Praetorius, Terpsichore

IMSLP recently added a file with the part-books for Michael Praetorius' Terpsichore (1612) (link). In celebration of that event, here are three examples. The pieces (in score) are discussed, along with many others, in my essay Ascending Cadence Gestures: A Historical Survey from the 16th to the Early 19th Century (link). Edited versions of the text are given here along with a facsimile of the cantus part.

Number 35 is the first of the more than 160 courantes in the volume. In the second strain the range F4-C5 is established firmly at the beginning, C5 held, then a partial descent occurs midway, and the pattern is repeated, at which point the range F4-C5 is covered yet again and expanded by one for the cadence on D. (Note: The score in modern notation was transposed up a fifth.)

n147: "Incerti" = author of the melody is unknown. This is one in a series of courantes in once-transposed Dorian mode (final G; one flat in the signature). In the first strain see 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, leading to G5 in the end.

n265 is a three-strain ballet, without notated repeats. The first strain ends with the long note in the middle of the third system. The second strain ends with the last long note in the fourth system. 

In effect this ballet is really two strains, as the third is a close variation of the second. The point of interest is in the cadences for the second and third strains: the first of these cadences lies (and is somewhat buried) in the lower register, ending on F4, but the second is made very prominent by transposition up the octave, ending on the same F5 that started the strain.

Music in 17th century Vienna, part 2

Continuing the series of posts on music by Johann Heinrich Schmelzer, here is another courante from from DTÖ volume 56. The suite is titled Partita ex Vienna, and its five numbers are Branle de village, Courente, Sarabande, Brader Tantz zu Wien, and Alio modo. I have no further information on the piece, as the introduction to volume 56 was published separately (that is, not included in the music volume).

In terms of melodic design, this is the simplest of the pieces in this series of posts: strong emphasis on ^5 throughout and an uncomplicated treatment of the upper register resulting in a simple ascending Urlinie.

Music in 17th century Vienna

Johann Heinrich Schmelzer was one of the leading musicians in the Viennese court in the seventeenth century. His career is closely associated with Leopold I, the Holy Roman Emperor from 1658 to 1705 (Schmelzer died in 1680).

Particularly known throughout his life as a violin virtuoso, Schmelzer joined the court musicians as a young teen, though the first record of an official appointment is in 1649, when he would have been in his mid to late twenties. He was director of instrumental music no later than 1658, and three volumes of his own music were published between then and 1664. It is possible that Antonio Bartoli was influential in Schmelzer's training as a violinist. The senior musician came to the court in 1624 (at the age of 19) and became widely known as an excellent violinist. He was appointed Kapellmeister in 1649, after which time he focused on the introduction of Italian opera to court performances.

The music readily available to me is instrumental: sonatas for one or more violins, and orchestral music for ballets incorporated into operas or meant for other staged performances. Dances from suites discussed in this series of posts come from DTÖ volume 56, Wiener Tanzmusik in der Zweiten Hälfte des Siebzehnten Jahrhunderts, edited by Paul Nettl (1960).

This courante is typical in its treatment of tonal spaces in the principal melodic part. A clear definition of the fifth A4-E5 is reinforced at the beginning of the second strain. A fairly complex treatment of the upper register ensues. The primitive Urlinie, ^5-^7-^8, that I have traced is probably the best abstraction for bars 19-28, but the reader will note that I have not attempted to "finish" the analysis by incorporating the several unfoldings.

Biographical information from "Johann Heinrich Schmelzer" and "Antonio Bartoli," by Rudolf Schnitzler and Charles E. Brewer, articles in Oxford Music Online. Brewer has also published a book on the topic: The Instrumental Music of Schmeltzer, Biber, Muffat and their Contemporaries (New York: Routledge, 2016).

Chambonnieres, Pieces de Clavecin (1670), sundries

This is the final post in the series on Chambonnieres's Pieces de Clavecin (two books, 1670). Three pieces from book 1 offer "sundry" examples -- figures that didn't fit into the first four topical groups, which were two types of rising lines and two types of lines that overshoot ^8 to reach ^9.

The allemande that opens suite 3 initially runs an octave from F4 to F5, a coupling of ^3 to ^3. What immediately follows in the descent, however, suggests an interval frame ^1-^3 (as D5-F5) in bar 3 (not marked), which then expands to C5-F5, the latter remaining stable to the end of the strain. The upper voice marks a neighbor-note figure about ^8.

