Administrative post: updated links to some files

Early next year, Dropbox is changing the public folder to a shared folder. Therefore, I have moved all files that were formerly on Dropbox to Google Drive. Here is an alphabetical list with the new links:

Chopin, Prelude in E Major, op. 28n9: link.

Guide to my blog Hearing Schubert D779n13: link.

Guide to the blog Hearing the Movies: link.

Haydn, Sonata in Ab major, menuet, my graph, page 1: link.

Haydn, Sonata in Ab major, menuet, my graph, page 2: link.

Haydn, Sonata in Ab major, menuet, score: link.

Haydn, Sonata in Eb major, II, my graph, page 1: link.

Haydn, Sonata in Eb major, II, my graph, page 2: link.

Haydn, Sonata in Eb major, II, score, page 1: link.

Haydn, Sonata in Eb major, II, score, page 2: link.

Minor key progressions (table): link.

Neumeyer, handout for 2010 Society of Music Theory presentation: link.

Neumeyer research vita: link.

Schubert dance table: link.

Revised Playford essay published

I have published a heavily revised version of my essay/documentation John Playford Dancing Master: Rising Lines (link to original). The new version is, appropriately, titled John Playford Dancing Master: Rising Lines, Revised and Updated. It can be found on the Texas Scholar Works platform here: link to revision.

Here is the abstract:

This updates and substantially revises two publications of mine on the Texas Scholar Works platform: John Playford Dancing Master: Rising Lines (2010; 2015) and the corresponding section in Rising Lines in Tonal Frameworks of Traditional Tonal Music (2015). The main goal was to provide higher quality graphics, but I have also written a new introduction as well as new analysis and commentary for almost all of the dances.

Minor key essay

I have gathered the posts in the minor key series into an essay that has been published on the Texas Scholar Works platform: Ascending Lines in the Minor Key.

The essay contains all posts from the series, along with a newly written "concluding comment."

Here is the abstract:

The minor key poses obstacles to rising cadence gestures, and the number of compositions with convincing linear ascents is small. This essay assumes a mostly traditional Schenkerian point of view and studies that limited repertoire of pieces, which includes 17th and early 18th century music relying on the Dorian octave, and compositions by a variety of composers from Johann Walther and Thomas Morley, through François Couperin and Beethoven, to Brahms, Hugo Wolf, and Carl Kiefert.

Minor key series, part 14 (Dorian and Aeolian octaves), continued (2)

Here are the third and fourth of four dances from Michael Praetorius's collection Terpsichore. The four are ns104, 147, 148, and 295, and all have been discussed elsewhere on this blog.

(3) Here is my comment on n148 from the earlier blog post:

n148 is in once-transposed Dorian; it has three strains but none is marked with a repeat sign. The final cadence is unusual in the uppermost voices in its string of parallel sixths. These help us to separate the ground notes from the diminutions in the cantus. (link)

The play of "major/minor" (B/Bb) in the first strain is striking (though, I observe once more, not uncommon in the era), and the small clash of E natural/Eb in the cadence is of interest.

(4) Here is my comment on n295 from the earlier blog post:

. . . one of the pieces where the melody is of uncertain authorship. Here is a highly profiled motive with a scalar ascent and an unusual stepwise drop after a falling fourth (circled), something that would be frowned on in a 16th century counterpoint class. It's repeated, transposed, in bar 3, then at the original level in bar 5, and finally the scale is realized as a complete ascending octave. The second strain (not shown) is unusually short: four bars of a repeated chord plus cadence. The final strain "fixes" the motive (circled) with a third rather than a fourth and moving by step within the interval. Even stronger scalar figures follow to end with an unusual, direct [Dorian] ^6-^#7-^8.

