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:

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.

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

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 16^th of beat three: F#—E over B—A.

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 16^th of beat three (G—F# over C—B) and the other near the fourth 16^th of beat three, only slightly misaligned.

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

 

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

 

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 64^th note’s worth of misalignment prevent kitten death? I suggest that the answer is no. A dotted 64^th 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

 

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

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

 

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.

Detecting Errors in Benward & Kolosick’s Ear Training

Ever 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:

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.

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 7^th. 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:

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.

Other Part-writing Problems

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

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

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.

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.

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:

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.

For the Time Being: Fresh Advent Reflections from Auden and Messiaen

After reading a tweet from Alan Jacobs about his forthcoming edition of W.H. Auden’s For the Time Being: A Christmas Oratorio, I decided that I would read Auden’s poem this Advent season. I am glad I did. The oratorio is exceedingly rich, so rich that reading one time through seemed woefully insufficient. So I read it again. And then a third time. I eagerly anticipate Jacobs’s new edition of Auden’s poem (set to be released in May 2013) because as a novice at reading poetry, I am certain that many of Auden’s allusions are lost on me.

As I read, I stumbled upon something else. I cannot remember my initial motivation for doing so, but I found myself working through a portion of Auden’s work while listening to Olivier Messiaen’s monumental piano work Vingt regards sur l’Enfant-Jésus (“Twenty Meditations on the Baby Jesus”). I began reading the opening of the section of Auden’s poem entitled “The Summons” in which the Star of the Nativity takes voice (I am that star most dreaded by the wise, / For they are drawn against their will to me) and thought it interesting that the Star also becomes a character in Messiean’s meditations. Along with the Father, the Spirit of Joy, the Virgin mother, the Prophets, Shepherds and Magi, and the Son Himself, the Star takes watch over the Christ child (Movement 2: “Watch of the Star”). 

Coincidence? Probably, I thought, but I had to pursue the idea further. I then discovered that Auden’s poem was published in 1944 (though written in 1941-42) the same exact year Messiaen’s work was composed. More and more correspondences began to emerge.

Both Auden and Messiaen are preoccupied with time. Messiaen’s fascination with time is well documented and is manifest most explicitly in a work written during his time in a concentration camp—The Quartet for the End of Time. In Vingt Regards, the ninth image is subtitled “Watch of Time,” and its music betrays a timelessness typical in Messiaen’s style by way of symmetrical scales (“modes of limited transposition”), non-retrogradable (palindromic) rhythms, and cyclical structures.

Auden’s very title, For the Time Being, suggests that time is a central concept in his telling of the story of Christ’s birth. References to time abound throughout the oratorio, “Time” often being capitalized and paired with Space. Christ emptied Himself of his infinity and eternality when he entered our Time and Space. Below are just two passages of many from Auden’s oratorio that allude to time:

We who must die demand a miracle.
How could the Eternal do a temporal act,
The Infinite become a finite fact?
Nothing can save us that is possible:
We who must die demand a miracle. (Section: Advent III)

[The Second Wise Man:]
My faith that in Time’s constant
Flow lay real assurance
Broke down on this analysis—
At any given instant
All solids dissolve, no wheels revolve,
And facts have no endurance—
And who knows if it is by design or pure inadvertence
That the Present destroys its inherited self-importance?
With envy, terror, rage, regret,
We anticipate or remember but never are.
To discover how to be living now
Is the reason I follow this star. (Section: The Summons I)

Both Messiaen and Auden make reference to the Word. In Auden we read: From the beginning until now God spoke through his prophets. The Word aroused the uncomprehending depths of their flesh to a witnessing fury, and their witness was this: that the Word should be made Flesh. (Section: The Meditation of Simeon) In the preface to his score, Messiaen says of movement 12 (“The Omnipotent Word”), “This child is the Word who sustains all things by the strength of his word” (“Cet enfant est le Verbe qui soutient toutes choses par la puissance de sa parole…”). Notice Auden’s similar use of both “Word” and “word” in Mary’s response to Gabriel at the Annunciation:

My flesh in terror and fire
Rejoices that the Word
Who utters the world out of nothing,
As a pledge of His word to love her
Against her will, and to turn
Her desperate longing to love,
Should ask to wear me,
From now to their wedding day,
For an engagement ring.

