Friedrich Erhardt Niedt’s (1674-1708) Die Musicalische Handleitung, written during the early years of the eighteenth century, appears in three parts.[1] The first was published in 1706 and again in 1710. The second part also dates from that year, followed by a second edition edited with extensive commentary by Johann Mattheson in 1721. The third and final part appeared only posthumously in 1717 and was, too, edited by Mattheson. In 1708 Niedt wrote a small work entitled Musicalisches A B C zum Nutzen der Lehr- und Lernenden that included the requisite material that must be learned prior to commencing with Die Musicalische Handleitung such as reading the staff, the values of notes, meter, and so on.[2]

Niedt’s treatise has attained notoriety for at least two reasons. First, as a work that begins with the fundamentals of playing the thoroughbass at the keyboard and then applies these principles to musical composition, it remains as the most complete written account of how thoroughbass and composition are related, the latter based upon the former. Second, the method of teaching composition via the thoroughbass was endorsed by no less than J. S. Bach, whose own Vorschriften und Grundsätze zum vierstimmigen spielen des General-Bass oder Accompangnement of 1738 is said to be based upon Niedt’s opening chapters.[3] It is of course unlikely that Niedt himself was Bach’s source for this approach to pedagogy, Niedt having probably learned the Bach family techniques from organist and composer Johann Nicolaus Bach, Sebastian’s cousin, while a student at the University in Jena. Pamela Poulin, both Niedt and Bach’s translator, suggests that Bach may have valued Niedt’s work for the attention it gives the beginner in progressing from thoroughbass to composition and adds that Niedt’s treatise was apparently popular in its day due to the large number of extant copies. It was also, Poulin notes, one of the only thoroughbass manuals from the early eighteenth century to have appeared in German. [4]

The present essay will have occasion to draw on this work from time to time. The main concern, however, is Niedt’s treatise, and we will proceed with an overview of the work while contextualizing some of its features. Certain passages whose meaning is not immediately apparent will be discussed with respect to some of Poulin’s more problematic explanations and interpretations.

The first part establishes the fundamentals of thorough-bass playing before applying different techniques of variation to them. Niedt begins, however, with a parable where the wanderer, who is also telling the story, enters the company of a group of musicians who have gathered to play, quaff and discuss musical matters. The entertaining tale settles on Tacitus’s account of his musical experiences, given at the request of Florimon, the group’s leader. The content of Tacitus’s narrative is in fact an autobiographical account of Niedt’s own real-world musical experience and gives impetus to the project as a whole. A pleasure to read, it is also revealing of the concerns facing practical musicians in Germany at the time. At issue, and indeed the reason Tacitus’s story was solicited in the first place, was the polemic surrounding the demands of contemporaneous music vis-à-vis the older German Tabalatur and the General-Bass, or thorough-bass. Tacitus tells first of his strict master who taught the Tabalatur, a clunky system of notation and a pedagogy that relied heavily on either memorizing or playing familiar pieces from notation. Its flaw was that the method hindered excellence in extemporization as well as composition, creating what Niedt calls, “paper organists.”[5] Tacitus tells of his graduation from the old Master and acquiring of a job as an organist in a nearby town. After enduring public embarrassment when it is revealed that he cannot read the thorough-bass, Tacitus sought the tutelage of a renowned master who could alleviate this.[6] Seven years with the Tabalatur could not approach even one year of lessons in the thoroughbass, thus the power of the newer method.

The treatise proper begins with an account of the word Bassus and the difference between a basso continuo as such and the General-Bass, where the right hand of the Clavier is involved with bringing harmony to a bass.[7] Since playing the thorough-bass involves both consonances and dissonances, Niedt sets out to explain the consonances and dissonances themselves. Perfect consonances cannot be altered and are the perfect fifth and octave, and although Niedt takes note of the fact that the perfect fourth is usually counted among these, he does not pursue this on the count that this is a work for beginners. Additional consonances, “sound well together with the fundamental voice” and they are both thirds and both sixths, the imperfect consonances.[8] The perfect dissonances of the fourth, false fifth and eleventh, are so categorized because they “originate from perfect consonances.”[9] That the fourth derives from the fifth on the grounds that it sits atop the fifth within an octave seems clear. Less clear, however, is Niedt’s claim that the false fifth derives from the octave (perhaps because it bisects this interval) and that the eleventh is derived from the fifth. The augmented fourth is not mentioned. Functional notions, they lack serious theoretical scrutiny. In addition, Niedt stipulates further that it is possible to have consecutive thirds and fourths together (i.e., parallel 6/3 chords) and even two false fifths. Niedt’s remark that an eleventh is a prepared fourth seems sensible, although he does not explicitly distinguish in this instance between an eleventh or fourth as a suspension and any fourth found in the upper voices of a thoroughbass realization, such as, for instance, the fourth between a sixth and a third in a 6/3 chord. The imperfect dissonances are the second (which is not prepared), seventh and ninth (which are), and are derived most often from the imperfect consonances. Again, Niedt is not explicit and Poulin does not comment on this, but he seems to be intimating their origin as suspended intervals that resolve into imperfect consonances, but this is not entirely clear with respect to the ninth. Niedt adds the condition that, unlike the perfect dissonances, they cannot be used consecutively.

