Praetorius, Terpsichore, part 8: ns 148, 265

The Praetorius series of posts began more than a week ago. To close it out, here are two numbers—a courante and a ballet—that share ascending cadence gestures but otherwise are not closely related in design.

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.

n265 is a three-strain ballet, also without notated repeats. In effect it is really two strains, as the third is a close variation of the second. See below, where the second and third strains are aligned. The point of interest is in the two cadences, the first of which lies (and is somewhat buried) in the lower register, ending on F4, but the second of which is made very prominent by transposition up the octave, ending on the same F5 that started the strain.

Praetorius, Terpsichore, part 7: ns38, 41, 75, 104, 110, 111

Another selection from the many courantes in Terpsichore. All but one are in two sections. Here the focus is on the second strain where the upper range, usually ^5-^8 in the mode of the final, is reached early and then its top is either maintained to the end or, more likely, the music drops to the lower end of the range, to move upward again in the cadence.

n38: The lower fifth of the Aeolian octave is presented immediately (arrow plus circled E5), then inverted two bars later to the upper fourth E5-A5, within which a clear descent is followed by a quick ascent to the cadence. Note, incidentally, that the courantes do use hemiolas but only very rarely have suspension dissonances in the cadence, in keeping with the simplicity and directness (and perhaps the rapid tempo) of the popular dance these musics served.

n41: Once A5 is reached in the cadence of the first strain, it is held throughout the abbreviated second strain (only 6 bars, as shown, or more in the manner of a coda or refrain than a separate strain).

n75: The registral patterning of the melody in the second strain is analyzed below. The score is given under that for reference. At (a), a full triad outline (upper bracket) that persists (lower bracket), then at (b) an abrupt shift upward to D5-A5; at (c) a slight settling back to C5-G5, or as it goes on, really D5-G5, which is filled with a line (at c2) to reach the cadence.


(score for n75)

n104: 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.

n110: A courante with just one strain. The pattern is similar to that in n75: a triad outline to start, an abrupt transposition of the framing interval, and a cadence. Here the initial triad is also G major, and the second is D major but lower (fourth octave) not higher as in n75; the cadence is to D rather than G, and the ascending line is clear and direct.

n111: The first strain has features very similar to those of n110, but the space A4-D5 is emphasized almost immediately, and it is the D major triad that is elaborated by bars 2-3. The ascent to the cadence is only marginally longer (3 bars rather than 2 1/2) but is full of diminutions.

In the second strain the D major triad frame is even more obvious (box), and there is a descent/ascent linear pair leading to the cadence. (The opening on G and close on D reflects a pattern that is not uncommon in the Mixolydian mode, the mode with a G final that is here transposed to D, requiring the one-sharp signature.)

Praetorius, Terpsichore, part 6: ns 35, 76, 147, 161, 162

This post picks up on several earlier ones to offer additional examples of strong linear motion across the last phrase of a strain or the entire section. These are all courantes, three with melodies by Praetorius, the other two "incerti."

n35: the first of the more than 160 courantes in Terpsichore is in two sections. In the second strain the range C5-G5 is established firmly (a), G5 held, then at (b) a partial descent, and the pattern is repeated from (c) through (e), at which point the range C5-C5 is covered yet again and expanded by one for the cadence on A. (It's not marked, but note the 6-8 cadenza perfetta in the cantus and tenor (middle voice).)

n76: this is the first strain of three. A strong contrast of arpeggio and descent through the octave (first bracket) with a long plodding line back up through that octave (second bracket and beamed line) to a cadence on G5.

n147: 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.

n161: another melody of uncertain authorship. In two sections, where the second has unusual imbricated rising and falling lines, the former shown in the box, the latter in the beamed line.

n162: by Praetorius, in two sections. The second is 10 bars long, and another very deliberate linear ascent to the final takes six of those bars.

Praetorius, Terpsichore, part 5: ns 92-96

Here are five courantes. They are consecutive in Terpsichore and are also closely related to each other by certain features (Praetorius tries to group similar dances when he can). Like the majority of the many courantes, these are in two sections (others are in three sections, like the galliards we've examined in previous posts).

In this group the focus on the fifth range C5-G5 in the first strain is of interest, with a rise toward a cadence on G5 (a pattern we've also seen in some galliards recently).  Note also that these courantes show the typical treatment of the 6-8 cadenza perfetta between the upper and middle voice ("tenor") in five-part writing.

n92:

n93:

n94:

n95:

n96:

Praetorius, Terpsichore, part 4: ns 295, 304

Yesterday we saw a strongly directional, step-wise figure running across almost all of the second strain in n308. Here are two more galliards with similar figures of differing lengths.

