantically, proves far more reluctant (and even occasionally hostile).

In Gaudy Night, Harriet has returned to her alma mater, Oxford University, to help the dons at the (fictional) women’s Shrewsbury College solve a mystery — not a murder, but a “poison pen” who has been sending hateful, harassing notes to various targets. (Poison pens were the Internet trolls of 1930s Oxford, apparently.)

Eventually she calls upon Wimsey for aid, despite some awkwardness arising from the fact that she’s spent the last four years rejecting his many marriage proposals. The novel’s subplot — fans might argue it’s the main plot, cleverly shrouded in the poison pen mystery — revolves around Harriet’s struggle to reconcile her feelings for Wimsey, and desires as a woman, with her fear of losing her hard-won individual identity and independence… a not-insubstantial concern for women of that era, especially those, like Harriet (and Sayers herself), of high intelligence.

That tension finds the perfect musical metaphor in a scene set in a small antiques shop, where Harriet has allowed Peter, for the first time, to buy her a gift (a set of antique ivory chessmen that has captured her imagination). Wimsey spots an old spinet piano in the shop, and knocks out a couple of tunes, finally getting Harriet to sing along for a rousing rendition of Morley’s Canzonets for Two Voices — “tenor and alto [twining] themselves in a last companionable cadence.” It is here that he makes his famous observation about preferring counterpoint to harmony. (Pardon Jen-Luc Piquant for a moment while she swoons. Swooooon.)

What does he mean? Well, Wimsey is the epitome of the urbane, cultured aristocrat, particularly when it comes to music. (There are references to a youthful dalliance with a Viennese opera singer, courtesy of his rather louche nephew, St. George.) Among other things, Wimsey understands the importance of “texture,” which Wikipedia defines as “the way the melodic, rhythmic, and harmonic materials are combined in a composition.”

“Counterpoint” derives from the Latin phrase punctus contra punctum, or “point against point,” and that’s exactly what it means. It’s used to describe an intricate inter-twining of two or more “voices” in a musical dialogue (whether human or instrumental is irrelevant), that are harmonically related, but don’t share the same contour and rhythm.

Which is really just a fancy way of saying, if you’ve got two lovely examples of melodies that sound different, and progress independently rather than in perfect sync, and yet somehow they sound harmonious when you combine them — why, then you’ve got yourself some mighty fine counterpoint. It’s quite difficult to pull off, as University of Washington music professor John Rahn explains in Music Inside Out: Going Too Far in Musical Essays:

“It is hard to write a beautiful song. It is harder to write several individually beautiful songs that, when sung simultaneously, sound as a more beautiful polyphonic whole. The internal structures that create each of the voices separately must contribute to the emergent structure of the polyphony, which in turn must reinforce and comment on the structures of the individual voices. The way that is accomplished in detail is…’counterpoint’.”

The result, when done well, can be breath-taking.  Consider Harriet’s ruminations as she watches Wimsey during a performance of Bach’s Concerto in D Minor (for two violins):

He was wrapt in the motionless austerity with which all genuine musicians listen to genuine music. Harriet was musician enough to respect this aloofness; she knew well enough that the ecstatic rapture on the face of the man opposite meant only that he was hoping to be thought musical, and that the elderly lady over the way, waving her fingers to the beat, was a musical moron. She knew enough, herself, to read the sounds a little with her brains, laboriously unwinding the twined chains of melody link by link. Peter, she felt sure, could hear the whole intricate pattern, every part separately and simultaneously, each independent and equal, separate but inseparable, moving over and under and through, ravishing heart and mind together.

Ahem. Jen-Luc is now wondering why it suddenly got so warm in here. This, for those unfamiliar with Bach’s masterpiece, is what Wimsey hears:

You can listen to the second movement and third movement as well. And as you listen, savor how the two violins each play their own melody, and yet somehow what emerges is this gorgeous interplay between the two instruments, two equal parts coming together to form a complex whole. It’s the perfect metaphor for how two strong, independent and intelligent people can maintain their individuality and yet, together, form a whole that is greater than the sum of its parts. In romance, as in music, it is no mean feat to achieve this, but Wimsey’s preference for a strong, equal partner — because of, rather than despite, the challenge — is what makes him a thinking woman’s heartthrob. He likes his music, and his women, polyphonic.

Bach, too, was a master of counterpoint, particularly of the fugue (and not so bad with the ladies, either: he married twice and fathered 20 children, although only 10 survived to adulthood). In fact, the opening movement of Concerto in D Minor that you heard above has a fugal lead-in. His most famous work, The Well-Tempered Clavier,  is comprised of two volumes, each with 24 prelude and fugue pairs, corresponding to each major and minor musical key.

It’s worth taking a moment to explain what is meant by being musically “well-tempered.” For centuries (i.e., before the 15th century), the preferred system for tuning instruments was that developed by Pythagorus: it was based on frequency intervals in perfect fifths (or a ratio of 3:2).