Following chapter on clefs and meters, Niedt introduces the harmonic triad, or Trias Harmonica. He defines this entity as, “a coupling [Zusammenkoppelung] of the third and the fifth when these are added to a fundamental tone.”[10] He also enlists the terms Radix omnis harmoniae and Radix unitrisona, the latter circumscribing the third and fifth into a single structure, “so that one in three and three in one are miraculously joined together here.”[11] Additionally, triads can be simplex, aucta (increased) or diffusa. All of these terms originate in the work of Lippius, writing 100 years earlier, and his tradition. Absent, however, are any of his speculative efforts or indeed any of his concepts of what we would call inversion.[12]

Niedt then gives a small set of general rules to assist in playing the thorough-bass. The first rule states that the written thorough-bass is to be played in the left hand with the voices indicated by the figures played in the right hand. In a footnote, Poulin states that Bach changes the rule to say that the left hand, “may play, together with the right hand, the other voices as well.”[13] This explanation is not found in Bach’s restatement of the rule in Precepts and Principles, which appears virtually unaltered. If Bach did formulate a rule on the participation of the left hand with playing the figures, Poulin does not tell us where he has done it. Adding further confusion to what is essentially a trivial matter, Poulin, in her commentary on Bach, points to two contrasting views of this rule she finds in the text. The allegedly contrasting formulation states that

The thorough-bass is the most perfect foundation of music. It is played with both hands on a keyboard instrument in such a way that the left hand plays the written notes, while the right hand strikes consonances and dissonances.[14]

The difference between playing the figures and striking consonances and dissonances is so slight that it is difficult to see what the point of the cross-reference actually is.

Further rules deal with appropriate registers and another states that the third is taken with the figures, except where a 2 or a 4 is indicated. After giving the standard rule of thumb that parallel perfect consonances can be avoided when the hands move in contrary motion, another rule follows dealing with the avoidance of these intervals. Rule 7 reads:

Zwo Quinten und zwo Octaven zu vermeiden / ist diss der beste Vortheil dass man die Sexte mit zu Hülffe nimmt / und damit umwechselung hält.[15]

Poulin translates this as, “In order to avoid two fifths and two octaves, the best choice is to get help from the sixth and thus obtain a rearrangement [of tones].”[16] Her decision to translate umwechselung as “rearrangement” is influenced by her interpretation of the rule, which, she claims, suggests “that one of the two chords in root position be arranged into first inversion.”[17] It is likely that this rule covers situations where an unfigured bass (i.e., a 5/3 chord) occurs on two consecutive pitches bass notes, where consecutive octaves and fifths would necessarily arise. It is certainly true that inverting one of the chords would avoid the error, but this presupposes quite a drastic fix, all the more so considering an understanding of chordal inversion as such is nowhere to be found in the treatise.

F. T. Arnold translates umwechselung as “alternation,” something much closer to the word’s ordinary meaning, “exchange,” and a much more sensible choice here. Such an interpretation suggests the insertion of a sixth prior to the second 5/3 chord, thereby creating a third chord. This is a sensible reading, although Arnold over-thinks the issue by assuming that the interposed chord might also contain a fifth (i.e., making an interposed 6/5 chord), something not at all implied by Niedt’s rule. Example 1 shows another scenario posed by Arnold where the bass moves down by step. It is true that the F does not resolve properly—Arnold’s reason for rejecting the example—but it is not clear that Niedt himself would object to such a voice-leading.[18] Moreover, Arnold also suggests that the rule is to do with composition, which seems implausible, as the rules so far have dealt only with the most rudimentary aspects of playing the thorough-bass at the keyboard.