In n295, 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.

In n304 (by Praetorius himself), rising figures fill out intervals fairly quickly (C5-G5 in the first strain) or more slowly (the same interval in the second strain; a descent from G5 in the third strain). The three cadences are nearly identical, moving stepwise to the final/tonic (angled line in bar 6 of each strain), then "trilling" about it with eighth-note diminutions (bar 7). I've marked the voice exchanges to confirm that the notes on the beat in the cantus are the ground notes of the melody and the other eighth notes are the diminutions.

Praetorius, Terpsichore, part 3: n308

A galliard in three strains, n308. In the first strain, the register crowned by G5 is established immediately (circled), moves down through an octave (bar 4), then is recovered in its upper fifth (C5-G5) to close (circled).

The second strain covers the same ground in reverse, although in a very different manner: the lower fourth is touched immediately (first bar), then abandoned for the upper fifth (C5-G5), which Praetorius moves within (bracket) and through (beamed line) for the remainder of the strain. The cadence is at the top of the register. Note that the alto voice doesn't realize the cadenza perfetta (it would have gone to G4, not B4): in four-part writing there is a strong bias toward ending with a complete triad, even if this means abandoning the proper cadence (the first strain shows the other option—an incomplete triad—which is much less common but does allow for the 6-8 motion). In five-part writing, on the other hand, one can always realize the 6-8 (or, very rarely in Terpsichore, the 3-1).

The third strain (not shown here), incidentally, covers the same fifth to begin, then wanders about the octave more freely before ending on C5.

Praetorius, Terpsichore, part 2: n50

The courant (courante, corraunt, etc.) in Praetorius's time was closely related to the jig or gigue, and therefore quite different from the later, much subtler and slower French court dance (spelled courante) that also became a staple of late Baroque dance suites. The relationship can be seen in the opening of n50, with its firm triple meter, dotted rhythms, and (atypical) arpeggio figures—these latter are bracketed.

In Terpsichore, the many courants are in either two or three strains. In n50, the openings of the second and third strains pick up one or the other of the opening motives, making for a nicely compact melodic design (it should be noted, though, that this is one of the melodies Praetorius marks as "incerti").

The point of interest is the ending of the first strain. A straightforward cadential move from ^6 through ^7 to ^8 can cause problems in the voice leading if the bass simply moves, as here, from IV to V to I. Praetorius solves the problem with diminutions that create "inserted" intervals between the bass and a potentially offending voice: 8 between two 5s at (a), and 10 between two 8s at (b). His method was standard in polyphony of all sorts (including improvised) in the sixteenth century.

I have published a new PDF essay on the Texas Scholar Works platform. The title is "Scale Degree ^6 in the 19th Century: Ländler and Waltzes from Schubert to Herbert." And here is the abstract:

Jeremy Day-O’Connell identifies three treatments of scale degree 6 in the major key through the nineteenth century: (1) classical ^6; (2) pastoral ^6; and (3) non-classical ^6. This essay makes further distinctions within these categories and documents them in the Ländler repertoire (roughly 1800-1850; especially Schubert) and in the waltz repertoire after 1850 (primarily the Strauss family). The final case study uses this information to explain some unusual dissonances in an operetta overture by Victor Herbert.

Other composers include Michael Pamer, Josef Lanner, Theodor Lachner, Czerny, Brahms, Fauré, and Debussy.

My publication page on Texas Scholar Works is: Neumeyer.

Praetorius Terpsichore, part 1: ns 283-285

This is the first post in a series. The enterprising and prolific Michael Praetorius published a volume of more than 300 dances in 1612. These included 22 bransles, 163 courantes, 48 voltas, 43 ballets, 30 passamezzos and galliards (some but not all of them paired), and 12 other dances. All are set in 4 or 5 voices and, as Praetorius notes in his subtitle, are appropriate for performance in social situations. He is also generous in giving credit to French dance master Francisque Caroubel, whose melodies (mainly the bransles) Praetorius sets. Still the majority are Praetorius's own melodies, with a relatively small number labeled unknown (incerti).

Roughly 10% of the pieces have rising cadence gestures in one of their strains, more often the last than the first or an interior one. Here are three samples of interior strains to begin.

Among the galliards (a fast triple dance with only occasional play between rhythms in 3/2 and 6/4), n285 is typical in having three strains. The opening of the piece is shown below, along with all of the second strain, where the register of G5 is established immediately, the range of the melody being from there down the sixth to B4. The simplicity of the approach and the clarity of the cadence figure itself are characteristic.