Both Auden and Messiaen provide meditation on the contemplation of Mary over her Baby. The character of the opening of Messiaen’s 4th movement (“Watch of the Virgin”) matches so perfectly the combination of motherly love and arresting apprehension with its hint of self-doubt in these words that Auden provides for Mary:

O shut your bright eyes that mine must endanger
With their watchfulness; protected by its shade
Escape from my care: what can you discover
From my tender look but how to be afraid?
Love can but confirm the more it would deny.
Close your eyes.

Sleep. What have you learned from the womb that bore you
But an anxiety your Father cannot feel?
Sleep. What will the flesh that I gave do for you,
Or my mother love, but tempt you from His will?
Why was I chosen to teach His Son to weep?
Little One, sleep. (At the Manger I)

It’s almost as if either Messiaen had read Auden’s poem and decided to write incidental music or Auden had heard Messiaen’s music and penned these words to accompany. The stanza that immediately follows makes allusion to the cross that looms over the manger and corresponds, therefore, to Messiaen’s Theme of the Cross that appears throughout the work, particularly in the seventh movement (“Watch of the Cross”).

Dream. In human dreams earth ascends to Heaven
Where no one need pray nor ever feel alone.
In your first few hours of life here, O have you
Chosen already what death must be your own?
How soon will you start on the Sorrowful Way?
Dream while you may. (At the Manger I)

I don’t suspect that Messiaen had somehow read Auden’s oratorio prior to composing Vingt Regards. Perhaps it’s more a matter of the time being exceedingly ripe for a fresh contemplation of the story of God’s intervention into a world torn by war and strife. Both artists had gone through strife in their own personal lives as well during this time. Messiaen spent time in a Nazi concentration camp following the defeat of his homeland (much of Vingt regards being composed during the liberation of France), and Auden experienced both a failed relationship and the death of his mother in a short span of time as well as increasing criticism from the literary world following his 1939 conversion to Christianity.

 For all the similarities between these two great works of art, differences are also present, of course. Messiaen’s rendition of the nativity is an Inter-Trinitarian one of great joy (though Messiaen’s musical “joy” always carries a hint of the tragic, a hint of the cross). Auden presents us with a version of Christ entering a messy and fallen world. As Peter Steinfels once said in a NY Times article devoted to the oratorio, “Whatever joy Christ’s coming may ultimately promise, the poem makes clear that faith, like love, will not be easy.” Combined, Messiaen’s magnificent work and Auden’s rich oratorio provide fresh thoughts during a season so filled with clichéd sentimentality.         

Chromaticism in Schubert’s Die schöne Müllerin

I have entertained the thought of using one single piece of music for teaching all of chromatic harmony. There are several advantages in doing this. The students get an in-depth look into the world of one single composer and piece, and develop an intimate understanding of and appreciation for that composer’s sound world. Through the study of a single great work of music, the students also come to a better understanding of what it is that makes a work a “masterpiece” (providing the single piece is well chosen). An obvious disadvantage is that focusing on one single piece limits the breadth of exposure to a wider variety of music and composers. But if students receive such wider exposure in other courses (e.g. music history sequence), then the advantages afforded by such devotion to a single work of music, a masterpiece, may be well worth it. Underlying such a single-masterwork approach is a pedagogical supposition that it is better to demonstrate to students how one approaches great works of art and how one enters the world of that piece of art rather than gaining a surface knowledge of a wider array of art works. The learning strategies practiced through in-depth study of a single work are transferable to all other works. In this pedagogical approach, quality supersedes quantity. The instructor should teach students how to learn rather than focusing on conveying  content per se.

One work that is particularly well suited for the single-masterwork approach is Franz Schubert’s Die schöne Müllerin. Almost every single concept of chromatic harmony (that is generally taught in an undergraduate music theory sequence) can be found in this great work. I already use many examples from the lieder of Schubert and Schumann. Students tend to connect with these smaller-form pieces with an immediacy that does not happen with other works, as their texts and text-painting seem to draw students in quickly.

To demonstrate the potential for using Müllerin for teaching chromatic harmony, I have created a chart of the entire song cycle showing where each concept of chromatic harmony is represented. One might enjoy the use of Italian, German, and French flags for corresponding augmented sixth chords and the use of the Neapolitan (ice cream!) flag! (It has become a tradition in my Theory III class to eat Neapolitan ice cream on the day the topic is covered. Each class must discuss amongst themselves which flavor (chocolate, vanilla, strawberry) corresponds to which chord member of the N6, and each year I get different responses.)

In creating the chart below, I’ve just about convinced myself that Müllerin will indeed be a “required text” in my Theory III class beginning next fall. What a great song cycle of gem after gem!