It is interesting to note that Bach also gives this rule nearly verbatim. In Poulin’s translation:

In order to avoid two [consecutive] fifths and octaves, the [Niedt: ‘best’] choice is to get help from the sixth and thus obtain a rearrangement [umwechselung] [of tones].[19]

Poulin again chooses “rearrangement” in her translation but offers a contrasting explanation of the rule, mentioning (but not citing), one of Mattheson’s footnotes, where he writes:

The chord in which the sixth or the third is doubled is called by the French la petite Sixte, the little sixth. I call it the pure sixth and consider it only a helper in an emergency, where two octaves or two fifths would spoil the music. The best advice here is alternation [umwechselung], especially since two in a row of this petite Sixte may not be written either, because [parallel] fifths and octaves would unfailingly result.[20]

While some of Mattheson’s wording suggests an affinity for the situation under consideration (namely, two consecutive 5/3 chords implied by an unfigured bass), its actual context is completely different. Mattheson’s footnote pertains to Niedt’s advisory that the octave be only rarely included in 6/3 chords and that the sixth or third be taken instead when using four voices. According to Mattheson, the alternation in question would occur between 6/3/6 or 3/6/3 chords in four voices, as consecutive iterations of either figure would indeed, as he says, “unfailingly” result in parallel perfect consonances.[21] Owing to the different contexts of Niedt’s rule of thumb and Mattheson’s explanation of doublings in parallel 6/3 chords, Mattheson’s remarks cannot be invoked as an explanation. One could probably conclude on the basis of all this that 5-6-5-6 figuring is what is implied.[22]

The following chapter deals with how one is to treat an unfigured bass, each note of which requires the fifth to be taken with the third. Although Niedt does not, in the remainder of the treatise, deal encyclopedically in the manner of Heinichen with playing triads with each chord tone (in Niedt’s language, the discant, alto and tenor) in the upper-most voice, he does stress that unfigured basses ought to be practiced in this manner and gives the same passage re-voiced accordingly. This principle is applied to the avoidance of parallel fifths and octaves, where an alternate voicing can evade this situation. In addition, Niedt has already planted the seed for techniques of variation when he suggests that the right hand and left hand be played in patterned arpeggios.[23]

Chapters VIII and IX are the exposition proper of how to play most of the common figures. It is not preceded by a table of figures, as in Bach and elsewhere, but the order of presentation does reflect the general convention of such works, namely where 5/3 and 6/3 chords appear first, followed by dissonances increasing from “2.”[24] Each point is introduced as a rule and Niedt begins with chords of the sixth, with which the third is always taken. Additionally, Niedt adds that the octave (i.e. root) is not to be doubled and his example (Rule 2, Chapter VIII) bears this out. It is important to note that Niedt does not explicitly differentiate the chord D© F B as “V6” of E minor from a C E A chord, or “ii6” in G, the way we would, although his initial rule does stipulate that bass notes with accidentals are not to be doubled in the thorough-bass. The doubling rule in this instance thus serves as a warning not to double the leading-tone, although it is by no means theorized as such. If anything, his rule is as much about playing 6/3 chords in three-voices, thus limiting the possible parallel issues for beginning thorough-bass players.[25]

After giving two more rules dealing with accidentals and alterations in the figures, Niedt, remaining on the subject of accidentals, states that where B¨/A, E/F and B/C stand adjacent one another, that the sixth is taken above A, B and E whether indicated or not. This seems a sensible corollary to the rule on not doubling sharpened or flattened notes in the bass—theorized by us and presumably intuited by Niedt as a rule against doubling the leading tone—but may in fact reflect quite an anachronism in the treatise. The semi-tones that Niedt identifies are, or course, the three specific semi-tones found in the hard, soft and natural Guidonian hexachords. Similar rules have been articulated by may other thorough-bass writers in one form or another, either functioning primarily as a way of indicating that the third scale step takes what we could call a I6 chord or as a warning against doubling a leading tone. Lorenzo Penna, for instance, has a rule stating:

Each note of the bass is accompanied by thirds and fifths or their compounds except for mi [the lower note of a semitone], which ordinarily uses thirds and sixths or their compounds.[26]

This may reflect an anachronistic aspect of Niedt’s pedagogy and certainly sits curiously in a treatise that accepts key signatures up to five sharps and flats. There is no tonality as such in Niedt, and we ought not to judge him for it, but it perhaps a trifle surprising to see him relying on such a rule to convey this idea when a good deal more was clearly as his disposal.