In n284, the second strain initially stretches the register to an octave, starting from below, on G4 (line), but stays in the upper half once G5 is reached. In this case, each cadence note receives a consonant chord as harmonization. As point of information, like n285, the cadences in the first and third strains are on C.

One of the rare densely imitative settings in Terpsichore, the second strain of n283 (a passamezzo) uses the same figures and registers as the two galliards above but in a more varied and florid manner. Note the deliberate stepwise motion upward in the cadence, with diminutions of scale degree ^6 (assuming here a Mixolydian octave).

(Comment: The two galliards, ns284-285, are derived from this passamezzo, though in a freer manner than would be suggested if we called them variations (note that the second strain of n284 is much closer to n283 than is the second galliard, n285). This method of variation/adaptation is commonplace in the 16th and early 17th centuries.)

On the "March" Prelude in Chopin's Opus 28, part 2

In part 1, I cited Carl Schachter's recent analysis of this Prelude, with its Urlinie from ^3, where ^2 had to be "supplied by the imagination of the listener" (61). I also indicated my priority in this reading of the background, having written about it twice in 1987.

In February, Emily Ahrens Yates presented a paper titled "Surface Motives in Tonal Music and Their Influence on Our Readings of Background Structures" at the TSMT conference in Belton, TX. In the well-established tradition of motive-driven Schenkerian readings, she "show[s] how ascending surface motives of 5̂ to 8̂ are composed out, are evident in the middleground and foreground levels, and are replications of an ascending Urlinie background structure resolving the conflict in readings between motivic parallelisms of rising motives and 'Ursatz parallelisms'" (from the abstract).

Emily shared her analysis with me beforehand. It was entirely convincing, and I now wonder why anyone (including me, you understand) would ever have proposed a background descent from ^3 at all: each of the march's three phrases is wholly occupied with rising stepwise gestures (and the subsequent relaxation from them), the "one-leap-too-far" quality of the Ab 6/4 chord in bar 8 is certainly accentuated/confirmed by its unstable status as a harmony, and the one truly remarkable thing in this musical context is the ending, which is the only one of the three phrases that refuses to drop away from its rising line from ^5 to ^8 (awkwardly chromatic though it is).

Additional comment: "each of the march's three phrases is wholly occupied with rising stepwise gestures (and the subsequent relaxation from them)": note that each rising phase is longer and each relaxation phase is shorter than the last. In the first phrase, ten rising beats are followed by six falling ones (numbers depend on where you place the three beats of E4). In the second phrase, twelve rising beats are countered by four falling beats. And of course in the third phrase, sixteen rising beats are not countered at all. What surely emerges as thematic in this march, then, is the withering away of descent, regardless of the dramatic surge into bar 8.

More than that is the Sisyphian struggle against a chromatic weight that bears down the already heavy diatonic chords in the second and third phrases. I have boxed those passages in the score below:

It is not difficult to "reconstruct" the diatonic version of all this, the state of the march "before" its chromatic deformation, its suppression by a half-step. (The notion of lowering to flat keys as expressive is something we've seen in Schubert, who dropped the "violin keys" of D and A to Db and Ab in his waltzes.) Here is the diatonic bass for the two chromatic passages.

What is truly remarkable -- and dramatic -- then is not the "one-leap-too-far" Ab6/4 chord, but the sudden emergence of the diatonic from the chromatic depths. The staircase down to those depths is also the way back up:

An entire slow movement of a heroic sonata is sketched in this miniature—an invitation perhaps to a skilful improvising pianist to fill it out.

On the "March" Prelude in Chopin's Opus 28

The steadily rising scale figures in each of the three phrases of Chopin's E-major Prelude are emphatic and obvious (so is the sudden drop at the end of the second phrase). In a recently published book The Art of Tonal Analysis: Twelve Lessons in Schenkerian Theory (Oxford University Press, 2016; edited as a labor of love, I suspect, by Joseph Straus), Carl Schachter says that "some people analyze this piece with an Urlinie that rises a fourth: B-C#-D#-E. I think, however, that it is quite possible to hear instead a very subtle and wonderful descending Urlinie, but to do so one has to be quite un-literal in one's use of the theory" (56). [You can read the chapter on two preludes in the Google Books preview window.]