Mathematically, the fifth was deemed the most “pure,” and hence the most ideal, but as is often the case, the practical applications were less than perfect. Other musical intervals, like the major third, would end up so badly out of tune, in comparison, that a major chord (normally consonant) would be unbearably dissonant. This is colorfully known as a “wolf interval.”

This preference for Pythagorean tuning limited musical expression to the most simple harmonies, and to pieces that didn’t change key (modulate) very much. Anything that didn’t fit this narrow mold just didn’t work musically. But, well, that kind of simplistic perfection can be boring for those who like a bit more complexity in their music (or their relationships).

Later composers (beginning around the 17th century) liked to play with their melodic themes, transposing and modulating keys with wild abandon to explore every possible nuance. They needed a different tuning method to do so: specifically, they needed “well-tempered” instruments, in which the 12 notes in an octave on a keyboard, for example, were tuned in such a way that one could play in most major and minor keys without the jarring dissonance of the “wolf intervals” ruining everything.

Freed from the constraints of Pythagorean tuning, new musical compositional techniques flourished, including the fugue. The defining features are two or more voices, each building on a theme (or subject) that is introduced at the beginning and keeps recurring throughout until the two voices come together at the end. Much like the three-act structure of a story, you’ve got three sections: the exposition, the development, and the recapitulation, where one returns to the original theme.

For instance, here’s Bach’s Prelude and Fugue No. 2 in C Minor from The Well-Tempered Clavier (the fugue kicks in about midway through):

Note that it begins with a simple declaration of the main “subject” (theme), using one “voice” in the primary (tonic) key. The second voice soon chimes in with an “answer.” Essentially, the answer is a restatement of the subject, transposed into a different (but related) key, often with slight alterations to accommodate that key change (a tonal answer versus a “real” answer that is identical to the stated subject). That initial call and response is the exposition. In the development, the musical dialogue continues by adding new variants on the original statement and answer (middle entries) as a counter exposition. Finally, in the recapitulation, we hear a restatement of the exposition and counter-exposition.

That’s the most basic structure for a fugue, although there are many, many more complex variants. Incidentally, the word fugue is derived from the Latin fuga, which is related to both fugere (“to flee,” like Harriet) and fugare (“to chase,” like Wimsey). Coincidence? Perhaps not. One suspects Sayers knew her Latin.

Bach was known for entering contests whereby he would improvise a fugue on organ or harpsichord based on a suggested musical theme. But fugues aren’t just for Baroque composers, nosiree! There’s tons of videos on YouTube featuring hit pop songs reworked into more  elaborate forms. True, the structure of your average pop song is fairly simplistic: verse, chorus, verse, chorus, bridge, chorus is the standard form. And its texture is dominated by chords and harmony, with very little in the way of polyphony (i.e., little counterpoint); there’s usually only one main melody, not two or more weaving in and out as the song progresses.

But if there’s one thing popular music knows how to do, it’s fashion a catchy “hook.” A really good improvisor, in the spirit of Bach, can easily transform a relatively simple pop song into, say,  a fugue, taking that hook through a series of intricate twists and modulations, making it truly polyphonic.  For instance, here’s Lady Gaga’s “Bad Romance” reworked into fugue form by Giovanni Dettori, and performed by a full orchestra:

This seems a particularly apt choice, because the original tune opens and closes with a brief segment of synthesized harpsichord — designed to evoke that telltale Baroque counterpoint. It’s also in keeping with the song’s lyrical theme of lovers engaged in an intricate series of fugue-like maneuvers to establish the balance of power in their relationship. The imagery in Lady Gaga’s original video is one of a rich and powerful man who “buys” a strong, sexy woman, presumably for his pleasure — except she doesn’t want to be chattel (“I’m a free bitch, baby!”), and ultimately her own power consumes him.

That’s the danger of opting for complexity over simplicity: the fugue form is not for amateurs, and more than one hapless composer has wrecked him (or her) self on the rocks of this demanding compositional technique. If one melody is stronger than the other, if the timing isn’t perfect, if the modulated keys aren’t chosen carefully, ultimately, you’ll get jarring dissonance instead of the thrilling polyphonic interplay that makes for a successful fugue.

Which is why Harriet is so reluctant to give into her feelings for Wimsey. As the aseptic Oxford scholar, Miss DeVine cautions her, a marriage between equal intellects is inherently risky: “You can hurt one another so dreadfully.”

“Polyphonic music takes a lot of playing,” Harriet tells Peter during an interval in the Bach concert, approaching the thorny issue of her fears of yet another bad romance within the cloaking metaphor of counterpoint.

“You’ve got to be more than a fiddler. It needs a musician.”

“In this case, two fiddlers — both musicians.”

“I’m not much of a musician, Peter.”

Peter, to his credit, recognizes the difficulty. “I admit that Bach isn’t a matter of an autocratic virtuoso and a meek accompanist. But do you want to be either?”