To finish this appendix on modes, I return to two more pieces I have written about earlier: the courantes from the D minor suite by Elisabeth Jacquet de la Guerre: link 1; link 2. In both pieces we can see the full flowering of minor-key focus (despite the Dorian signature) but at the same time -- in courante n1 -- vestiges of modal chromatic practice in the approach to the final cadence. In the first section of n2 (below), Bb is used strictly throughout, with the only exception a passing B-natural in the left hand in the penultimate bar. In the second strain, the same applies, the exception this time being the "raised" ^6 in the right hand in the final cadence.

In courante n1, the play of Bb/B-natural and C-natural/C# in the final bars reminds one of music from 60 or 70 years earlier. (The two courantes were published in La Guerre's first collection of keyboard pieces, 1687. She was 19 at the time; a prodigy, she was already a decade into her professional career.)

With this, the minor key series is concluded.

Minor key series, part 14 (Dorian and Aeolian octaves), continued (1)

Johann Walther's ATB setting of the Easter chorale Jesus Christus, unser Heiland (from 1524) shows the relatively rare case of conflicting signatures: once-transposed Dorian in alto and tenor, twice-transposed Aeolian in the bass. The chorale, in the tenor (boxed below) avoids the Dorian ^6, using all other scale degrees within the octave G3-G4. Against this, alto and bass engage in a play of chromatic cross-relations, which, as I noted in the previous post, is far more common in music of the 16th and 17th centuries than our usual counterpoint rules would have us believe.

The final phrase of the chorale (circles below) is embellished via the ubiquitous pre-cadence flourish of small notes, and there the Dorian ^6 finally does appear in the tenor -- not surprisingly, as the alto and tenor move in parallel thirds through the figure. The alto starts with notes of the final chorale phrase and makes an easily heard chromatic connection from F5 to F#5 across the phrase. I would regard the alto here as a descant voice; to analyze in Schenkerian (Salzerian/Novackian) terms, the Urlinie would reside in the tenor.

Nevertheless, there is a point of historical interest in the alto's descant. I quote from my essay Rising Lines, p. 17 (link to the essay):

[One] source of rising lines comes from five-part vocal (but more often) instrumental music, where the cantus (or topmost) line takes on the character of a descant. . . . When the cantus "loses" its descant character and acts as a principal upper voice, rising structural lines are easily achieved. This change is parallel to the one that occurs in the first half of the nineteenth century, when—even though the force of a century-old cliché that demands descending cadential formulas is still strong—composers sometimes "forget" to relegate ascending lines to [their usual position in] the coda. 

A dance from John Playford's English Dancing Master (first edition 1651); music only, without dance instructions. For more information on "Madge on a Tree" go to an earlier post on this blog: link. The Dorian signature and the ascending Urlinie are obvious features. At the asterisks, note E-natural expressing the Dorian ^6 in a striking way in the context of G minor and Bb major triads, then Eb as a simple neighbor note ornament to D5.

Here are the first two of four dances from Michael Praetorius's collection Terpsichore. The four are ns104, 147, 148, and 295, and all have been discussed elsewhere on this blog.

(1) Here is my comment on n104 from an earlier post:

A shift to minor quality in the second strain, with a fairly leisurely descent/ascent pair that use both F# and F-natural in each half of the figure. (link)

A modern-sounding major/minor contrast is achieved between the strains: Mixolydian in the first, once-transposed Dorian in the second -- except that the consistent use of Eb (asterisks) renders the scale Aeolian in sound. Exceptions in the cadence (boxed) are routine embellishments.

(2) Here is my comment on n147 from an earlier post:

. . . author of the melody unknown; this is one in a series of courantes in once-transposed Dorian mode (final G; one flat in the signature). The box shows a simple linear ascent to the cadence on D5. In the second strain, the figure in part or whole occurs four times in a row.  (link)

Here, as we have seen in some earlier cases, inflections of E as Eb produce an Aeolian sound in the first half of the first strain, but move toward a cadence on D brings back the Dorian ^6 as E-natural in bars 5-8. The final measures of the second strain are exclusively Dorian in sound.

