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:

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!

Economy Goldberg

I shared with my former composition teacher C. Curtis-Smith a mutual fondness and admiration for Bach’s Goldberg Variations. After my studies with Curtis-Smith at Western Michigan University from 2001 to 2003, I decided to make what I thought would be an interesting, if not entirely practical, arrangement of the Goldberg. I must have been inspired by learning that 13 new variations were being commissioned by the 2004 Gilmore Keyboard Festival from 13 different composers including William Bolcom, David Del Tredici, Lukas Foss, Fred Lerdahl, Jennifer Higdon, Bright Sheng and Curtis-Smith.

For my arrangement, which I completed during my 2004-05 year at the University of Iowa, I figured that with a 32-measure long structure and with 30 variations, I could include one measure from each variation and bookend the entire arrangement with the first and last measures of the theme. (Some variations are 16 measures, in which case I considered 32 half-measure units.) I was skeptical that I could make such an arrangement work out from a musical standpoint, but in the end I was surprised at how well it did work. It still has its awkward turns and transitions, but that was to be expected. I was also pleased that very few notes were changed in terms of octave displacement. I remember the process being a tedious one, especially with regard to dealing with the variations in minor. I also remember not being satisfied with the first attempt and having to scratch all but the opening few measures.

Here it is. Listen to a midi realization here.
A PDF version is available at www.lukedahn.net/Scores/EconomyGoldberg.pdf.

The shift from measure 12 to 13 may be the most awkward transition in my estimation. Not only is there a shift from simple meters to compound, there is a harmonic awkwardness with the downbeat of m.13 suggesting a I6 chord while the remaining part of the measure projecting a pre-dominant (IV or ii) harmony. The awkwardness is created by the fact that measure 13 comes from Variation 3, the canon at the unison, which  contains slight harmonic reorientations in order for the canon to work.

The alternation between 3/8 and 2/4 in measures 17 through 20 may not be the smoothest passage, though the complex-meter effect alleviates the awkwardness, as does the coincidental motivic imitation between m.17 bass and m.19 treble.

Obviously the shift to minor at measure 25 is dramatic, but this couldn’t much be helped. The minor variations (15, 21 & 25) had to be lumped together in a very carefully placed position since many of the diatonic chords between D major and d minor are quite incompatible. (For example, the submediant is tonicized in measures 20 through 24, which means E minor when in D major and Eb major when in D minor.) I figured that a dominant sonority would provide the best way of exiting the minor mode segment since the V chord is the same in both modes.

Hymn Tune Composition: Color-Code Application

Two weekends ago, I spent a good part of my Saturday evening composing a new hymn tune at the request of my pastor. I had mentioned to him that if he came across a hymn that he felt needed a more appropriate tune, I would be happy to help, as I have been wanting to do more hymn tune composing. He wanted us to sing Psalm 130 on Sunday but only had a version set to the tune MARTYRDOM, which while a nice tune, did not adequately match the deep lamenting of the Psalm. So I set about composing a new tune for Martin Luther’s paraphrase of the Psalm. Our hymnal did have Luther’s paraphrase set to the tune AUS TIEFER NOT, a tune attributed to Luther himself, but the version of the tune in our hymnal was too metrically irregular to facilitate good singing. A version of the tune with some rhythmic modifications compared to our hymnal is available here. Incidentally, Bach composed two wonderful works based on the tune: a 6-voice chorale prelude and a cantata (more info here). I knew Bach’s chorale setting of the tune, found at the end of the cantata, but did not put 2 and 2 together until after composing my own version.

At any rate, having my color-coded analysis fresh in mind from a recently written blog post, I found myself thinking of ways of applying the color code during the composing of the hymn. I literally began thinking in color. The more I thought about it, the more I began to realize that if the color code is useful at all, hymn tune composition may be one area that it is most useful. The hymn tune writer is concerned with matching the expressive subtleties of the text in a chordal setting, and it is the expressive musical qualities that the color code was devised to highlight (rather than other musical features such as large-scale form).