The chart can be found (and likely more easily read) here.

Enharmonic Spellings in Brahms Intermezzo in A Op.118, No.2

For the past few years, I’ve used Brahms’ ever-popular Intermezzo in A major Op.118 No.2 in my Theory III course as a kind of preparation for writing final analysis papers, and for good reason—it’s tightly-knit structure makes it ideal for motivic analysis, it provides great examples of chromatic harmony (plenty of secondary chords, mode mixture chords, and even “simultaneities”), but most importantly, it’s undeniably gorgeous and students, I find, become quickly attached to it.

This year, when we came to the central hymn-like passage in F# major (mm.57-64) which serves as a kind of “eye of the storm” for the entire piece, we questioned why it is that Brahms enharmonically spells two chords right at the passage’s center:

The two chords in red represent a iiø65–V progression tonicizing the a# minor chord that follows. But rather than using the proper spellings of b#ø65 and E# major, he switches to flats. Why did he not write it this way:

The easy answer, the one I’ve always reverted to, is that he wanted to avoid those pesky double-sharps, making it easier for the pianist to read. But is this really a satisfactory answer? I think not. One might argue that reading the resulting augmented and diminished melodic intervals is just as awkward as reading double-sharps, not to mention the awkwardness of seeing so many flats in juxtaposition with so many sharps. Also, while it’s true that the key of A# minor (seven sharps) is perhaps a bit more cumbersome than Bb minor (five flats), this is only a briefest of tonicizations and not a full modulation. One might understand a composer switching to an easier spelling for an extended passage, but for two chords??

I thought perhaps the F major chord might be referring to something else in the piece. From the home key of A major, F major is flat-VI, a good example of mode mixture, and mixture plays a big role is defining the Intermezzo’s overall character. An F major chord does appear in measures 20 to 21, but making a case that the m.60 F chord is referring to these measure seems a stretch.

Perhaps he’s placing visual emphasis on the piece’s precise midpoint. These two chords come at the center of this “eye of the storm” passage in a work whose overall form is a palindromic arch form. With 116 measures in the entire piece, these two chords sit almost precisely at the midpoint. Is this what he’s doing? A tepid “maybe.”

I wanted to see if there were instances of this kind of seemingly-arbitrary enharmonic respelling in other late Brahms piano works. The first passage that caught my eye is a very similar kind of passage in the very next piece in the Op.118 set–the Ballade in G minor. The central section of the piece finds its way to the chromatic mediant key of B major (via a wonderful non-resolution of a V7/iv in mm.38-40). The B major section sets out but soon modulates to d# minor (via a reinterpretation of a V7/IV chord as a German +6 chord), a key which requires the use of numerous double-sharps. Listen here.

It’s true that switching from d# minor (6 sharps) to eb minor (6 flats) does not lessen the number of accidentals, at least it shows that Brahms had no phobia against double-sharps!

Then I remembered two passages from second Intermezzo from the Op.117 set.

First, measures 4 to 11. Listen here.

The  music, in B-flat minor, arrives in measure 8 at what sonically sounds like an F#/Gb minor chord, though it is enharmonically spelled untriadically (new word?) as Gb-A-Db. However, this enharmonic spelling is not arbitrary but rather is perfectly understandable, being driven purely by the voice-leading of the passage. The chord is not functioning as an f# minor chord but more as a simultaneity or an “apparent” chord. The obstinate A-natural, which stubbornly refuses to move to the expected Bb at m.8 (in order to create either a i chord or deceptive VI following the V chord at the end of m.7), retains its leading-tone function in anticipation of the Bb to come in measure 10. (The measure 9 chord is also a fun one to analyze! An enharmonically spelled ivø7?? A iv chord with the leading-tone substituted for the fifth of the chord (tonic), creating some kind of dual-functioning “plagal dominant”?? A “simultaneity” perhaps.)

So as interesting as this passage is, it sheds no light on the Op.118/2 passage containing enharmonic spellings, a passage driven not by voice-leading but by harmonic progression . Let’s move to the other fascinating passage in this Op.117/2 Intermezzo.

Measures 20 to 23. Listen here.

In the somewhat tonally-ambiguous measures immediately preceding these, a low Db in the bass serves as a dominant orienting this brief passage in the key of Gb minor(!), which would have as its key signature (count ‘em) 9 flats. Respelling these measures as F# minor (3 sharps) would result in 6 fewer accidentals! Yet, Brahms keeps the Gb minor spelling.