Minor key series, part 14 (Dorian and Aeolian octaves)

In the introduction to this minor-key series (link), I wrote the following:

At the end of the series, I will add posts with a couple additional counter-examples (from Beethoven and Offenbach) and other posts with historical context about the Dorian octave, the examples coming mainly from Praetorius and Eyck.

Beethoven was here recently (link), but not Offenbach: when I wrote the introduction, I anticipated finding something in Orpheus in the Underworld, but even there Offenbach wrote in the major key! In this appendix on rising figures and the modal octave, the example list does include Praetorius and Eyck, but also Morley, Walther, and La Guerre, as well as a dance from Playford.

The Dorian and once-transposed Aeolian modes are an interesting case in point for the complex history of modes, scales, harmony, and keys in the 17th century.  We'll start with the simplest examples: characteristic, conservative treatments of each.

Among the earliest posts on this blog (from 2014) is a series on rising lines in music by Jacob van Eyck, from the Fluyten Lusthof. Here is one paragraph from the introductory post (link).

As is well-known, in the 1640s the Dutch flutist Jacob van Eyck published a pair of remarkable volumes called Der Fluyten Lust-hof: vol Psalmen, Paduanen, Allemanden, Couranten, Balletten, Airs, &c. Konstigh en lieslyk gefigureert, met veel veranderingen. As the subtitle announces, the pieces -- all for solo flute (or solo treble instrument) -- range from Calvinist psalm tunes and well known chorales (such as Vater unser in Himmelreich) to dances and popular tunes. All of them are dressed with "divisions" (diminutions, or the technique that "breaks" a long note into smaller notes), most with multiple versions (met veel veranderingen).

In van Eyck's setting of an old tune, "Wel jan wat drommel" (which is discussed in the introductory post linked to above), we can see a firm maintenance of the Dorian scale, except for leading-tone inflections for the cadence to A in the first section and for the cadence to D in the second section. At "x" we might expect a player to lower the B to Bb, but at "y" the B makes sense as is. In fact, the expressive contrast between Bb at "x" and B nearby at "y" would by no means be out of place in this era (as we'll see in some subsequent examples). At "z1" and "z2", B is a given because the leading tone G# has already been heard.  In the second section, "m" and "n" are appropriately B, as the entire passage sits in the upper tetrachord and the leading tone is heard no less than four times.

"Modo 2" indicates the first of two variations. The "gebroken" version of "x" still suggests a possible Bb and the contrast between a flat for the downward line from C5 to G4 and a natural for the upward line from G4 back to C5. At "z1", it seems unlikely that Bb would sound given the proximity to the leading tone and cadence on A (see "z2"). At "m" and "n" the same constraints that dictated B rather than Bb throughout in the theme continue to apply to the diminutions.

In "Modo 3," the second variation, the diminutions come down to mostly eighth notes. At "m" Bb seems much more likely now, to avoid a tritone leap from F4 to B4 -- and of course suggests that van Eyck may have assumed a player would use Bb at this point in the theme and first variation as well. At "n" again, B is clearly meant throughout, first because of the focus on C5, then in figures that follow from the leading tone G#. At "o" it's hard to know what to make of the two notated tritones (at "p" the tritone G-C# is heard again). Unless we want to invoke possible misprints, the first B could be done as Bb, but all others at "o", "p", and "q" are B-naturals.

The figure below traces the diminutions in the closing cadences of Modo 2 & 3 back to the theme. The asterisks show the clichéd escape tone figure, where D-C# is embellished by an upper E. In the box, the escape tone even receives its own elaboration. These are excellent early examples of what be called the mirror to the leading-tone third: the not uncommon case where ^2 embellishes a more basic ^#7.