The second courante from suite 4. Very similar to the first example but the interval frame F5-C5 is stretched out and confirmed over a longer distance.

The first courante from suite 5. The minor key always causes problems for ascending lines. Here Chambonnieres creates an audible "break" between Eb5 and E-natural5. The octave line traced from G5 to G4 and including Eb5 is obvious, but any earlier note connecting to E-natural5 is not. One might prefer to hear A5 (bar 14) connecting to G5 (bar 14) and then to the cadential G-F#-G in bars 17-18.

Chambonnieres, Pieces de Clavecin (1670), lines with ^9 = ^2 (2)

Yesterday's post began the third of five topics: rising lines that overshoot ^8 to reach ^9 then fall back to close. Today's examples are three courantes from book 2

Suite 1, courante 1. An opening fifth line touches each triad note in turn (circled notes), reaching ^5 by bar 3. The second strain doesn't define a focal tone, so that I have left the ending "open" in the sense that ^2 moves to ^1 (last three bars) but the beam is left open at the beginning. This seems to me the only musically satisfying linear scheme. The internal line, on the other hand, is plain as day—unfolded through the fifth G4-D5.

Suite  2, courante 2. The unfolded fifth appears again at the end of this courante. Overall, the tonal frame is ^5-^8, and the closing cadence generates a largely abstract upper voice ^8-^9-^8 (abstract because of the temporal distance covered between ^8 and ^9).

Suite 3, courante 3. The circled internal line is—atypically—subordinate to the unfolded fifth in the fourth bar from the end. Scale degree ^2 ( = ^9) is expanded across two bars.

Chambonnieres, Pieces de Clavecin (1670), lines with ^9 = ^2 (1)

So far in this series of posts on the two books of harpsichord suites by Jacques Champion de Chambonnieres, I have discussed two topics: simple rising lines, and longer, usually more complex rising lines. Of the five topical groups total, the third and fourth both focus on scale degree ^2. Today's post is about rising lines that overshoot ^8 then fall back to close. The examples are three courantes from book 1.

Suite 1, first courante. The cadence in the first strain is to III (C major) and involves a rising line -- circled notes. Because E5 is nearby and very plainly defined, the lower line is internal and the motion asymmetrical -- scale degrees mark the descending third line.

Suite 1, double to the courante (the only double in the two books). In the characteristic diminutions of the double, closely tied to the original, nothing is different in the cadence to the first strain.

Suite 2, second courante. Here the internal line is more muddled (^6-^5-^7-^8-^9?) and the local support for ^3 not so stable (inverted triad), but the end result is the same.

Chambonnieres, Pieces de Clavecin (1670), long lines (3)

The last examples for long lines (ascending figures in the cadence that span more than a fourth) come from book 1, suite 3, a sarabande and a gigue.

The opening of the sarabande slowly moves a line up from ^1 to ^3, giving more emphasis to the earlier notes rather than the ^3 that ends the line. Similarly to Book 2, suite 4, second courante, the long ending line here meanders a bit from an uncertain starting point (G4 in bar 18? F4 in bar 19? Perhaps even the eighth note D4 in bar 18, to make the line an octave?). The play of ^7 and ^#7 is also found in D minor/Dorian mode courantes by Elizabeth Jacquet de la Guerre.

By contrast, the sixth line ending the gigue is much simpler and more direct.

Chambonnieres, Pieces de Clavecin (1670), long lines (2)

Two pieces from book 2, suite 6: a gigue and the third of three courantes.

The gigue gives more attention to melody in the left hand than is typical of many dance-movements, including the courantes. This textural play is common in keyboard gigues throughout the seventeenth century. At (a) a clear focal note ^5 and accented notes in line down to ^3, after which at (b) the bass carries the melodic interest, as it does again at (c) and (d). The bass continues through the end of the section while the right hand at (e) brings an uncluttered octave line to the cadence. At (f) is the cadenza perfetta that we might expect where both right and left hands carry melody.