A rule on Cadenz-Clausuln introduces a host of new figures without fanfare. Such cadential patterns include sevenths, 4-3 suspensions, 6/4s and even 7-6-5 passing tones. They are apparently to be memorized and encoded into the hands for the purposes of this context, namely ends of phrases. He does at a nota bene where he introduces preparation, described by Niedt here and throughout the remainder of the treatise as Liegen oder Zuvorliegen, that is, lying or lying before in the hand. The following rule deals with running notes in the bass and dictates, essentially, that the appropriate figure need only be taken at the level of the half note. This directly connects to the variations of a thorough-bass to come in Part II. Parallel thirds (tenths) can be added.[27]

The ninth rule of Chapter XIII explains 5/4-3 and 5/4-# with respect to preparation and the tenth says that 6/4/2 and 4/2 are struck without preparation, although he will add later in Part III that the bass has in fact been held over. Rules dealing with figures 6/5 and 5-6 come next, a pairing apparently based on figures alone and not at all how we would consider them harmonically. In the case of the former, Niedt acts in accordance with our normative conception of preparing the “chordal seventh,” indicating that the fifth (Niedt discusses only the false fifth) must always be prepared. In the latter, Niedt says the fifth may be prepared when the bass ascends, but need not when the bass descends.[28] The final rule of the chapter simply states that the sixth is taken with the false fifth whether indicated or not.[29]

Chapter IX deals with dissonances of greater figures, namely sevenths, ninths and elevenths. Sevenths are prepared when the figure 7 stands a lone, to which the third is always added and the fifth where appropriate. The 7-6 suspension follows, again according to figures alone and not modern harmonic theory. The case of 7/5/3 is interesting and it is one we will have more to say about later. For the time being, Niedt calls it an “ordinary chord” [gemeiner Schlag], as he had described the 6/4/2 chord, by which me most likely meant that they required no preparation due to their status as “ordinary.” For Niedt, the seventh in this figure need not be prepared and his example indeed shows what we would call dominant seventh chords with the chordal seventh appearing unprepared. Perhaps more strangely, none of the sevenths resolve downward, a peculiar feature given Niedt’s usual—if unstated—sensitivity to what we would call chordal sevenths.

The figure 7/5/4-3 features the prepared fourth and the fifth and third accompany the prepared tone. Figures 11/9-10/8 and 7/5 are treated in the expected manner. With regard to 7/5, it is interesting that Niedt clearly differentiates between 7, 7/5/3 and 7/5 as different sounds that are treated accordingly; 7 appears mostly with 3 only, 7/5/3 all at once does not require preparation and 7/5 in three voices requires that both the seventh and fifth be prepared. On the other hand, Niedt’s example for 7/5 chords includes a four-voice 7/5 chord with an added third, a IV7 chord, where the sevenths and fifth are prepared. Niedt’s view on the difference between a “subdominant” 7/5/3 and a “dominant” version are, of course, left unstated but he will return 7/5/3 chords in Part II, which, together with Mattheson’s commentary, provides a modicum of additional context.

A short chapter on two- and three-voiced fugues and the role that figures play follows. His point is that sometimes tenor or alto lines can be the lowest and that in these cases the figures refer to these “higher basses.” Even the link between thorough-bass and fugue has a distinctly Bachian ring to it.[30]

Like Heinichen 5 years later, Niedt addresses the issue of how to modulate whilst improvising, allowing one to slip back to the main key “skilfully and yet imperceptibly” so as not to “offend the ears of the listeners.”[31] Niedt’s discussion lacks the polemical dimension of Heinichen, who, in his later treatise, was at pains to justify the full palette of 24 major and minor keys and their relationships to one another, as well as to assist composition and improvisation.[32] Niedt posits no circle in advance, but rather proposes three implied circles, through which he demonstrates how one modulates with minimal effort. Example 2 shows the three “circles” Niedt utilizes in his demonstrations. Heinichen goes through his circle in six different ways, encompassing more relationships than Niedt, but arguably at the cost of pedagogical clarity. Specifically, while Heinichen does indeed activate every possible key, his method tends not to foreground patterns of figures, although there are similar ways of establishing keys that do tend to recur. Niedt, by contrast, is utterly consistent, showing identical figures for each modulation, which is certainly consonant with his aim to address the beginner.[33]