Here is his Example 3.10, which shows the middleground and background shapes of the upper voice:

For the record, I was the first to assert the abstract pitch design by which a primary line descends from ^3 (while a secondary line rises from the lower ^5). I did this in a footnote to a well-known article, "The Ascending Urlinie" (Journal of Music Theory 31/2 (1987); in fn28: "Pieces which appear to use a rising line from ^5 but in fact do not include Chopin, Prelude in E Major, op. 28, no. 9; [instead it is] a three-part Ursatz with line from ^3 above; ^2 implied in the cadence."

In another article published the same year, I provided a graph: from "The Three-Part Ursatz," In Theory Only 10/1-2: 28.

This gives less emphasis to the arpeggios, but my point was to place attention on the inversion of the third G#-B to the sixth B-G#, in line with middleground transformations that I identify in the article. Here is a schematic version of the example below showing this:

Finally, here is a link to a facsimile of my sketch from 1982: holograph sketch of Op28n9.

16th century cadences, part 8: Vecchi, duet n22

Continuing the census of cadences in the duets of Orazio Vecchi, I look at the twenty-second (btw, there are 38 duets in all). Here are 12 cadences, including a closing cadence with a rising line to ^8 (G5 in the Mixolydian mode). I admit, however, to having relaxed my rules (see part 7, yesterday's post) and counted an evaded cadence (n6) and both cadences in a cadence pair (ns 7 & 8). Without those, there are 10 cadences, six of which are 6-8 and four are 3-1.

I suspect the slight bias toward 6-8 in the two duets by Vecchi would be erased in bicinia where the two voices are in the same range. I may take up that question at another time, once I find a suitable repertory. (Lassus's duets aren't good for this work because he emphasizes very long phrases, so that even the lengthy un-texted duets have no more than 2 or 3 cadences.)

16th century cadences, part 7: Vecchi, duet n21

In the same year as Gastoldi, Orazio Vecchi published his own book of instructional duets. I have chosen two of them for the sake of a census of cadence types: n21 in today's post, n22 in tomorrow's. Granted, these pieces are somewhat arbitrary constructions, but I suspect that the numbers in "proper" compositions will be similar.

I tried to focus on clearly articulating phrase-ending cadences. I did not include evaded cadences or brief cadence-like figures that are obviously within longer phrases. On those terms, the duet has 11 cadences, six of which are 6-8, and five are 3-1. Cadence types are distributed more or less evenly throughout. Of particular interest is that every one of the 6-8 cadences is different, something obviously useful for pedagogical illustration.

16th century cadences, part 6: Gastoldi, n12

Following up on yesterday's post about wedge shapes in cadences, here are opposing cadence figures, both for 6-8. The two cadences are at beginning and end of the piece. In the first case, motion is down in both voices and is especially pronounced in the tenor. In the second case, a stream of parallel motion is interrupted in the final few beats as the tenor reaches a high note, E4, and then descends firmly by step.

16th century cadences, part 5: Gastoldi, bicinium n3

Twenty years after the publication of Lassus' two set of duets, Giovanni Gastoldi published his first book of music for two voices. Like most pieces in the category of bicinia, these were most likely intended primarily for instructional purposes, rather than for performance. (The importance of the repertoire of didactic pieces is recognized and provides the pedagogical foundation for Peter Schubert's excellent textbook Modal Counterpoint, Renaissance Style (Oxford 2007, second edition).)

Among the internal cadences in the third duet are a pair that neatly illustrate my point today. In two of the three pieces by Lassus (from parts 2-4 in this series of posts), the voices largely approached the cadence in the same direction—up, of course, since I was bringing out the historically significant idea of rising cadence gestures.

Contrary motion is entirely possible, too: in the cadence pair below, the 3-1 is approached in a closing wedge, 6-8 in one that opens. Both express broadly basic motion in each of the cadences: 3 closing into 1, 6 opening out to 8.

It is important to note, however, that there is in fact no necessary directional bias in either of the two cadence types, 3-1 and 6-8. Subsequent posts will attempt to make that clear.

16th century cadences, part 4: Lassus, bicinia with text n14

Another texted duet borrows from the Magnificat. "Fecit potentiam . . ." is in KJV "He hath shewed strength with his arm; he hath scattered the proud in the imagination of their hearts" Luke 1:51. Here a short first phrase ("Fecit potentiam") is without cadence, but the second is very clear (for "in brachio suo"), involving three thirds and two 2-3 bass suspensions.

The conclusion again is the point of interest, however: now familiar rising gestures in connection with a 6-8 cadenza perfetta, but note that the approach in the upper voice is repeated, a less likely option than a more varied, but still mainly stepwise figure.