The courante is simpler: ^5 at the outset, repeated (circled notes), clean descent to ^2 by bar 4 (not marked), then a line of the sixth up to the cadence. I haven't remarked on it, but the root position D: I tucked in between the two dominants in bar 7 has occurred several times already, and we will see it again. This one is rhythmically more prominent than most, the result of the courante's characteristic hemiola (switch to 3/2 time) for the penultimate bar.

Chambonnieres, Pieces de Clavecin (1670), simple lines (2)

Two courantes, from the fifth and sixth suites of book 2, respectively, give us additional examples of what I have been calling the simple rising line from ^5 to ^8.

A firmly established focal note ^5 (D5) is presented at the beginning. A line ascends from it at the end, in tight coordination with the bass. Note that the ascent happens twice -- this is one of the only instances in Chambonnieres's two books of the petit reprise, a repetition of the final few bars, usually embellished, that became a standard part of performance practice by the early eighteenth century.

In the courante from suite 6, an ascending octave line begins the piece and an ascent from ^5 ends it. Here again, harmony and line are closely coordinated. The dal segno sign indicates the point to begin the petit reprise.

Chambonnieres, Pieces de Clavecin (1670), long lines

The first group of examples (two previous posts) showed simple rising lines. This second—and much larger—group reveals longer lines, from a sixth to an octave. Most of these are not so easily situated in comprehensive figures as were lines from ^5 to ^8, either because focal notes aren't clear or because the line would need to be divided in some way.

The two books of suites each have one pavane and one galliard, though not paired as was routine at the beginning of the seventeenth century, when the galliard often was written as an elaborate variation of the pavane. This (see score below) is the galliard from book 2, shown in its beginning and ending. Note the long descending octave line in the opening. By now this shouldn't be surprising: recall that, in the first post in this series, I commented on "a characteristic—and very strong—tendency to shape melodic units of 3 to 5 measures or more in entirely or mostly unidirectional lines."

In the B-section, a line ascends from ^3 (as E4) to ^8, then promptly descends again, note by note. The close is still another line, an octave ascent from C4 to C5. Overall, then, C5 is readily heard as the focal note, and it is eventually regained by lines from below.

Another unusual time signature for a sarabande, 6/4 (not the 3/2 signature familiar from eighteenth century sarabandes like those by Handel). This sarabande closes the third suite in book 2. A focal note ^8 (as D5) at the beginning is eventually recovered in the ending of the piece by means of a sixth line that's not quite diatonic (note G#, not G-natural) and where ^8 is gained early (third bar from the end). This "wandering about ^8" is as common in the final cadence as the unidirectional melodic shapes are elsewhere (or, I should say, everywhere).

Book 2, suite 4, second courante: similar to the sarabande above in that an initial focal note—the F5 at the top of an interval frame this time (see boxed notes and circle in the beginning)—is recovered by means of a long line at the end of the piece. Here ^8 truly doesn't arrive till the final tonic, and the beginning of the line is not coordinated with harmony, a fact that suggests we would have to divide it in some way if we were carrying out a detailed, hierarchical linear analysis.

Chambonnieres, Pieces de Clavecin (1670), simple lines (1)

The fifth suite of the first book has two sarabandes; this is the opening of the second one. An emphasis on arpeggio rather than line in the first three bars turns into a pair of linear progressions that would not be out of place a century later: a linear descent from ^5 to ^2, at which point another line ascends through a PAC to V. The one bit not so likely in 1770 is the cadenza perfetta shape at the end: interval sequence 6-8: E3/C#5 to D3/D5.

A courante in suite 1 closes its first strain with a simple rising line over III (circled), but this is clearly subordinate to a stretched-out descending line from E5 (a: ^5 at the beginning, then C: ^3 in bar 5 to ^2 to begin bar 6 and ^1 in bar 7).

This canaris (alt: canarie, a close relative of the gigue) closes the fifth suite. The melodic shapes are similar to the courante above, in that a simple rising line to the cadence is an internal voice, and both ^3 and ^2 are stretched out across the previous measures. The close is now in the tonic key.

Book 1, suite 2: A curious sarabande whose notation is atypical—a mixture of 3/4 and 6/4 (the consistent 3/4 meter of the first example above is much more common until late century)—but whose design is less odd than it looks at first: a small binary form with written out, slightly varied repeats. Section B in its first statement ends with the PAC in bars 21-22. Boxes identify a parallel place in the first statement and the varied repeat. Angled lines show the rising line repeated several times over the course of the section. In every case it is probably another inner line like the ones above, but the presumed focal tone, E5, although certainly clear enough in its registral position, is not at all well-supported harmonically. At x, it must contend with a marked dissonance in the bass; at y, the triad is not in root position. However, if one must have a focal note, I don't see a better alternative.