If one suggests that the VI chord would have to be spelled as an E double-flat major chord (rather than as the less cumbersome D major) in order for it to function as the Neapolitan in the oncoming key of Db major (which it does), let’s remember that such a consideration of function did not prevent Brahms from spelling A# minor’s functioning dominant as F major in Op.118/2.

Therefore, it seems this passage provides us with an example counter to the one discussed in class. Explaining the Op.118/2 respellings as being done “for ease of reading” seems less convincing.

[Incidentally, the Op.117/2 passage just referenced reminded me of that wonderful extended passage from Schubert's 4th Moments Musicaux written in F-flat major (8 flats). Schubert has taken the liberty in other pieces of respelling such keys, and in this case, respelling F-flat major as E major would have made perfect sense considering the latter's close relationship with the piece's home key of c# minor. But he leaves it as F-flat major.]

So back to Brahms 118/2. If the 117/2 passage puts a dent in my toss-away explanation for the respellings in 118/2, then why does he respell these two chords in the center of Op.118/2? I am sure that someone out there has written a dissertation on enharmonic spellings in Brahms and that someone has unlocked the mystery surrounding these particular measures. I’d love to hear other explanations. In the meantime, I’m inclined to believe that the best answer is the one provided by a students three seconds after I asked the question: “Why did Brahms spell these chords as Eb and F rather than D# and E#?”

“Because he felt like it!”

“Fixing” Bach’s D Major Fugue from WTC2, bwv874

I have recently been looking quite a bit at a few preludes and fugues from Bach’s second book of the Well-Tempered Clavier, and the D major fugue, one that I played as an undergraduate student, has particularly caught my attention. The fugue takes on an almost choral character rather than a pianistic one, due primarily to its rather placid subject, which can be divided into two motives.

(For a PDF of the entire score, click here.)

Interestingly, the opening X motive implies G major more than it does D major, and the absence of C# in the entire subject infuses it with a slight tonal ambiguity that Bach exploits throughout the fugue. This fugue is one of the mostly tightly-knit ones in the WTC books, with Y in particular pervading the fugue from beginning to end. The fugue is 50 measures long, and considering the quarter note as the beat unit, disregarding the “cut” time signature, there are 200 beats. (Hereafter, beat numbers will assume the quarter-note beat, for sake of clarity.) In only 39 of those 200 beats is no instance of the Y motive present, and in only 9.5 of those 200 is no instance of X or Y present. Of the 873 notes in this fugue, 436 of them, almost exactly half, belong to an instance of Y. Doing the math, that’s 109 instances of the Y motive!

However, the fugue’s tightly-knit structure is not the primary reason for this blog. Rather, it is the interesting passage that occurs from measure 21 to measure 25. Take a look and a listen:

http://www.youtube.com/watch?v=u52wmdXCtsk&feature=results_video&playnext=1&list=PL29E6F4CD368F8A04#t=01m29s

As you can see from the colored markings in the example above, Bach has included three consecutive cross-relations in this fantastic passage. If a student of mine submitted a passage such as this, my response would likely be to ask whether he had ever actually played through his part-writing being fairly certain that he had not.

So, I thought I would do Bach a big, big favor and fix his questionable voice-leading. Okay, not so much. But I wanted to “fix” the passage simply to see how easy (or difficult) it would be to do so. I thought this process might somehow give insight into why he wrote what he did.

I found the task of “fixing” the passage not very difficult at all. In fact, I came up with four different fixed versions.

FIX #1

Listen here.

Fix #1 is perhaps the simplest fix, with all three cross-relations being eliminated. On measure 22.3, the tenor voice’s D# has been changed to D-natural to match the soprano’s D-natural. The bass has been changed from A to B, since the A makes less harmonic sense without the D#. The E#-E cross-relation is eliminated by the simple removal of the E#. The G#-G cross-relation is removed by the change in the soprano from G# to G-natural. I slid the alto’s G over one half-beat in order to make the S and A more independent.

Easy fix! However, the fix comes with effects detrimental to the overall passage from a purely musical standpoint. The primary weakness, to my ear, is the overemphasis of B, both in the bass and as a harmony. The bass’s B2 in measure 22 (beat 3) has no freshness since the B2 was heard in m.21. Also, the F# chord heard on beat 3 of measure 23 no longer has its wonderful stabilizing function. In Bach’s version, that F#2 in the bass takes the important role of reorienting the tonality. In my version, the B minor chord in measure 22 ruins the need for reorientation.