The simple setting I composed ended up being very Bachian. This was both perfectly fine with me as long as it was appropriate for facilitating good congregational singing of the Psalm and perfectly understandable given the extent to which I’ve been immersed in Bach’s chorales. In fact, the final phrase bears a striking resemblance to that of Bach’s well-known Jesu meine Freude chorale (“Jesu, Priceless Treasure”), both having identical bass lines. Other Bachian features include the number of voice-exchanges, the cadential formulas, and the soprano-tenor imitation in the final phrase.

A black and white copy of my setting is available at www.lukedahn.net/Scores/Psalm130.pdf. A color-coded version is below. One of my most color-conscious decisions was to save the highest saturation of brighter colors for phrases 5 & 6.

Other color-coded thoughts (The color-code is described here): Given the prevalent use of the minor mode, more light green notes naturally appear due to inflections of the 6th and 7th scale degrees. I balked at which color to render the alto’s G# in measure 4. Does the raised scale-degree 4 of an Italian augmented sixth chord tonicize the dominant? If so, it should be light purple or bright red. Does it create a chordal dissonance in this root-less chord? If so, it should remain maroon. Or is it more characteristic of a lower chromatic neighbor tone? It so, it should be light green. I chose maroon (NH) since it both creates a dissonance with the bass (augmented 6th) and is considered a chord tone, and since it becomes an activated tendency tone, gravitating to scale-degree 5.

Hymn Tune Styles

I also began thinking about how the color code might render hymns of different styles. What I have in mind here in particular is the late 19th century American hymn tradition as compared to other (mostly European) traditions that predate it. I will put my cards on the table here and say that I find the former to be lacking in deep and subtle musical expressiveness as compared to the latter. This may be unfair, and it may simply reflect the fact that as a composer, I habitually listens to virtually all music in a composerly way. (This manner of listening is part of the baggage that comes with being a composer and this baggage becomes a real problem when it inhibits involvement in corporate worship, which it frequently does.) I acknowledge, on the other hand, that these simpler American hymns are better for some people at facilitating the concentration on the hymns’ words (although one might wonder just how much concentration is needed for a hymn such as this: Shall we gather at the river / The beautiful, the beautiful river / Gather with the saints at the river / That flows by the throne of God.)

At any rate, you probably by now know the kinds of late 19th c. American hymn tunes I have in mind: simple triadic harmonies (usually just 3 of them, but just 2 is not unheard of!), slow and regular harmonic rhythm, homophonic texture, folk-like melodies, occasional dotted rhythms, and (worst of all!) occasional double lower chromatic neighbors! (Wince!) Composers of these kinds of hymns tunes include Robert Lowry (1826-99) (What Can Wash Away My Sins; Shall We Gather; I Need Thee Every Hour), Philip Bliss (1838-76) (I Am So Glad That Jesus Loves Me; Wonderful Words of Life), William Doane (1832-1915) (I Am Thine, O Lord; Near the Cross; To God Be the Glory), and James McGranahan (1840-1907) (I Know Whom I Have Believed; I Will Sing of My Redeemer; There Shall Be Showers of Blessings).

Now that I’ve thoroughly maligned an entire hymn tradition, let’s compare color-code renderings of two hymns from the differing traditions: I Know Whom I Have Believed (tune by James McGranahan) and Praise, my soul the King of Heaven (tune, named LAUDA ANIMA, by British Composer John Goss (1800-1880)). In an (half-way) attempt at fairness, I chose a hymn tune by a contemporary of McGranahan rather than turning to composers from earlier periods (e.g. Johann Crüger). I tried choosing an American, but I honestly could not find a late-19th century American hymn tune composer that stood against the tradition I just lambasted. (I’m sure there has to be some out there.)

I Know Whom I Have Believed

Praise, My Soul the King of Heaven (Tune: LAUDA ANIMA)

The McGranahan tune is one that I grew up singing in church and one that I liked as a child. Aside from the green opening notes (which would be rendered green only on the first verse, of course), the only colored notes appearing are four orange notes (orange representing prepared non-harmonic tone dissonances, like suspensions). Two of these, on the words “be-liev-ed” and “com-mit-ed”, could easily have been rendered light blue since they are dissonant fourths above there basses and can be thought of as part of the IV64 chords they harmonize. They function, however, as double suspension figures (along with the soprano in each case). I could very easily have chosen a hymn from this tradition that would be rendered entirely black.