Van Eyck, Courante. I have written about this piece here: link. What might seem a subtle difference in the present day was assuredly not in much of the 17th century. This courante is in "D minor" (key signature of one flat), but properly in once-transposed Aeolian mode (the mode on A transposed up a fourth or down a fifth). The presence of Bb gives the scale a different color than the Dorian -- in any case, historically, the Aeolian mode was associated with the Phrygian, not the Dorian. The Bb is carefully maintained in the courante and its two variations, with the exception of the end of variation 2 ("Modo 3"), where the turn of the cadence up toward ^8 would surely change the notated Bb to B-natural in performance.

Next, the beginning and end (untexted) of Thomas Morley's madrigal "Leave, alas! This tormenting" (1595) are given below. Notation for viols is by Albert Folop and is available on IMSLP. I show the opening to demonstrate that it is clearly twice-transposed Aeolian (up two fourths produces a key signature of two flats). Several expressive Eb's emphasize the mode's characteristic sound, and the voice entries are in the expected positions (on D and G; not G and C, as would be the case if this were twice-transposed Dorian).

The madrigal is 88 bars long. The Aeolian octave is strictly maintained throughout, with just these two exceptions (before the end): two measures for a cadence on D (mm. 30-32 b1) and the first statement of the closing cadence below (at mm. 53-61).

The latter and its twin  (mm. 79-88) at the end of the piece are indistinguishable from the Dorian because of the repetition of a rising figure (in boxes) that requires E-natural. The structural upper voice in the cadence, also using this line, makes the adjustments we would expect for an Aeolian cadence.

Minor key series, part 13 (partimento)

This post is the second about partimenti by Francesco Durante. Here was the first one: link.

The progressions I used in the earlier post were short formulas; this is an entire binary-form composition of more than 50 bars. There are four elements: A1, bars 1-15, PAC in E minor; A2, bars 16-28, PAC in E minor; B1, bars 29-42, PAC in A minor; B2, bars 43-54, PAC in A minor.  Here it is on the Monuments of Partimenti website, among a rather large number of examples with first inversion seventh chords (6/5s): link.

In the first section, it is easy to hear a middleground upper voice descending from ^5, interrupted in the cadence:

For my detailed example, I will use the final section (B2, bars 43-54). An almost entirely stepwise melodic line comfortably fits Durante's bass, although I took one liberty in assuming iv6 rather than VI in bar 50:

And that same line can as easily be "re-routed" at the end to achieve a rising line. The only additional digression from Durante's figures is critical, however: F5 becomes F# at the end of bar 51. I don't regard this as an obstacle, as (assuming the transcription is correct) the figures in the partimento are obviously incomplete: the student experienced enough to realize this piece effectively would surely also have the ability to make (presumably small) adjustments in improvisation/performance.

Here are the final five measures realized in three voices.

At first glance, an incomplete line (or what I have elsewhere called a "primitive line") fits with the bass of figure g (that is, i-i6-iiø6/5-V-i), but neither i6 nor iiø6/5 support a tone at the same level as the others.

A better, musically more satisfying solution gives due prominence to the subdominant in both its minor and major forms. Underlying this is a simpler variant of figure b (with IV, not IV followed by ii).

Minor key series, part 12 (Beethoven)

Beethoven's 32 Variations in C minor, WoO80, were composed in 1806 and published in 1807. The lack of an opus number might be related to the composer's rejection of the work later in his life. Certainly, its evocation of the Baroque chromatic chaconne bass and continuous variation design seems out of place among the large-scale, heroic music of Beethoven's middle period (he also wrote the Third Symphony and the Violin Concerto in 1806, for example). And not only is WoO80 rather old-fashioned for the first decade of the 19th century, but it also is not up to the standard of the "Eroica" variations written earlier (1802) or the Diabelli Variations written much later (1819/1823).

To the point here, the theme offers an obvious opportunity for a rising line in the minor, an opportunity that Beethoven does not exploit, however, as we shall see below. There is one rising line among the 32 variations, but it is in the maggiore variation 14.