That, really, is the heart of the matter. Harriet tried to be the meek accompanist in her first, failed relationship, with disastrous results. She is equally uncomfortable in the role of autocratic virtuoso, having bored very quickly of an amorous younger suitor whose intellect and abilities were too far below her own. That leaves her with the options of celibacy — losing herself in her writing and/or scholarship — or risking an even more painful romantic ruin by entering into an elaborate fugue with Wimsey. Pull off that delicate balancing act, however, and the result is a bright and shining love for the ages.  Fortunately for Sayers’ readers, Harriet finally succumbs to the allure of the counterpoint, accepting Wimsey’s final proposal in appropriate Latin:

“Placetne, Magistra?”

“Placet.”

And now Jen-Luc Piquant is a weepy pixelated puddle on the floor because it’s just so beautiful! (sniff)  We leave you with Glen Gould’s classic tongue-in-cheek composition, “So You Want to Write a Fugue,” in which he exhorts us all not to be daunted by the polyphonic challenge, but to embrace it. Like Wimsey and Harriet.

Check out these related posts!

The Science of Mysteries: An Overdose of Strychnine (Deborah Blum on Agatha Christie’s The Mysterious Affair at Styles)

The Science of Mysteries: Shock, Trauma, and the First Real War (Ann Finkbeiner on Dorothy Sayers’ The Unpleasantness at the Bellona Club)

The Science of Mysteries: For Whom the Bells Toll (Jennifer Ouellette on Dorothy Sayers’ The Nine Tailors)

The Science of Mysteries: Instructions for a Deadly Dinner (Deborah Blum on Dorothy Sayers’ Strong Poison)

The Science of Mysteries: Watch Where You Fall In (Ann Finkbeiner on Josephine Tey’s To Love and Be Wise)

The Science of Mysteries: Total Eclipse of the Heart (Jennifer Ouellette at Discovery News, on Jane Langton’s Dark Nantucket Noon)

The Science of Mysteries: Of Granular Materials and Singing Sands (Jennifer Ouellette on Josephine Tey’s The Singing Sands)

Jennifer Ouellette About the Author: Jennifer Ouellette is a science writer who loves to indulge her inner geek by finding quirky connections between physics, popular culture, and the world at large. Follow on Twitter @JenLucPiquant.

The views expressed are those of the author and are not necessarily those of Scientific American.



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  1. 1. voyager 8:11 pm 02/3/2012

    Male English major here. Got a split brain over this fine article. Regarding Sayers’s ruminations on Wimsey’s state of mind while they both listen to a piece of music and she’s reading his face….did anyone else but me flash on the classic Car Talk story about the man and woman riding in a car, with the woman projecting furiously, silently onto him her own intricate thoughts of every possible state–none collapsed into reality by real observation–of their relationship and where it’s going, when all he’s actually thinking about is his last oil change?

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  2. 2. dubina 5:53 pm 02/6/2012

    Holmes and Watson?

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  3. 3. Necrophony 2:25 am 02/7/2012

    Though I’ve read a fair amount of Sayers and share her enthusiasm for Thomas Lovell Beddoes, I hadn’t been following the counterpoint between Vane and Wimsy (their last names were hardly chosen by accident, though, given their homonyms, I can see why you’ve chosen to refer to Vane by her first).

    But one thing I can tell you: The difficulty of counterpoint is as overrated as its beauty is unacknowledged. And I don’t think there’s a musician alive who would say they “preferred” counterpoint to harmony for the simple reason you can’t have one without the other. The more precise thing to say would be that one preferred counterpoint (line against line) to *homophony* (melody against chordal accompaniment).

    As a small child who learned to play piano from Bartok’s Mikrokosmos series and the Anna Magdalena Notebooks, I used to listen to my older brother play Bach’s four-part fugues and dream of the day when I, too, could split my mind into multiple personalities and so learn to imitate god. (A friend of mine with Dissasociative Identity Disorder is fascinated with splitting the semitones of the chromatic scale and one of his personalities has become a microtonal composer.)

    Luckily, that day came a few years later and, even before it did, the Bach’s sinfonias and inventions had taught me enough to write examples of my own, causing my teacher to declare I had “counterpoint in [my] bones.”

    I have since composed many fugues and other works (the real trick is not to make them complex — that’s easy — but to make the individual lines breathe), as well as prosodic equivalents inspired by interdisciplinary poets like Thomas Campion and Sidney Lanier. I’ve also written essays on prosody and music notation — all in the attempt to convey the joy of counterpoint in words.

    Understanding counterpoint is like being able to see a double image in non-boolean terms — to see its very gestalt. If a person is willing to concentrate and make that first leap, so that they can perceive contrapuntal lines at once, then the world of simultaneity will open to them and they will at last know Bach’s profound awareness, will know why he wrote extremist poetry, and why his *augenmusik* illustrated tears graphically within the music (that’s how emotional he really was). One of the lessons I had to learn as a young performer was how to play the Sinfonia in G Minor — a heartbreaking thing of endless Corellian suspensions — without weeping like an idiot. So moving was that webwork of independent lines that I had to steel myself in order to convey it without being overwhelmed myself.

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  4. 4. Necrophony 2:32 am 02/7/2012

    One last thing. The most accurate *parallel* language W[h]imsey could have used would be this: I prefer polyphony to homophony.

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