The John Goss tune is a favorite of mine. There are many reasons why I think the tune is so musically appealing, several of which are in stark contrast to the style McGranahan represents. I particularly love the way the first phrase contributes an asymmetry to the large-scale phrase rhythm of the hymn. Phrase 1 is the only 5-bar phrase (with special agogic emphasis on the word “heaven“) and renders the hymn’s phrase structure as 5+4+4+4+4+4. The harmonic rhythm accelerates in phrase 2 (quarter-note changes) after a stable phrase 1 (half-note changes). The idea of accelerated harmonic rhythm is quite simple, but it’s effect here is significant, for it supplies momentum heading into the middle phrases which are even more harmonically charged. Goss saves any tonicizing for these middle phrases (no chromaticism in phrases 1 & 2 or 5 & 6) – the rising diatonic bass line from phrase 1 now becomes chromaticized in phrases 3 & 4. In the process, the subdominant, the supertonic, and the mediant are each tonicized in turn before achieving a full modulation to the dominant. Phrase 3 also begins with the same half-note harmonic rhythm as phrase 1, but the slower pace cannot be sustained; the harmonically-charged bass ascension will not allow it. Phrases 5 and 6 return to the tonic key (by transforming the PAC in phrase 4 into an HC) and to a diatonic harmonization. In contrast to phrases 1 & 2, here we get a rhythmic activation (passing tones) that provides an added sense of elation appropriate for the “Praise Him” repetitions. Phrases 5 & 6 provide a wonderfully satisfying conclusion: the ascending bass line returns once again, and Goss has brilliantly utilized the 1-7-6-5 line from phrase 1 (“King of heaven”) to bookend this wonderful, thoughtfully-constructed hymn tune.

“Expressively Charged” Tones: A Color-Coded Analysis of Bach’s Db Major Prelude (WTC2)

One of the most poignant expressive devices in tonal music is the transformation of a single tone from being consonant and stable to being dissonant and unstable, at which point the tone seeks to return to a position of stability. Such a transformation is eventuated by a change in the tone’s immediate surrounding. The tone, through this transformation, becomes activated. This basic concept is referred to as the prepared dissonance in music theory terms, and the paradigmatic exemplification of this device is the suspension figure, which contains three parts: the consonant preparation, the dissonant suspension, and the consonant resolution. The dissonance is further emphasized by being accented metrically, being placed on a strong beat relative to its resolution.

The suspension figure has been widely used by composers in all periods from the early Renaissance to the present day, but it seemed to have a special place for Baroque composers guided by the Doctrine of the Affections. There are even Baroque pieces that seem to about the suspension.

The prepared dissonance is expressively charged, one might say. The strength of that charge depends on various factors in its immediate context. The charge might be intensified, for example, if the duration of the preparation is extended. Or the charge might be weakened by a particular device’s repeated use so that its effect becomes attenuated.

One of the most intensely charged prepared dissonances occurs when the moment of dissonance corresponds with a tonicization introduced by chromaticism which induces what can be called a scale-degree reorientation so that the dissonance takes on a less stable scale-degree function relative to its preparation.

To illustrate, look for a moment at the opening measures of Bach’s well-known C major prelude from the first Well-Tempered Clavier Book 1. (Click on the image to embiggen.) Audio

In measure 2, the blue C4 is a prepared harmonic dissonance created by the change of harmony in the upper voices.  In chordal terms, it is transformed from being the root of the measure 1 chord (C major) to being the seventh of the measure 2 chord (D minor seventh), a shift from the most stable of chord members to the least stable. This C4 seeks out stability and finds it by sliding down to the B3 in the following measure, the downward stepwise resolution being the normative path of resolution taken by chord sevenths. The remaining light blue notes in the example are prepared dissonances of the same kind as this measure 2 C4.