The following chapter spells out the acceptable keys, up to and including five sharps and flats. Niedt lists both Dorian and Aeolian forms of C and G minor, something reflected in his figuring for G minor in the first example of Chapter IX, i.e., the absence of a ¨ with the 6/5 chord on C. It may or may not be a misprint, but the G leading to D minor bears a 6/5/¨, suggesting that Niedt was in the habit of including it.[34]

Niedt’s second part is titled Handleitung zur Variation and constitutes the main achievement for the treatise, the feature for which it is most remembered. His project is to link composition and extemporization with the study of thorough-bass and the method proceeds in the following fashion. He first treats possibilities of varying intervals in the bass, including cadential patterns. Each interval from the first scale degree is treated in ascending and descending fashion. The space is filled in with passing tones and arpeggios exhibiting various rhythmic configurations. This approach to variation reflects the Figurenlehre tradition, particularly the work of Wolfgang Caspar Printz, in whose Phrynis Mitilenæus, oder, Satyrischer Componist there is a mini-treatise on variation and invention, where he treats different ways in which purely melodic intervals are to be varied.[35] Both authors emphasize the necessity of variation in various walks of life. Of course there are differences, as Niedt’s presentation will have harmonic implications, where as Printz seems chiefly concerned with training vocalists. Niedt also presents his variations lumped together with a minimum of theorizing their differences, presumably appealing to the innate musical sympathies of the reader. Printz is much more deliberate in his categorization of the figures into Einfach, Zusammengesetz (strung together) and within these genera, vermengten (blended), schwebenden (beating), schwermend, springende, and so on.[36] Within these he treats specific figures, each with Latin and Italian names such as Figura Bombilans (loud, beating Figuren are set together). There is even a special vocabulary for the traversal of intervals under the umbrella term Tirata, e.g., Defectiva (fifth filled), Perfecta (octave), Aucta (greater than an octave).

Niedt turns his attention to an actual bassline (C-G | D-A | F-C | G-C||, unfigured, all in half notes). He fills in each of the intervals by concatenating the different possibilities just enumerated, also illustrating the same bassline in the context of different meters and dance styles. One aspect of this demonstration deserves comment. In moving from A to F, Niedt’s variations often exhibit accidentals in an otherwise purely diatonic context. For instance, the variation atop page 89 decorates the bass note A with an upper neighbor B¨ before descending to F in step-wise fashion. He repeats this accidental in two other examples on the same page as well as in several additional instances in the chapter, all of which involve neighbor tones to A. Played with a Bª the passage sounds noticeably out of the style and yet the inclusion of B¨ passes without comment, presumably relying on musical intuition. Harmonically speaking, it is almost as if Niedt is treating the F (either explicitly as F major or even perhaps implicitly as D minor in first inversion) as a Stufe of its own, so great is its influence that it seems almost to demand a B¨.[37]

Niedt then applies the idea of variation to the right hand of the thorough-bass. He shows different ways of varying triads before moving onto variations involving his original rules dealing with the various figures. This is the crucial step in Niedt’s pedagogy. Although there is no discussion of dissonance treatment with respect to meter, he clearly carries over the same metric understanding laid forth in the opening part. Many of the right hand variations, though, are rather chordal in nature, as opposed to linear, something that at times solicits objections and even recomposition from his commentator and editor Mattheson.[38]

Some controversy arises as Niedt treats once again his rule regarding unprepared sevenths within the figuring 7/5/3. Niedt’s example shows a cadence in D major with the dominant decorated by a lower neighbor G in the bass, which is the note that takes the 7/5/3, forming a “IV7” chord. This contrasts with the examples given in the corresponding rule in Part I, which contained a dominant seventh chord, with the seventh resolving upwards. Of course, in the thorough-bass tradition, the figure 7/5/3 meant any seventh, fifth and third, whereas today we would want to differentiate these two uses by invoking the concept of function, namely dominant and pre-dominant. This confusion prompts a lengthy footnote from Mattheson, in which he states:

In my practice, they [unprepared 7/5/3] usually occur right before the cadence and have a major third, when the major seventh is used. However, if the seventh is minor, then the third is minor and also needs no number here.[39]