One may also notice the G-C# augmented 4th that is created in the subject’s soprano appearance in measure 23. So fixing the three cross-relations came at the cost of inserting a questionable melodic interval (not that Bach avoided augmented melodic intervals entirely (see the Crucifixus from the B minor Mass!)), not to mention the fact that the passage a much blander and far less interesting.

FIX #2

Listen here.

In Fix #2, the D# is restored to the tenor and Bach’s D#-D cross-relation is fixed by giving the soprano a D#. The A in the bass is kept this time, though contrary to Bach’s version I actually resolved the measure 22.3 implied V42 of E minor (V42/iv in the key of B minor) normatively, to a first inversion E minor chord on the following downbeat. To achieve this, I removed the E# in the tenor, thus eliminating the E#-E cross-relation.

This fix restores the reorienting function of the bass’s F#2 on measure 23.3. It also adds import to the D-naturals that appear in the upper voices on measure 24.1 since the soprano’s D5 in Bach’s version is changed to D# in mine. I also like the manner in which the two Ds in m.24 are approached, really giving a sense of arrival which for the soprano is further emphasized by its agogic accent.

Fix #2 is also not without its faults. First the D#-G augmented 5th in the soprano (mm.22-23) is certainly problematic, and the D# is awkwardly left unresolved when the E minor chord arrives on measure 23.1.

FIX #3

Listen here.

As in Fix #1, a strong B minor chord is inserted in Fix #3 on measure 22.3, eliminating the D#-D cross-relation. Unlike Fix #1, Bach’s E# in the tenor at measure 22.4 is kept, and the E#-E cross-relation is fixed by transferring the E# to the alto. This E#4 extends the tonicization of F# minor and perhaps heightens its arrival on measure 23.3. The G#-G cross-relation is removed by changing the G-natural on measure 23.2 to G#, letting it slide down to G-natural only on beat 3. The G# may seem a little awkward with B minor being implicated (A# appearing in the tenor), though the aural effect is not overly awkward. The beat 2 G# can be simply heard as a remnant of the tonicized F# minor key area.

One may notice the B-E# diminished fifth in the alto’s fugue subject in measures 22-23, yet this is not problematic, and of the 23 appearances of the subject in this fugue, three of them open with a diminished rather than perfect fifth (mm. 33-34 (S), m. 43 (B), and m. 45 (T)).

FIX #4

Listen here.

Fix #4 is the most adventurous. The D#-D is once again eliminated the same way it was in fixes 1 and 3. But here, the E# is respelled as an F-natural, and when combined with the added G-natural in the bass, creates a V7 of the Neapolitan key area. A root position Neapolitan appears, as expected, on measure 23.1, and with the bass moving to E on beat 2b, the N53 is transformed into N6, its usual bass position. Therefore, the E#-E cross-relation is eliminated by the respelling, and more importantly re-functioning, of the E# to make it F-natural. And the G#-G cross-relation is eliminated by the alteration of all tones in the first two beats of measure 23 to conform to the Neapolitan harmony.

Once again, the B minor chord on measure 22.3 may overemphasize B as a tonal center, but the more drastic shift into the Neapolitan key area alleviates this overemphasis and the return to B on measure 24.1 is once again satisfying, at least to a greater degree than it was in fixes 1 and 3.

BACK TO BACH’S VERSION

Obviously, Bach was well aware that the cross-relations could be fixed. The question remains: why did he write this passage the way he did? It most certainly wasn’t because the three appearances of the fugue subject in stretto fashion dictated or necessitated these cross-relations. At two different times in the second half of the fugue, all four voices are involved in a simultaneous stretto presentation of the subject. I began to look for other reasons.

I noticed that two musical ideas drive the passage in terms of voice-leading and harmony: descending chromatic lines and fully-diminished harmonies. The proliferation of chromatically-descending diminished chords results in an ambiguity of tonal center. Combine these chromatic descents with voice transference and you get cross-relations.

Using descending fully-diminished chords (leaving them unresolved) is not an uncommon technique. Similar passages are found in Bach’s oeuvre, and some later composers have made wide use of the technique as well (Chopin and Rachmaninoff in particular comes to mind. I’ve even blogged about their use of descending chromatic fully-diminished harmonies before.)

So perhaps the nature of the suspended harmonies in this passage allow for these cross-relations. But there may be a better or at least a more interesting explanation of the passage. From an aural standpoint, the first oddity may be the tenor’s E-D#-F#-E# line in measure 22. This fragment, of course, spells out the B-A-C-H monogram. I began looking for other instances of the B-A-C-H motive and here is what I found:

In addition to the E-D#-F#-E# instance of the monogram, which most recognizably announces the motive, each cross relation is involved in an instance of the monogram.