The chromatic chaconne bass in bars 1-6 moves against a rising line in the right hand, the overall result being to move both bass and melody from ^1 to ^5, but of course in opposite directions. The wedge goes one step further in the sforzando subdominant chord but then the simple octaves fall sharply (and quietly). The potential for a variant of an ascending Urlinie, however, is introduced by that subdominant chord -- I have marked how it might be realized in scale degrees. As it stands, the clearest implicit figure is a displaced neighbor G5-Ab5-G4 (bars 6 and 7).

In the variations, Beethoven makes much of the dramatic contrast between the first six bars and the cadence. Since he includes the rise-and-fall gesture in many cases, the clear expression of a rising line is not possible. Variation 5 is typical. The arrows at (a) chart the wedge in the melody, which does reach ^6, but then the convoluted drop-off leaves one assuming an implied completion of the neighbor figure, so, G6-Ab6-(G6).

The primary impediment to an ascending Urlinie in the variations is Beethoven's abandonment of the subdominant supporting ^6 for an expanded dominant, as in Variation 6, where bars 6-7 are a dominant seventh or ninth.

Variation 12 is the first of five maggiore variations. The arrow points to the sixth scale degree that ought to make a continued ascent in the cadence easy to manage.

Variation 14, finally, does realize a rising line. An initial ascent brings ^3 (at "x") up to ^5 (at "y"). A first attempt at the line from ^5 to ^8 follows (see "z"), and bars 7-8 do the work with clarity and resolve (thus, ^5 in bar 3 moves to ^6 in bar 7 and the line then finishes the ascent).

Minor key series, part 11 (progressions k-n)

Here are examples of more complex ascending figures, this time shown in four part textures. All of these are hypothetical in the sense that, although they are possible "mechanically," I have not yet found examples in the repertoire.

In figures k and l, the melodic line is completely chromatic. The underlying harmony in figure k is relatively simple, in figure l rather less so.

Figures m and n are variants of the fully chromatic line. In figure m, the chromatic ascent is interrupted for the sake of introducing a cadential 6/4 chord. Figure n varies figure k but at the cost of undermining the fully chromatic line (the first five chords prolong i and support a neighbor-note figure, ^5-^6-^5).

Minor key series, part 10 (Wagner)

The opening of the Prelude to Tristan und Isolde comes close to following figure i, in which ^#6 is supported by either a minor ii or major II. I say "close" with some caution, as three of the five elements are not represented as clearly as one would like. Tones of the tonic chord (for element 1) are minimally represented (some music scholars don't accept these tones as confirming the tonic at all). Element 2 is an unresolved dominant seventh chord in the middle of a sequence. Worst of all, element 5 is not the tonic to support ^8, but VI.

The reduced score below shows the opening's version of this progression, which returns in varied form as the ending.

Here is that "structural close." The passage from the beginning is reworked in the first 12 bars. I have boxed the ending to show the cadence. The end result is an abandonment of figure i for figure c (where ^5, ^6, and ^7 are all over V), but still with the deceptive ending. By the time the opening figure is repeated (second box below), the bass is G and the prevailing key has changed to C minor.

Minor key series, part 9 (Wolf; Brahms; Duparc) continued

Brahms, Op. 69n7, consists of two musically identical verses. The first is reproduced here.

The pairing of a simple rising line with a descending alto from ^5 is reminiscent of the Couperin passacaille, but here the alto descends more quickly. For much more on this song, possible analyses, and the text, see my essay Rising Gestures, Text Expression, and the Background as Theme: link. The section for which Op69n7 serves as the principal example begins on page 17.

Henri Duparc's "Lamento" was written in 1868, while the twenty-year old was a student of Cesar Franck, whose influence shows. Walter Everett (2004, 52) reads the pitch design in very nearly the way I do below, with ^5 prolonged for quite some time. then the line rising through A#4 to ^6 (B-nat4) and through C-nat5 to ^7 (C#5) and finally to ^8 (D5). The bass support is the tonic for ^5, nat-VI for ^6 (!), V7 for ^7, and the tonic again for ^8.   (Score notation is by Pierre Gouin and is available on IMSLP. My apologies for artifacts I've introduced in the first section below through compressing the width and moving measure 7 up a system.)