He then quotes from Niedt’s example in Part I, showing only the bass with the voice that bears the seventh. In both cases, the sevenths are unprepared and resolve upwards, which does not seem to draw Mattheson’s attention. Mattheson conceptualizes such events essentially as triads built above a bass note. He writes:

The 7/5, which is unprepared, and which is, in a way, an ordinary chord, i.e., a Haupt-Accord (namely, from the third above the bass note over which this figure is written, whether it be major or minor), usually prepares us for a cadence and, in minor keys, often contains a minor seventh and a minor third …[40]

Mattheson then shows such a situation in minor and major, in each case building a triad over G, figured 7/5, headed towards a cadential 6/4 over A, which then resolves to D. In both cases, it is clear that in minor a B¨ major triad sits atop the G, with a B minor triad occurring over G in major.[41]

Poulin provides additional commentary on the situation. She appears to side with Niedt, arguing that Niedt theorizes the sonority in question as an “ordinary chord,” and hence as requiring no preparation, while Mattheson does nothing to justify his position. In attempting to contradict Mattheson, Poulin mistakenly attributes the initial two examples of the footnote to Mattheson, when they have clearly been peeled off Niedt’s example of the 7/5/3 chord from the first part by Mattheson. In attributing two examples to Mattheson that are not in fact his own, Poulin overlooks the fact that Mattheson has indeed justified his position by appealing to practice, stating in both quotations above that these sonorities, though peculiar, do occur immediately prior to a cadence.[42]

Support for Mattheson’s invocation of practice can be found in the figured bass examples placed at the end of Bach’s small treatise in the “Additional Examples” section.[43] Already on the fourth beat of the first example Bach places an unprepared 7/5 over the pre-dominant scale degree (C). A similar situation appears at the end of the fourth bar leading to a cadence in D minor. At the conclusion of the first section of the example, only three bars later, there is a cadence in G minor, whose dominant is decorated by yet another an unprepared 7/5/3 chord in exactly the manner Mattheson has described. Further examples can be found in the same example (bars 12, 13, 17), as well as in other exercises in this section. Many, such as that found in #8 in the opening bar, are prepared, but instances such as those in #1 to suggest a strong connection with the practice described by Mattheson.

The remainder of the chapter finds composition and thorough-bass most closely linked. After an extended section on the various styles of the day, Niedt fashions a Prelude and Chaconne, two Allemandes, 2 Courantes + Double, Sarabande + Double, 3 Minuets, and Gigue all from a given figured bass. It is true that these alternate realizations do not stand as “analyses of one another”[44] and that most alterations are directly related to meter (3/4, 4/4, 6/8) and number of bars, i.e., the original passage contains nine bars in the first section, whereas Niedt shrinks the first section of his Sarabande to 8. There are moments, though, where the tonality is expressed with slight differences. The bassline begins by expanding tonic with a 5/3 and 6/4/2 on C, followed by a B bearing a sixth, another 5/3 on C, and thereafter an E, with the figures 6-5, leading to F (I—ii4/2—V6—I—I6-5—IV). In the first Allemande, the E6-5 takes a false fifth (B¨), thereby acting to tonicize the ensuing F chord, whereas the second Allemande maintains the Bª.[45]

Niedt’s third part was left unfinished at the time of his death, the author unable to address such genres as the Ode, Cantata, Aria, Serenade, and even opera. At the outset of Part III, Niedt establishes his conception of counterpoint as an extension of his remarks on preparation. So-called liegenden or Ketten-Contra-Punct (prepared, chain-counterpoint) is a principle of voice-leading enacted to coordinate with his rules of figured bass. Predictably, it involves a great deal of ties. A portion of this chapter deals with putting some finishes touches on the figured bass rules from the first part. For instance, Niedt points out that in the case of 4/2 and 6/4/2, the bass has in fact been prepared. He adds that with the 7/5/3 the seventh could always have been prepared, “but since it tickles the ear, such a liberty was taken [in Parts I and II].”[46] This seems true enough, and yet Niedt’s two illustrations of this involve (§24) three 7/5/3 chords, none of which are prepared in this manner, even in the five-voice example; nor could they have been, given the voice-leading of the passages. This is a problematic point of Niedt’s practice for which there does not appear to be a solid rationale, although all seventh chords (7/5/3 and their inversions) in the chapter with the exception of these examples are executed in the manner prescribed.

