2017 Patricia Carpenter Emerging Scholar Award J. S. Bach ...derekremes.com/wp-content/uploads/Remes_TP_Vol-42[FINAL].pdf · bass chorales. Bach’s chorale harmonizations are still

For as much as we admire J. S. Bach’s music, we know relatively little about how he

taught composition. One thing we do know is that Bach began instruction with figured-

bass chorales. Bach’s chorale harmonizations are still part of the curriculum today,

but they are usually used to teach harmonic analysis, not composition—that is, we use

the same materials (chorale melodies), but to different ends. Thus, developing a clearer

understanding of Bach’s pedagogical methods can inform modern-day pedagogy. But

since very few pedagogical resources by Bach are available for study, inferences must be

made from writings by his students and contemporaries.1 Fortunately, new manuscripts

from Bach’s circle of pupils have recently come to light, promising further clues.2

Among these new sources is the Sibley Choralbuch, rediscovered and assessed

anew by Robin A. Leaver (2016). Contrary to Philipp Spitta and Hans-Joachim Schulze’s

earlier appraisals, Leaver argues convincingly that the Sibley manuscript is indeed the

lost Choralbuch that Breitkopf listed for sale in 1764. The description of the Choralbuch

in Breitkopf’s original catalogue reads: “Complete choral book with figured basses for

1 Einige Reguln ([1725] 1899) is conclusively attributed to J. S. Bach, whereas the authenticity of Vorschriften und Grundsätze ([1738] 1994) is contested, though it likely stems from Bach’s immediate musical culture. See Braatz (2012) regarding its authenticity.

2 The recent discovery of a new multiple-bass source from Bach’s pupil Johann Christian Kittel (1732–1809) prompted Susan McCormick’s recent dissertation, which—with the exception of the Sibley Choralbuch—catalogues all of the known chorale books stemming from Bach’s pupils and grand-pupils (McCormick 2015, 4–9, 62–63, and 140).

J. S. Bach’s Chorales: Reconstructing Eighteenth-Century German Figured-Bass

Pedagogy in Light of a New SourceDerek Remeš

In a recent study by Robin A. Leaver, the Sibley Choralbuch (Rochester, NY) was re-identified as likely stemming from J. S. Bach’s students in Dresden from around 1730–40 (2016). The manuscript contains 227 figured-bass chorales—melodies with single figured basses—and thus matches the first part of C. P. E. Bach’s description of his father’s teaching method, where students first received a figured-bass chorale and added two inner voices. Later, students composed their own basses and figures. Here, the plural “basses” is significant, because several “multiple-bass” chorale sources have also come to light in recent years, many stemming from J. S. Bach’s students, Kittel and Kirnberger, who discuss this technique in their treatises. These sources suggest that a little-known, keyboard chorale tradition also played an important role in Bach’s pedagogy. The present article attempts to reconstruct this pedagogical process using contemporaneous German sources.

2017 Patricia Carpenter Emerging Scholar Award

THEORY and PRACTICE Volume 42 (2017)30

240 melodies in use in Leipzig.”3 Leaver shows that the manuscript in Sibley Library

matches Breitkopf’s description in four key points: 1) it is a “complete” book for the

full church year; 2) it contains the same number of melodies (the difference due to how

one counts); 3) it contains the same number of pages; 4) the melodies were common in

Leipzig (ibid., 24). Only the price remains in doubt, as Schulze had pointed out—he

believes 10 Thalers to be too low (1981, 129–30). It seems likely that the price was

low because Breitkopf was uncertain as to the book’s value, the style being so different

from Bach’s published vocal chorales. Indeed, this was the reason Spitta dismissed the

Sibley manuscript, for he believed the style to be too simple for Bach. Spitta examined

the Sibley Choralbuch in or before 1880, concluding that “The volume exhibits, neither

in Bach’s handwriting nor in the composition of the chorales, a single trace of Bach’s

style or spirit.”4 The settings in the Sibley Choralbuch are indeed simpler than Bach’s

more harmonically adventurous keyboard settings for congregational singing,5 but

that is precisely the point—the Sibley Choralbuch implies that Bach began his teaching

in a much simpler, more homophonic style than is typically assumed. Leaver’s new

assessment is that the Sibley Choralbuch likely stems not from Bach directly, as the

Breitkopf description suggests, but from Bach’s circle of pupils in Dresden from about

1730 to 1740. The present article investigates the Sibley Choralbuch in a theoretical

light following these findings.6

As Leaver has argued, the settings contained in the Sibley Choralbuch suggest

that there were two separate Bach chorale traditions: the first is the well-known