In addition to the prepared dissonance being one of the most expressive devices of tonal music, the appearance of a new tone is also an expressively salient event. As mentioned before, many (though certainly not all) such new-note appearances induce a scale degree reorientation through the tonicizing of pitches other than the prevailing tonic. Returning to the example above, the light purple F#4 in measure 6 is a newly appearing tone and reorients the immediate foreground into a G major tonality. The pink C4 here is a prepared dissonance similar in nature to the C4 of measure 2. However, not only does this C4 undergo a transformation from a harmonically consonant chord member (third of the A minor) to a harmonically dissonant one (seventh of the D Mm7), it undergoes an additional transformation from a scale-degree 1 orientation to a scale-degree 4 orientation, the latter being an activated scale-degree, particularly when combined with a dominant sonority as it is here. Therefore this C4 is doubly-charged expressively. (One might even say it is triply-charged in comparison to the C4 in measure 2 since its preparation is comparatively lengthened.)

Nothing said here is the least bit groundbreaking. The prepared dissonance is one of the most basic devices in tonal music; one might even say it is a foundational element to its expressiveness. Likewise, the recognition of the expressive affect that fresh new tones can have in a foreground texture is hardly a brilliantly perceptive insight. But as a composer, I am always contemplating how it is one might harness the expressive power in those deeply moving works in the traditional tonal idiom and adapt it to other expressive languages. The purpose of the color-coded analysis described below is therefore more an attempt to push to the forefront of my own composerly mind those basic devices which I think give tonal music much of its expressive power than it is an attempt at a comprehensive analysis of tonal music.

The color-code scheme is as follows:

• There are four labels—P, N, H & S. P represents a prepared dissonance; N represents a newly appearing tone; H represents a harmonically dissonant, and therefore activated, tone; S represents a tone whose scale-degree function has been reoriented (via tonicizing chromaticism). Therefore, wherever an S appears, an N should be nearby (with the possible exception of a tonicization of a minor key’s submediant–that is, its relative major key).
• There are eight colors in all representing combinations of the four labels above. Four colors are devoted to prepared dissonances (P) and four are devoted to newly appearing tones (N).
• Here are the eight colors:

Light Blue – PH – A prepared dissonance whose dissonance is harmonic (as opposed to a non-chord tone dissonance).
Dark Blue. – PS – A prepared tone that undergoes a transformation to a less stable scale-degree function by way of a tonicization.
Pink – PHS – A prepared dissonance whose dissonance is harmonic and which undergoes a transformation to a less stable scale-degree function by way of a tonicization.
Orange – P – A prepared dissonance whose dissonance is of the non-chord tone variety and/or a dissonance whose resolution is achieved not by its resolving into a stable relationship with the surrounding harmony but rather by the resolution of the surrounding harmonies to it (exemplified best by the pedal tone).
Light Green – N – A newly appearing tone which is neither harmonically dissonant nor involved in a tonicization (e.g. a chromatic passing tone, or a mode mixture tone (e.g. Picardy third)).
Maroon – NH – A newly appearing tone that is harmonically dissonant.
Light Purple – NS – A newly appearing tone that carries with it an unstable scale-degree function (ti, or fa when in a dominant sonority) (within the key tonicized by the new tone).
Bright Red – NHS – A newly appearing tone that is harmonically dissonant and that carries with it an unstable scale-degree function (within the key tonicized by the new tone).

• Generally speaking, the brighter the color, the more expressively charged the tone (all other contextual factors being equal).
• The S tones which either are dissonant or are newly appearing (N) are close together on the color spectrum: pink, purple and red. These colors indicate shifts in tonal centers, whether temporary or not.

Here is a color-coded version of the first half of the D-flat major prelude from Bach’s Well-Tempered Clavier Book 2: (Right-click on the image to embiggen in a separate window.)

As an analytical approach, such a color-coded strategy is obviously limited in scope. To name just one limitation, while this Bach prelude may be particularly well-suited for the implementation of such a strategy given the extent to which the harmonic voice-leading accounts for much of the piece’s expressiveness, the strategy says nothing of the larger-scale melodic trajectory that gives the music most of its forward propulsion. Much like roman numeral analysis, it falls short of significant analysis, stopping primarily at the level of description. Where it perhaps has an advantage over roman numeral analysis is in its highlighting (literally!) of those tensional elements embedded within the surface texture which can account for at least part of the music’s expressiveness.  In addition, it also accentuates linear aspects that are left untouched by roman numeral analysis. Still, like roman numeral analysis, it requires accompanying explication.