Chambonnieres, Pieces de Clavecin (1670)

Jacques Champion de Chambonnieres (1601-1672) was the first of the celebrated school of French harpsichordists (claveçinists) in the seventeenth and eighteenth centuries. As a curiosity that pleases me but which is hardly an odd bit of news about someone involved in the French court in that era, Chambonnieres was also an excellent dancer.

Near the end of his life, Chambonnieres published a number of volumes of his compositions. In this series of posts, I will look at pieces from Les Pieces de Clavecin Livre Second (1670), using the edition and notation of Steve Wiberg (Due West Editions, 2008) available on IMSLP: link. Apologies for artifacts introduced in editing the graphics for use here.

The second book consists of six suites, and as it happens there is something of interest to us in every one of them. The posts in the series cover five topics:

Simple lines from ^5 (includes V: ^5-^8 to end first strain)
Long lines (6th or more) from below to ^8
Line from below but where ^9 is clear above
Line up to ^9 to end first strain
Others  

I will augment the demonstration with similar examples (not analyzed) from book 1, which also was published in 1670 and is laid out in the form of five suites (six if you separate out the final three pieces in G major from those in G minor preceding them).

To begin then, here is a simple ascending line from ^5 in the first of three courantes in the second suite of book 2. The line F: ^6-^7-^8 is both clear and simple, but in addition this courante is of interest here because it shows a characteristic—and very strong—tendency to shape melodic units of 3 to 5 measures or more in entirely or mostly unidirectional lines. The line that opens this courante is typical, as is the wave-like motion of the whole: first up in vigorous manner, then down and up again to close.

Additional examples of simple lines to close a section or to end a composition will be found in the next post.

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 8b (Bacquoy-Guedon, LeRoux, Böhm)

Alexis Bacquoy-Guedon published a dance treatise in the 1780s. I have written about his musical examples before, on my dance music blog: link; and also twice on this blog: link, link,

The last of the posts linked to above shows his 4th Menuet in G major, with its trio, which is the item of interest here.

The underlying figure g (simple ascent with ^#6 and i-IV-V-i) is revealed by adding a likely bass below the Urlinie:

I discussed a two-harpsichord gigue and a courante with an added contra partie by Gaspard LeRoux in the continuation post of part 3: link. Here is another piece from the same collection (1705), this time a sarabande with 11 variations. To avoid confusion in case you look at the score yourself, I will follow the numbering Fuller uses, where the sarabande (theme) is called couplet 1, the first variation couplet 2, etc. (The 1705 edition has no labels.)

In one common French design for a published suite, a larger scale piece, usually a chaconne, ends the suite of dances and character pieces. Here the design is almost that: (unmeasured) Prelude, Allemande, Courante, "La Bel-abat," Piece sans titre, Gigue, Sarabande [with variations], Menuet. As elsewhere in the collection, the sarabande itself is provided with an alternative trio arrangement, but the variations are given just a continuo bass. I am uncertain what that signifies for an actual performance option.

The first phrase of the sarabande is reproduced below in Alfred Fuller's edition. I will not cite any more of it in order to respect copyright. In the 1705 edition, however, the left hand part is written in baritone clef (like the bass clef but a third higher), and so I will present the alternate trio version of the theme instead.

The six phrases of the theme are distributed in the common asymmetrical design where A has two and B has the other 4. Section A ends in III, and midway through section B we reach V in a half cadence. What is remarkable is that in the solo version, Le Roux uses the dully repetitive figure of the first treble part in the entire B-section, not the considerably more interesting melody of the second treble part.

Phrases 5 & 6 in couplet 2 (that is, the first variation) are shown below. I have "transposed" the left hand part to the common bass clef. The cadence in the upper register is striking, but from a traditional Schenkerian viewpoint, we have to call the uppermost voice boundary play growing out of two cover tones--see the graph below the score.