Niedt’s most vivid demonstration of the chain-counterpoint style is illustrated by two sets of two contrasting four-voice settings of an identical figured bass.[47] In one harmonization, there are no suspensions as well as many more leaps in the tenor and alto, a setting “famous organists sometimes have not felt ashamed to do.”[48] The proper harmonization presents suspensions and impressively smooth voice-leading, sounding altogether more modern, as opposed to the somewhat brutal progression of root-position chords, each struck anew, of the previous example. Niedt provides further demonstration of the point with another set of contrasting figured bass realizations, this time substituting 6/5 (i.e., ii6/5) for the original IV chord, as well as the usual suspensions. Thus Niedt betrays an innate knowledge of the sub-dominant function but couches his explanation in terms of voice-leading instead of function.[49]

In another important passage of Part III, Niedt addresses doubling issues in the case of parallel 6/3 chords as well as harmonizations of ascending and descending scales. Taking them in order, Niedt complains that ill-conceived settings of parallel 6/3 chords may seem correct to the eye but in fact contain hidden fifths and octaves. He proposes instead to elaborate the passage with suspensions and vary the tone that is doubled. All this is summarized in Example 3.[50]

Niedt also gives three examples of ascending and descending basses, each of which take a variety of figures and traverse the same complete major scale. Although there is no mention whatsoever of rules of the octave[51]—and indeed there is an absolute minimum of commentary—Niedt instructs the reader that “it [is] very necessary and useful to familiarize oneself very, very well with the following progressions. Then one will become accustomed to them and be more apt to recognize the correct meaning.”[52] The examples are not given in the context of a key as such, and there is barely any mention of the structure of the bassline.

What can be inferred from their positioning in the chapter? First, the basslines resemble the preceding basslines (dealing with parallel 6/3 chords), in that they maintain continuous, step-wise motion in one direction. This puts the possibility of parallel 6/3 chords in play, and perhaps Niedt is showing a way to use them sparingly in the context of other figures. Second, these compact examples exhibit quite a rich palette of figures, and perhaps Niedt is also providing guidelines for utilizing a highly varied harmonization. Of course, the next example (§37) is not to do with scalar basses at all, and instead seems to focus on a highly chromatic bassline which supports a properly connected right hand realization. The overall context is still chain-counterpoint and it could also be that Niedt is simply giving several diverse examples set in the desired manner. Niedt’s order of presentation is confusing, although each of these thorough-bass harmonizations do relate intimately in that they are present a variety of figures in the chain-counterpoint style. At this stage Niedt also introduces one final rule, this one dealing with 6/4/3, in which case the 3 is prepared.[53]

The chapter on counterpoint concludes with a memorable condemnation of modes, of which Niedt writes, “I break out in a cold sweat at the mere thought of these follies and I would certainly have to purge myself from both directions if I spoke or wrote much about this matter.”[54] The treatise draws to a close with short discussions of canon, about which Niedt has nothing kind to say, the Church Style and Cavatas, this chapter containing a complete setting of a chosen aria and recitative. Niedt’s comments are not particularly technical and are largely to do with text setting and general principles of appropriate organ playing.

Niedt’s treatise is of value to us for its methodological clarity in fusing thorough-bass technique with composition and extemporization. It is, of course, also a very detailed, if only introductory, snapshot of the Bach family tradition of teaching and some believe there to be intimate connections between the treatise and some of Bach’s other pedagogical work.[55] It is not difficult to hear Bach’s music as an ingenious stringing together of “licks,” a hearing which suggests affinities with Niedt’s presentation. Niedt’s treatise offers us an angle to approach Bach’s musical language. Moreover, Niedt includes a rudimentary musical circle five years before Heinichen first published on the subject. Niedt should be studied as an idiosyncratic but powerful early eighteenth century counterpoint treatise, in the anti-species tradition, on thorough-bass and composition, although given that it is an introductory text and there is little in the way of detailed deliberations, further work could still be done to explore Niedt’s order and manner of presentation with respect to other contemporaneous treatises on the subjects he touches, as well as how he may fit into the musica poetica tradition. Certainly there is evidence of contact given Niedt’s Jesuit education, lists of variations (though trimmed of much rhetorical jargon) and mentioning of such figures as Printz and Kircher.[56] Further study of Niedt may profit from the consideration of these factors.