Choralgesang tradition based on four-part chorales from Bach’s cantatas and passions;

the second, Choralbuch tradition, is not vocal but keyboard-centered.7 Because the

second, Choralbuch style was often improvised, there remains less evidence of its

existence. The Sibley Choralbuch is therefore significant because it sheds light on this

lesser-known, keyboard-based, Bach chorale tradition. While the Sibley Choralbuch

provided the impetus for Leaver’s claim that there were two separate Bach chorale

3 “Bachs. J. S. Vollständiges Choralbuch mit Noten aufgestzten Generalbasse an 240 in Leipzig gewöhnlichen Melodien. 10 thl” (Schulze 1972, 166). Unless otherwise noted, all translations are my own.

4 “Das Büchlein zeigt aber weder Bachs Handschrift, noch auch im Satze der Choräle eine Spur Bachschen Stiles und Geistes” (Spitta 1899, 108n149). Translation by Clara Bell and J. A. Fuller Maitland.

5 These include In dulci jubilo (BWV 729a), Gelobet seist du, Jesus Christ (BWV 722a), Vom Himmel hoch (BWV 738a), and Lobt Gott, ihr Christen, allzugleich (BWV 732a).

6 A modern edition of the Sibley Choralbuch is forthcoming (Leaver and Remeš, eds. 2018).

7 Leaver terms the Choralbuch and Choralgesang styles “keyboard” and “vocal,” respectively (2001, 62; 2016, 29). I prefer the names “Choralbuch” and “Choralgesang” because these styles are not necessarily bound to specific instruments (i.e., keyboard or voice), though they often are.

Derek Remeš – Reconstructing Eighteenth-Century German Figured-Bass 31

traditions, I will draw on a variety of eighteenth-century German sources to substantiate

and develop Leaver’s hypothesis, with a particular emphasis on reconstructing

the pedagogical process of harmonizing chorales according to contemporaneous

sources. My main argument is that Bach’s chorale-based pedagogy bridges from the

homophonic Choralbuch style to the ornamented Choralgesang style through multiple-

bass realizations. The implications for pedagogy today are that we, too, should begin

in a simpler, homophonic style with a more consistent emphasis on outer voices and

thoroughbass.

The first part of this article describes Bach’s two-stage pedagogical method and

illustrates the Choralbuch and Choralgesang styles of realization. The second part

examines the first stage of Bach’s method, where the outer voices and and figured bass

are given. The third part investigates the second stage, where students compose multiple

original basslines and figures to a given chorale.

J. S. Bach’s Pedagogy and Choralgesang vs. Choralbuch Styles

C. P. E. Bach’s oft-quoted description of his father’s pedagogy is my point of

departure:

In composition [J. S. Bach] started his pupils right in with what was practical, and omitted all the dry species of counterpoint that were given by Fux and others. His pupils had to begin their studies by learning pure four-part thoroughbass. From this he went to chorales; first he added the basses to them himself, and they had to invent the alto and tenor [what I call “Stage 1”]. Then he taught them to devise the basses [note the plural: “basses”] themselves [“Stage 2”]. He particularly insisted on the writing out of the thoroughbass in parts. [Presumably later,] In teaching fugues, he began with two-part ones, and so on.

The realization of a thoroughbass and the introduction to chorales are without doubt the best method of studying composition, as far as harmony is concerned (Wolff 1998, 399).8

The quotation tells us that after teaching the basics of thoroughbass, J. S. Bach

introduced chorales in two stages, as outlined in Example 1. In Stage 1, students receive

a chorale melody in the highest voice, plus a bassline and figures, and are asked to

supply inner voices and ornamentation. Thus, Stage 1 focuses on texture, since the

outer voices and harmony are given. Sources relating to Stage 1 have single basses, like

the Sibley Choralbuch, which because of its water mark can be traced to Dresden around

1730–40 (Leaver 2016, 19–20). As Leaver mentions, Bach had three students active in

Dresden around this time: C. H. Gräbner (1705?–1769), W. F. Bach (1710–1784), and

8 Interestingly, C. P. E. Bach makes no mention of chorales in his Versuch über die wahre Art das Clavier zu spielen (1753/62).


G. A. Homilius (1714–1785). Since no relevant sources survive from Bach’s Dresden

students, I will turn to musicians outside the Bach circle to help illuminate Stage 1.