Below are some thoughts about the prelude, roughly in order of relevance to the color-coded  method of analysis:

1. The Db3 in measure 4 is pink (PHS) because it is a prepared harmonic dissonance (7th of the Eb major-minor seventh chord) whose scale degree orientation shifts from being a dominant pedal to being the subdominant of the tonicized Ab major key area. This pink note dissonance is especially charged expressively due to the length of its preparation (3 full bars of tonic pedal), to the extent of both the harmonic transformation (from the most stable root of the Db major chord in m.3b to the least stable seventh of the Eb seventh) and the scale-degree reorientation (from the most stable tonic scale degree to the activated scale degree 4) it undergoes. In an ideal world, my colors would have shadings that signify the relative strength of expressive charge within each category.
2. The chord in measure 15a is identical to the one in measure 23b, yet the application of this analysis renders them very differently colored, due to factors in each of their surrounding contexts. In measure 15, the Eb3 is rendered black because it is the expected resolution of the ascending bass line from the previous measure (C-D-Eb) and is heard as tonic. In measure 23, the Eb is rendered orange (H) because it is heard as a dominant pedal tone in an Ab tonality (even though the immediate chord is one that tonicizes A-flat’s dominant, Eb). The Cb4 is maroon (NH) for being a new note that is harmonically dissonant (the seventh of the D fully diminished chord it creates with the tones above, but also an unusual “dissonant 6th” above the bass which resolves downward to a P5 with the bass in the second half of the measure). The Cb in measure 23 is pink (PHS) because it is prepared in the preceding chord (though in another voice), it is a harmonic dissonance in the same way the measure 15 Cb was, and it undergoes a scale-degree reorientation since its function as scale-degree 6 (in the tonicized key area of Eb) is relatively less stable than the scale-degree 3 function it held in the previous half measure (in the Ab tonality). The measure 15 upper notes are light blue (PH) because all are prepared and none undergo scale-degree reorientation. In measure 23 the purple (NS) D4 and the pink (PHS) Ab4 would be light green and light blue respectively if the harmony did not involve scale-degree reorientation. The fact that one or more of these notes may have been analyzed differently, with different color renderings, indicates that decisions must still be made within this color-code method.
3. The first chord in measure 12 gives an indication of where my color-coded method is limited. The Eb minor seventh chord looks relatively black with only one light blue (PH) Db5, suggesting that the chord is relatively uncharged expressively. The color code fails to show that the chord is actually an unexpected resolution of the Db major-minor seventh immediately preceding it. Gb major is most likely expected, especially given the fact that all 6 dominant seventh sonorities heard prior to measure 12 resolve normally to the expected chords they tonicize. The Eb minor seventh chord is not extremely far afield from the expected Gb major (especially since all the the latter’s tones are embedded within the former), yet the deceptive resolution of the Db major-minor seventh is clouded by its being in first inversion putting the temporary leading tone in the bass and by both the Eb minor chord’s containing a chord seventh and its appearing in first inversion. In other words, we often hear V7-vi deceptive progressions but hearing a V65-vi65 deceptive progression is much less common. (A similar unexpected resolution occurs in measure 16, though color rendering marks it as more highly charged. More on this measure later.) In sum, in this color coded system there is the possibility of failing to highlight certain syntactical divergences such as unusual chord progressions.
4. Two notes (G3 in measure 6 and C3 in measure 20) have parentheses around them. Both notes are similar in function and were given parenthetical light blue (PH) color renderings because they can be heard as reappearing remnants of the previous chord, creating a kind of delayed retardation figure. The G3 in measure 6, for example, is heard in measure 5b, and its reappearance in measure 6 produces a kind of echo of the G-Ab resolution that occurs on the downbeat.
5. The first chord in measure 16 is quite interesting. Is it simply a simultaneity produced by the linear voice-leading driven by the two descending chromatic lines (Ab-G-Gb-F in the soprano; D-Db-C-Cb-Bb in the lower alto register)? That answer (or non-answer) does not do justice to the sequential progression embedded here. The issue is the F3 in the bass at measure 16. Why did Bach choose F?? Without it, the progression is much clearer. There are a number of parallels between this prelude and the C major prelude from WTC1 mentioned above. This measure 16 of the Db major, in my mind, corresponds to the infamously ambiguous measure 23 in the C major. How would you explain the F in m.16??