Reference: Everett, Walter. 2004. "Deep-Level Portrayals of Directed and Misdirected Motions in Nineteenth-Century Lyric Song." Journal of Music Theory 48/1 (2004): 25-58.

Minor key series, part 9 (Wolf; Brahms; Duparc)

I had intended this post to show a later 19th century treatment of figure g in Hugo Wolf's setting of Goethe's satirical "peasant" poem "Der Schäfer." Two things happened, however. First, I realized on examining the piece more closely that figure g is not the model; instead, it is a convoluted or distorted version of figure c. More on that below. Second, I remembered that I had just written about a minor-key Brahms song in the essay Rising Gestures, Text Expression, and the Background as Theme (published on Texas Scholar Works: link). Then, looking at the work materials for that essay, I found another Brahms song and also one by Henri Duparc (both are mentioned in Walter Everett's article that was the starting point for my Rising Gestures essay).

Neither Brahms song (they are, btw, Op59n1 and Op69n7) nor the Duparc "Lamento" uses figure g, so the end result is that this post may perhaps be best regarded as an excursus in the minor key series. The nineteenth-century theme will continue, however, in the following post, where I look at the opening of the Tristan Prelude in connection with figure i. After that, I'll finally introduce figures k-n, which as it happens lack examples in the repertoire, and two interesting cases—Beethoven's 32 Variations in C minor, WoO80, which ought to have a rising line based on its harmonic plan, but doesn't—and a movement-length partimento by Durante. The last entries in the series will form a longish appendix on 17th century Dorian-mode pieces.

In brief, Goethe's poem "Der Schäfer" is about a shepherd who is lazy and neglects his work but who suddenly perks up and becomes energetic and responsible when a woman accepts him. This turn happens in the final lines, and is set by Wolf with a rising line.  The first structural tone of the melody is unclear, largely because of the contortions in line and harmony—see the score below—but also because neither ^8 nor ^5 is confirmed in the subsequent passage.

At the end, on the other hand, the motion from ^5 is very clear, if also very chromatic in the voice and oddly chromatic in the harmony:

I have removed the text and isolated the harmonies in this reduction. Also note the labeling of local harmonies and functions.

A further reduction shows more plainly that the entire passage, excepting the final tonic, involves prolongation of the dominant.

The end result, then, is that "Der Schäfer" uses figure c (below), not figure g.

Brahms, op. 59n1, is another Goethe setting, "Dämmrung senkt sich von oben," a nature poem that Brahms sets in four verses, the first two in G minor, where the second is a slight variant of the first, the third is a "B-section" contrast that begins in Eb major, and the fourth in G major builds on material of the second half of verse 1. It is the last verse that concerns us here.

The ^5 I have marked at the beginning is without reference to anything earlier in the song. Whether the whole piece should be read from an abstract ^3 (Bb) or ^5 is an open question: I would favor the former in the early verses but the latter in the final two. Regardless, the motion from ^5 and the elongated dominant are unmistakable in verse 4.

Considerable attention is given the subdominant throughout the verse, including the approach to the cadence (see both IV and iv below). The close, then, uses figure c, where ^5, ^6, and ^7 are all over V -- but note that the alternatives for the voice lay bare the simple and ancient opening wedge of counterpoint where the ascent ^5-^6-^7-^8 is balanced by a descent from ^3 to ^1.

Nevertheless, Brahms does here what Schubert did in pieces we examined early in this series (link): he actually avoids the problem of the minor key by switching at the end to the major.

Part 9 continues in the next post: Brahms, Op. 69n7, and Duparc "Lamento."

Reference: Everett, Walter. 2004. "Deep-Level Portrayals of Directed and Misdirected Motions in Nineteenth-Century Lyric Song." Journal of Music Theory 48/1 (2004): 25-58.