These are Michael J. F. Wiedeburg (1720–1800), Justin Heinrich Knecht (1752–1817),

and Johann Gottlob Werner (1777–1822). All three were contemporaries with Bach’s

first generation of pupils, were active in central Germany, and at least two were admirers

of Bach.9 Even though Wiedeburg, Knecht, and Werner were not Bach pupils, the fact

that they describe, in detail, techniques which were likely common knowledge to

educated eighteenth-century musicians like Bach makes them particularly suitable

sources in the present context.

According to C. P. E. Bach’s quote, Stage 2 of Bach’s method focuses on outer-

voice counterpoint and harmony; only the chorale melody is given and the student’s

task is to compose increasingly complex basslines and inner voices. Sources relating to

this stage contain multiple basslines for each chorale. The writings of Bach’s students

Johann Christian Kittel (1732–1809) and Johann Philipp Kirnberger (1721–1783), as

well a musician outside the Bach circle named David Kellner (c. 1670–1748), will help

illuminate this second stage.

9 See Knecht (1795–98, 3:18) and Werner (1805, 4).

STAGE 1 STAGE 2

STUDENT RECEIVES Chorale onlyChorale, Bassline, and Figures

Inner voices and OrnamentationSTUDENT PROVIDES Bassline, Figures, and Inner voices

PEDAGOGICAL FOCUS Texture & Ornamentation Harmony & Two-Voice Counterpoint

Single-Bass Sources Multiple-Bass SourcesTYPES OF SOURCES

BACH STUDENTS

Dresden School (Sibley Choralbuch)

C. H. Gräbner (1705?–1769)

W. F. Bach (1710–1784)

G. A. Homilius (1714–1785)

J. C. Kittel (1732–1809)

J. P. Kirnberger (1721–1783)

MUSICIANS OUTSIDE BACH

CIRCLE WHO ILLUMINATE

THIS STAGE

J. D. Heinichen (1683–1729)

David Kellner (1670–1748)

M. J. F. Wiedeburg (1720–1800)

J. C. Knecht (1752–1817)

J. G. Werner (1777–1822)

Example 1Overview of J. S. Bach’s two-stage pedagogical method and related sources.

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Translation (text for verse one; not in original): “Now let us give thanks to the Lord and honor him on account of his gifts which we have received.”

Example 3. J. S. Bach’s setting of Nun laßt uns Gott dem Herren from Cantata BWV 165, O heilges Geist und Wasserbad

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œ œ œ œ œ œ œ ™ œjœ œ œ ™ œ

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Jœ œ œ œ œ œ œn œ œ œ œ œ œ œ

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Original key: G major. Text replaced for comparison with Example 2. Continuo doubles bass voice and includes no �gured bass.

3 5 7

Nun laßt uns Gott, dem Herr - en, Dank-sa - en und ihm ehr - en Von weg-en sein - er Gab - en, Die wir emp-fang - en hab - en.




Example 3J. S. Bach’s setting of Nun laßt uns Gott dem Herren

from Cantata BWV 165,O heilges Geist und Wasserbad.

Example 2. Nun laßt uns Gott dem Herren from the Sibley Choralbuch (anon. ms., likely Dresden, c. 1730–40)

Nun

Von weg - en sein - er Gab - en, Die wir emp - fang - en hab - en.

laßt uns Gott dem Herr - en, Dank - sag - en und ihm ehr - en

Translation (text for verse one; not in original): “Now let us give thanks to the Lord and honor him on account of his gifts which we have received.”

Tune Source: Selnecker’s Christliche Psalmen (Leipzig, 1587)

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3 6 9

11 13 16 19

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Example 2Nun laßt uns Gott dem Herren from the Sibley Choralbuch (anon. ms., likely Dresden, c. 1730–40).


Examples 2 and 3 illustrate the difference between the Choralbuch and

Choralgesang styles. In general, the Choralbuch style is vertically oriented: it is more

triadic, consonant, diatonic, and disjunct; moreover, it was often improvised in the

context of organ accompaniment for congregational singing, where only the chorale

was sung. In contrast, the Choralgesang style is horizontally oriented: it uses more

dissonant figures, suspensions, is more chromatic, and has faster note values and more

conjunct motion; in addition, the Choralgesang style was less often improvised, instead

being written out for concerted music where each of the four voices were sung.

All chorales in the Sibley Choralbuch are presented in the same manner and the

same style as Example 2: the chorale tune is provided in the soprano part along with

a figured bassline in a simple, unornamented style, as a student would receive in Stage

1 of Bach’s method. The student would then compose or improvise the inner voices,

either in a lesson with Bach, alone at home, or during the church service at the organ.