Tzimon Barto and Aberrant Tempi in the Rach 3

I have always loved comparing recordings. When I was younger I used to buy new (and old) recordings of the same pieces to compare with the ones already in my collection. Three works I particularly loved to search out in record stores are Bach’s Goldberg Variations, Chopin’s 24 Etudes and the Rachmaninoff 3^rd Piano Concerto. Whenever I have a hankering to hear one of these masterpieces, I have my personal favorite go-to recordings—Perahia or any Schiff performance for the Goldberg (if I need a Glenn Gould fix, which isn’t frequent these days, I much prefer the 1957 live performance to the two more famous studio recordings); Louis Lortie for the Chopin (Yes, Lortie! Perfect tempi, immaculate pedaling, amazing clarity, and enormous range of musical expression. Find it and treat yourself!); and Horacio Gutierrez for the Rach 3.

As I have mentioned before, I taught a class this past semester on Rachmaninoff (and two other composers). When wanting to revisit the Rach 3 while prepping for the course, I realized that I had lent out my Gutierrez disc of the concertos. So I had to turn to one of the other recordings on my shelf: Argerich (1982 with Chailly), Ashkenazy (1971 with Previn), Tzimon Barto, Bronfman, Janis (1958 with Munch), Watts, or Rachmaninoff himself.

For whatever reason, I opted for the least well-known in my collection, the Barto, the only pianist in my list above for whom I felt the need to give a first name.  So I pulled out the now-out-of-print EMI label recording which has Christoph Eschenbach conducting the London Philharmonic. (I’ve always been partial to Eschenbach since I grew up watching him during his stint with the Houston Symphony Orchestra.) Barto’s tempi, I remembered, are extremely broad compared to other pianists, and his touch more delicate. I know for a fact that this is not due to Barto’s limited capabilities. I heard him perform live Prokofiev’s monstrous Second Concerto with the Houston SO (also with Eschenbach conducting), and Barto’s formidable technique more than matched the weight required by this enormous, masculine work with its two huge cadenzas. Barto himself is hulking figure—a physical specimen.

At any rate, while Barto’s is not the most dazzling rendition of the Rach 3, it is one that I have always appreciated for its delicacy, clarity and vision. When most pianists plow quickly through the many dense passages at breakneck speeds, Barto plays in such a way and at such a tempo that every nearly note can be heard. You begin to hear things you didn’t realize were buried within Rachmaninoff’s rich textures. In fact, Barto plays many of the passages filled with rapid filigree as if he were playing Bach. Examples of these things later.

One particular passage in Barto’s rendition startled me as being so far removed from the standard interpretation that I barely recognized the passage at all! The passage in question comes in the second movement just before the final orchestral statement of the movement’s principal melody. The section is a contrasting one that features conjunct woodwind melodies that bear an affinity with the stirring principal theme that opens the first movement. (This occurs four measures after rehearsal number 33, or at the bottom of page 66 of this document (score page 64).) Rachmaninoff’s marking “Poco piu mosso” at this spot comes four bars after a “Tempo come prima” marking, which is to say, “Adagio.”

First listen to performance of the passage taken at a tempo that represents the typical interpretation (although perhaps nothing besides the tempo can be called “typical” in this performance!). This is Horowitz’s 1978 performance with Zubin Mehta and the New York PO. Horowitz’s tempo is mm=80.

LISTEN

Now here’s the same passage taken by Barto, whose tempo registers at mm=60!!

LISTEN

The great disparity between Barto’s tempo and that of every other performance of this passage I had heard led me to do some more detailed comparative research. Using my own personal library, the excellent CCM library resources and YouTube, I compared Barto’s performance with 22 others, most of which are considered to be staples in the Rach 3 discography. The chart below shows my findings. The names are color-coded by date—the green end of the spectrum represents the more recent performances and the red end represents the “ripe” old historic recordings. (Think tomatoes here, although I’ve never seen a green tomato turn blue before turning red.) (In some of the versions below, tempi fluctuated, but I chose the fastest steady tempo taken through the pertinent passage.)