Four other couplets use rising lines, three of them at the end, as in couplet 2 above. In couplet 6, almost continuous 16th-note arpeggios in the right hand are all set in the upper octave. In couplets 4 & 10, a clear descending cadence is placed in phrase 5, to which the upper octave in phrase 6 sounds like a coda flourish. The most interesting use of the rising line is the opening, not the end, of couplet 2 -- see below, where phrases 1 & 2 chart the octave from Bb4 to Bb5, step by step. (Note that I have not moved the left hand to bass clef this time.)   Below the score I have marked the sources of all these steps in the trio version of the sarabande theme, demonstrating again Le Roux's quite free attitude toward his theme (these are *not* simple figural variations).

The last example comes from one of the many German composers who imitated French keyboard styles and genres in the 17th and early 18th centuries: Georg Böhm, whose Suite in F minor contains a courante with an ascending Urlinie. Volume 1 of the Sämtliche Werke edition (published in 1952) includes eleven suites, two of them in F minor. This courante is from the second of those suites. Note that it uses the Dorian signature (three flats rather than the four we would expect for F minor).

Here is an analysis showing the background..

Finally, a background/first middleground graph, with the inner voice. I chose to show the bass for i6 with a closed note rather than an open note, but the outline of figure g is still clear.

Minor key series, part 6a (La Guerre)

See background information on Elisabeth Jacquet de La Guerre in this previous post: link.  The suite in D minor (with Dorian signature) from 1687 has two courantes, the first of which is discussed here.

The opening is in some ways a mirror of the opening in the second courante, where a slowly ascending, mostly linear figure coupled F4 to F5. Here a fully linear descent from D5 to F4 occupies the first three measures, but the larger figure is an initial ascent from the opening D5 to the first Urlinie tone, F5, in measure 4 -- marked in the score.

In the final measures, ^3, as F4, is clearly heard again in the typical internal cadence to the opposite mode (at "x"), then an insistently rising pattern starting at "y" leads upward through the octave, but—as in the opening—the larger figure goes the opposite direction as the Urlinie descends in an unequivocal way from ^2 to ^1 in the final two bars. The point of interest is "what might have been" -- at "z" natural ^7 gives way directly to ^#7 over the just established V harmony.

The notation here is from Steve Wiberg's edition, available on IMSLP: link.

Minor key series, part 3 continued

Gaspard Le Roux (1660-1707) was a professional keyboardist working in Paris. His Pieces de Clavessin, published in 1705, is a remarkable volume -- not only is the music in each of the seven suites skilled and aesthetically satisfying but each piece (excepting the preludes) is given in an alternate trio version for treble melodic instrument and continuo (where the treble of the keyboard part is realized). By way of an appendix, he adds a gigue in G major for two harpsichords and a contre partie (second part) that renders four pieces from the earlier suites into duos.

The gigue and the duo version of the courante in the seventh suite in G minor are of interest here. We'll start with the latter; here it is in the sequence of the suite. The solo version is at the top, the trio version at the bottom of the page. Note that a firmly descending melodic line in the cadence in the solo version (at "x") is counterpointed by a more complex and partly ascending line in the trio version (at "y").

Here is the page with the contre partie, which adopts the counterpointing line for its own closing cadence.

And here are two analyses of the ending (the notation is from an edition by Alfred Fuller). The original line (above) and its counterpoint (below) create a striking wedge figure (we will see this again in the gigue, below).

Asterisks show the complexity of treatments of scale degree ^6 (a reminder that the key signature is G minor/once-transposed Dorian). From this, the most plausible Urlinie for the contre partie rises from ^5 using the raised ^6 (E5), but this by no means erases the problem of Eb/E natural. A detailed analysis of the several structural levels would be quite an exercise. 

The Gigue for two harpsichords is much simpler by comparison. Here is the opening. Note the wedge shape approaching the cadence in the second phrase.

Le Roux uses the same figure in the interior cadence to the opposite mode and also in the ending, shown here again as an analysis using the notation of Fuller's edition. Although the rising line is shown as the upper voice, performance options—which are so rich in Le Roux's volume—might place the descending line above if the second harpsichordist takes advantage of the direction "en haut si lon veut" (an octave higher ad lib) [see Pierre's Gouin's edition on IMSLP: link]

For a detailed table of contents to Le Roux's Pieces de Clavessin, go to the bottom of the IMSLP page: link.