Example 3 is Bach’s vocal setting of the same chorale. Its numerous non-chord tones and

tonicizations are typical of the Choralgesang style. Such settings, which are often used

for harmonic analysis today, originate mostly from Bach’s cantatas and passions and

were originally written for choir. C. P. E. Bach writes in the preface to the first edition of

his father’s chorales in 1765 that he reduced them from four to two staves to make them

easier to read at the keyboard.10 This condensed format has led generations of musicians

and teachers to often mistake Bach’s vocal settings for keyboard music, even though the

inner voices are unidiomatic for the keyboard. Indeed, Emanuel Bach makes special note

of the “natural flow of the inner voices and bass, which are what above all distinguish

these chorales” (Wolff 1998, 379). Given their popularity today, it is surprising to learn

that C. P. E.’s first edition of his father’s chorales sold poorly. According to Matthew

Dirst, the chorales were “controversial even among admirers, who questioned their

style and utility while praising their creator’s mastery of Harmonie” (2012, 35). Abbé

Vogler (1749–1814) and Carl Maria von Weber (1786–1826) even deplore Bach’s vocal

chorales’ lack of “noble simplicity” and “dignity” (Blume 1974, 346).11 The newly

rediscovered Sibley Choralbuch implies the existence of a second, simpler, keyboard-

based Bach chorale tradition that was, in fact, quite similar to eighteenth-century norms

10 The chorales were “originally set out on four staves for four singers. They have been presented on two staves to accommodate lovers of the organ and the clavier, since they are easier to read in that form” (Wolff 1998, 379). Regarding the format of Bach’s chorales, see Dirst (2012, 44-47).

11 Critics of Bach’s vocal chorales may have also confused them for keyboard music, specifically congregational accompaniment, which was traditionally more conservative. For example, Johann Christoph Kühnau (1735–1805) acknowledged Bach’s settings as masterpieces but considered them too difficult and inappropriate for church (1786, iv).


for Choralbuch settings. In addition to its function in organ chorale accompaniment

during the church service, the Choralbuch style was likely the starting point in Bach’s

pedagogical method.

Stage 1: Adding Inner Voices and Ornamentation

In the first stage of Bach’s method the chorale and figured bassline are given,

and the student adds the inner voices. The fact that the outer-voices and figures are

predetermined focuses the student’s attention on textural matters—that is, the

number of voices and their degree of ornamentation. Example 4 outlines five types of

texture described variously in the writings of Knecht, Werner, and Wiedeburg. Types

1 and 2—the “Close [eng] Style” and the “Spread [zerstreut] Style”—are relatively

straightforward. Type 3 begins to add ornamentation. The bottom of Example 4 lists

Knecht’s subtypes 3.1, 3.2, etc. These add ornamentation to the bass alone, then to

the lower three voices, and then to all voices, including the chorale melody, ending

with Type 3.4, which uses imitative counterpoint in the accompanying voices. Type 4 is

the “Full-voiced [vollstimmig or vollgriffen] Style,” where the player supplies as many

notes as possible between the outer voices; as long as the outer voices move in good

counterpoint, parallel and direct motion with the middle voices is tolerated. Thus, the

“Full-voiced Style” affords organists and harpsichordists a degree of dynamic control

by varying the number of voices. Type 5 is the “Unison style” [im Einklang], which is

used exclusively in congregational singing and thus is not the focus of the current study.

Examples 5 through 9 work progressively through the types given in Example

4. Example 5 provides three different types of realization using the same chorale tune

as in Example 2, but in C major. Example 5a is Type 1, or the “Close Style.” Here the

right hand takes the upper three voices while the left hand takes the bass (often called

“keyboard style” today). Werner writes that the “Close Style” is the oldest type, already

known in Martin Luther’s time, but it is still in use in 1805. But according to Werner,

the “close style” is not suitable to human voices because the tenor is too high; moreover,

the “pleasing middle range of the organ lies unused” (1805, 4). Example 5b is Type 2,

the “Spread Style,” which essentially moves the alto voice of 5a down an octave. Werner

describes how this method is superior to the “close style” because it remedies the above-

mentioned problems: the tenor is now low enough to be sung and the middle range of

the organ is not ignored; moreover, according to Werner, the “spread style” is easier to

read (ibid., 4–5).

The “Full-voiced Style” appears in Example 5c, where, according to Knecht and

Wiedeburg, parallel octaves and fifths are allowed (Knecht 1795–98, 3:76; Wiedeburg


1765–75, 2:293-94). Examples 6 through 9 begin to add ornamentation. Example 6

is Type 3.1, an ornamented bass. Here Knecht adds passing notes in smaller values

than the chorale, which moves in half notes. In Example 7 Knecht offers three ways

of varying the lower three voices, keeping the chorale in the soprano unaltered.