16th century cadences, part 3: Lassus, bicinia with text n15

The last of the texted bicinia uses the same text as n6. Here again I have shown beginning and ending only, and here again the opening phrase is quite long and without cadence in my excerpt (probably this does have something to do with text painting, since the text is about "filling the poor with plenty"; KJV: "He hath filled the hungry with good things"). And here again the focus of my interest is the ending, which offers a more elaborately embellished cadence than did n6, along with even more emphatic rising gestures.

16th century cadences, part 2: Lassus, bicinia with text n6

This and several subsequent posts provide examples of cadences in 16th century bicinia, or pieces in two voices. The object is to discuss features and treatments of the two versions of the clausula vera (also known as the cadenza perfetta), intervals 3-1 and 6-8. An introductory post is here: link.

Lassus published two sets of bicinia in 1577. The first set of fifteen of these are texted, another with twelve are not. Among the texted duets, numbers 6 and 15 use the same text, "Esurientes implevit. . ." [KJV: "He hath filled the hungry with good things; and the rich he hath sent empty away," Luke 1:53; from the Magnificat]. I am not an expert in 16th century text painting and will not comment on that element. Which is another way of saying that I don't see anything obvious in the particular choices of figures or cadence types.

The opening and closing measures are in the example below. The points of interest here are that Lassus is not afraid to use the 6-8 cadence to close (that is, he shows no prejudice in favor of 3-1), and the overall gesture in the upper voice is rising.

Counterpoint and the rising cadence gesture

As we saw in yesterday's post, 16th century cadences with interval pairs 3-1 or 6-8, could be the ground or motivation for a rising melodic gesture, but the odds were against it, mainly because of suspension figures that provided additional downward momentum into the cadence.

In the abstract counterpoint exercises that were derived from 16th century music, the potential for rising cadential figures was, ironically perhaps, much greater than it had been in the actual repertoires those exercises were trying to model. There were two reasons for this: (1) the separation of figures into "species" served to isolate suspensions into a single type of exercise; (2) in two-voice instruction, it was routine to write one exercise with the ground or cantus above, then another with the ground below, a situation that guaranteed trading off the 3-1 and 6-8 cadences.

Beethoven studied strict counterpoint with Johann Albrechtsberger while Haydn was away in London. And it is here that the potential of a rising melodic gesture in counterpoint exercises came to fruition in music. Beethoven was apparently one of the first dance composers to make direct use of a rising cadence (but see below for a precedent from Mozart). Beethoven's 12 Deutsche Tänze, WoO8, were composed only three months after he finished his counterpoint studies with Albrechtsberger, but the first dance in the set follows an unexpected trajectory. It begins with a stepwise ascent from ^1 to ^3, elaborated and harmonized with an 8-10-10 voice-leading figure with the bass—this is one of the conventional figures of the partimento tradition. The second strain leads the melody in a determined way upward to ^8. The first dance in a set such as this one—like the menuets in WoO7, these waltzes were for a public ball—was often used as a refrain, so that Beethoven would have had incentive to make it memorable.

As it happens, Mozart had anticipated Beethoven by twenty years. His set of 12 menuets, K 176, opens with a similar promenade/refrain, and it uses virtually the same opening and closing figures.

On the clausula vera (3-1 or 6-8)

The articulation of cadences in sixteenth-century European music relied on the formula of third to unison intervals (if the parts are flipped, then it's sixth to octave). In each example just the beginning of a phrase in two voices is shown, followed by the cadence.

Here is an example from literally thousands of pieces showing the treatment of these figures. This is the fifth of Thomas Morley's Duets for Two Viols. In the opening phrase (mm. 1-5), a sixth (marked in m. 4) "prepares" a suspension dissonance that resolves into the 6 of the cadence: asterisks mark the 6-8. In the second phrase, similarly, a third D-F "prepares" a 2-3 bass suspension and the cadential 3-1 follows (note that the lower notated voice is actually higher in pitch at this point).

And here are the final two phrases, in which the cadence types are reversed: 3-1 first, then 6-8. Again note that the second cadence has the lower notated voice higher in pitch. Indeed, it is one of the uncommon instances of a rising cadential figure in notated ("art") music in the centuries before 1800.

Far more common in the sixteenth and early seventeenth centuries is to bring a string of parallel sixths down, often with suspensions, toward the 6-8. The example below is from the fifth of the texted bicinia (sometimes called "duets") of Lassus. Four sixth intervals in a row, three with suspensions, make for an inexorable drop to the cadence, and it is only the sudden turn to the final octave that stops the progression (and is a big part of the expressive and formal point).