Another Comparison: Beethoven Op.7 and Bach BWV1068

Beethoven composed his Piano Sonata No. 4 in E-flat major, Op.7 in 1797 in Vienna. Is it possible he had the first Gavotte from Bach’s Third Orchestral Suite in D major, BWV1068 in his ear at the time?

As I was playing through this Beethoven Sonata this summer, I noticed that a passage from the third movement bears a striking resemblance to the principal theme of Bach’s Gavotte. The pertinent passage in Beethoven’s work is in E-flat major compared to the gavotte’s D major key, and the principal melody of the former lies in the same register as the latter, being a mere half-step higher.

Listen and compare below. IMSLP links are here: Bach Beethoven

Bach, Orchestral Suite No.3 in D, Gavotte I

Beethoven, Piano Sonata in Eb, Op.7, movement 3, beginning at measure 70

For a closer comparison of the two passages, I transposed the Beethoven passage down a half-step to D major, the key of the gavotte, and put them side by side. Click the image to embiggen.

The short-short-long pickup figure combined with the descending 3rd—ascending 2nd contour is obviously a prominent one. The figure itself is rather commonplace, and I could perhaps just as easily have found any number of pieces predating the Beethoven Sonata with which to compare it. Yet, the way in which the Bach Gavotte was immediately conjured up in my memory when playing through the Beethoven passage leads me to believe there might be more to the connection.

Two additional correspondences between the passages may have contributed to the immediacy of my memory-jogging: 1) the nearly identical register the two melodies occupy being a mere half-step apart, and 2) the parallel thirds followed by parallel sixths in both passages (Fa-Re-Mi above Re-Ti-Do is followed by the opposite, Re-Ti-Do above Fa-Re-Mi). Furthermore, in both passages, the parallel figures are connected via a rearticulation of the dominant below: Fa-Re-Mi—(Sol)—Re-Ti-Do, etc.

In the Beethoven, the La-Fa-Sol (mm.75-76) that follows the repetition of the Fa-Re-Mi, Re-Ti-Do pattern maps onto the La-Fi-Sol that appears in measure 6-7 of the Gavotte, a figure that tonicizes the dominant. Both passages lead ultimately to a cadential 64 figure in the lowest register of both melodies.

There are other, more general similarities in these two movements. Other sections of both movements prominently feature a metrically shifted version of the short-short-long figure. a version placed on the beat. Beethoven seemed preoccupied with such metric shifts throughout his movement. (See for example measures 3-6 at the movement’s opening.) Bach’s Gavotte II, which immediately follows and is followed by Gavotte I in a minuet-and-trio-like da capo form, prominently features a metrically shifted version of the figure as well.

So back to the initial question: Is it possible Beethoven had the Gavotte in his ear, whether consciously or subconsciously, when composing this passage?

While my very cursory search for references to the Bach Orchestral Suites in several Beethoven sources in our college library turned up nothing, the  Grove’s article on Beethoven did shed a some light. In the section describing the early years after his move to Vienna in 1792, the author describes the rich Viennese musical culture highlighting the large number of aristocratic patrons actively supporting music, some of whom even “kept private orchestras.” One figure in particular, Baron van Swieten, with whom Beethoven was well acquainted, is identified as being “an early representative of the Bach revival.” He is said to be responsible for sharing the music of Bach with Mozart and Haydn, as well as Beethoven. The Baron connects LVB and JSB in another interesting way: he became the dedicatee of both Beethoven’s First Symphony and of Forkel’s 1802 biography of Bach.

So, yes, it is certainly possible that Beethoven heard the Bach Gavotte in Vienna and had the piece somewhere in his consciousness when composing his 7th Opus. And speaking purely intuitively as a composer, when comparing the two passages, the Beethoven has the look of one that might have been subconsciously derived from the Bach. I’m not sure exactly what I mean by that, and it’s probably all folderol. But way in which the Beethoven version looks like a truncated version of the Bach is just the way my not-entirely-conscious memory sometimes pieces together fragments of a piece of music lodged in the depths of my past experience. You probably know the kind of memory-jogging I mean. Right? Then again, this would imply that Beethoven’s brain worked in a way similar to mine. Not likely. Surely this is all poppycock!

I end with the entire Bach melody, with the second half being mapped onto the first. Fantastic music!