Obviously, my immediate reaction to the Barto performance as being aberrant from the standard interpretation was not without reason. I found no performances that came even close to Barto’s tempo. The Horowitz performance I linked above represents the median tempo of those on the chart, so for an even more drastic comparison, you might want to play the Argerich or Horowitz 1930 performance by following the links given below to compare with Barto.

But what to make of Barto’s rendition, aside from the aberrant tempo? My initial reaction to the Barto was that it was all wrong! However, slowly I came around to accepting and then even appreciating his interpretation. Today, I’ve grown to love it for its daring, its clarity, its freshness, and for the fact that it truly dances! Barto plays the passage as if it were a true 3/4 waltz to be danced to rather than taking it at the skipping pace that the notated 3/8 meter perhaps implies. What are your thoughts?

Below are links to the other recordings referenced in the chart, ordered by tempo. The YouTube videos (if linked) take you directly to the pertinent passage.

88 Horowitz 1930 (Coats/London SO)  (Info) (YouTube)
88 Argerich 1982 (Chailly/RSO Berlin) (Info) (YouTube)
88 Hough 2004 (Litton/Dallas SO) (Info)
85 Horowitz 1951 (Reiner/RCA Victor SO) (Info) (YouTube)
85 Gilels 1955 (Kondrashin/USSR State Symphony) (Info) (YouTube)
85 Gavrilov 1987 (Muti/Philadelphia SO) (Info) (YouTube)
83 Janis 1958 (Munch/Boston SO) (Info)
83 Kern 2001 (Conlon/Ft. Worth SO) (YouTube)
82 Watts 1960 (Ozawa/ NYPO) (Info)
82 Lugansky 2008 (Saraste/Oslo PO) (YouTube)
81 Rachmaninoff 1939 (Ormandy/Philadelphia SO) (Info) (YouTube)
80 Horowitz 1978 (Mehta/NYPO) (YouTube)
80 Gutierrez 1991 (Maazel/Pittsburg SO) (Info)
78 Volodos 1999 (Levine/Berlin PO) (Info) (YouTube)
77 Cliburn 1958 (Kondrashin/Sym of the Air) (Info)
76 Bronfman 1990 (Salonen/Philharmonia O) (Info)
76 Sokolov 1978 (Kitaenko/Moscow PO) (YouTube)
76 Pletnev 2002 (Rostropovich/Russian Nat’l O) (Info)
75 Bolet 1984 (Fischer/London SO) (Info)
74 Lang 2002 (Dutoit/NHK) (YouTube)
72 Andsnes 1995 (Berglund/Oslo SO) (Info)
71 Ashkenazy 1971 (Previn/London SO) (Inf0)
60 Barto 1998 (Eschenbach/London SO) (Info)

I can’t end this post without sharing a few more of my favorite passages from the Barto performance. Listen to the way in which he plays the filigree that accompanies the orchestra’s imitation of the haunting opening melody that opens the concerto. It’s as if he were playing a Bach invention, with rhythmic precision and virtually no pedal. The result is one of utmost clarity:

LISTEN

Barto tackles all such passages in the same crystalline manner, always playing with and not against or even alongside the orchestra, and always opting for a tempo that allows the soloist of any given passage, whether it be pianist or wind player, to sing the long melodic line, which is always of the greatest importance in Rachmaninoff’s music.

Listen to the clarity and sensitivity in this passage, also from the first movement, and to how the various soloists respond to the gracious spaciousness provided:

LISTEN

And have you ever heard this passage from the third movement played more delicately and serenely? (Headphones recommended for the full effect!)

LISTEN

Finally, here is one of those magnificent passages in which a small detail can elevate the music to sublimity. A relatively subdued presentation of an arch-like melody occurs in the piano. Listen then to the way in which the next phrase completely blossoms, giving the passage a sustained buoyancy and a resulting sense of jubilation! Notice again, the modest tempo allows for great clarity in the accompanying left hand and for its ability to sync perfectly with the churning strings.

LISTEN

When I was young and first discovering this piece, I always preferred the more dazzling recordings where the pianists achieved the seemingly unachievable, tackling the densest of passages at breakneck speeds. Nowadays, I would rather listen to Barto than Janis or even Argerich.