Example 8 shows two ways of ornamenting all voices, including the chorale melody:

Knecht gives the unaltered melody (for singing) in the top staff of Example 8a and

the ornamented version (for playing) in the middle staff. Example 9 is Knecht’s

subtype 4.2, a variation on the “Full-voiced Style” where parallels are not allowed.

According to Knecht, five- and six-voice textures are possible in this style, as shown

in Examples 9a and 9b, respectively. As these various harmonizations show, the types

outlined in Example 4 introduce progressively more complex textures: we began with

an unornamented, Choralbuch style (Example 5) and ended with six independent

voices in a more ornamented, flowing, Choralgesang style (Example 9b). Were such

ornamentation techniques unique to Knecht? Or is it likely that, after beginning

T E X T U R E

TYPE 1 2 3 4 5

NAME CLOSE STYLE SPREAD STYLEORNAMENTED

STYLEFULL-VOICED STYLE UNISON STYLE

NUMBER OF VOICES

Four Four Four or Five Five to Nine One

EXAMPLES IN THIS PAPER

Ex. 5a Ex. 5b Exx. 6, 7, 8 Exx. 5c, 9 none

DESCRIPTION

- Homorhythmic with upper three voices in close position

- Wide gap between bass and tenor

- Older method, for beginners

- Simple rhythms in opening position

- Tenor is lower than in the close style

- Harder because left hand and pedal are now independent

- More active rhythm, still in open position

- All voices may be ornamented, even the soprano

- Bach’s chorales from the cantatas belong to this type

- Usually parallel 5ths and 8ves are allowed in the middle voices if the outer voices move in good counterpoint

- Avoid thirds in the left hand (too thick)

- Single voice doubled in three or four octaves with pedal

- Used in congregational singing for variety

KNECHT’S SUBTYPES

- 3.1: Ornamented bass & varied harm.

- 3.2: Ornamented A, T, and B

- 3.3: All voices ornamented (also chorale in soprano)

- 3.4: Contrapuntal, canonic, or fugal ornamentation

- 4.1a: Thick chordal texture; middle voices may have parallel 5ths and 8ves

- 4.1b: Variation: Hold chords half value, always sustaining the soprano

- 4.2: Five or six independent ornamented voices without parallels

Example 4. Five textures for realizing a �gured-bass chorale from Knecht (1795–98, 3:20, 36, 82–107), Werner (1805, 1–9), and Wiedeburg (1765–75, 2:293–96)

(3:82–107)

Example 4Five textures for realizing a gured-bass chorale from Knecht (1795–98, 3:20, 36, 82–107),

Werner (1805, 1–9), and Wiedeburg (1765–75, 2:293–96).

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a) Type 1: Close Style (3:20) b) Type 2: Spread Style (3:36)

[alto and tenor are near-exact inversion of those in Ex. 5a]

c) Type 4.1a: Full-voiced Style with Parallels (3:75)

[parallel �fths and octaves]

Example 5. Three styles of realizing Nun laßt uns Gott dem Herren, from Knecht’s Orgelschule (Leipzig, 1795–98)

Example 6. Type 3.1: Varied bass (and harmony) using Liebster Jesu, wir sind hier, from Knecht’s Orgelschule (Leipzig, 197–98, 3:83)

Example 7. Type 3.2: Varied middle voices and bass using Nun danket alle Gott, from Knecht’s Orgelschule (Leipzig, 1795–98)

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Example 5Three styles of realizing Nun laßt uns Gott dem Herren,

from Knecht’s Orgelschule (Leipzig, 1795–98).

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˙˙ ˙ ˙

˙˙˙

˙˙ ™

˙ œ ww Ó ˙ ˙

˙ ˙ ˙ ˙ ˙ ˙ wwww

Ó ˙ ˙ ˙ ˙ ˙ ˙ ˙ w Ó ˙˙˙ ˙ ˙ ˙ ˙ ˙ ww Ó ˙ ˙ ˙ ˙ ˙ ˙ ˙ www








{™™

™™

C

C

&#

˙ ˙ ˙ ™ œ ˙ ™ œ w ˙ ˙ œ œ w

?#U

#u

˙ ˙ ˙™


˙œJœ ™ ˙œJ

œ ˙ ˙ œ w ˙ ww



œ œ œnœ w

{ {

{

C C

C C

&#

&# U

?# ?#u

&# U

?#

u



˙ œ œ œ Ó ˙ ˙ ˙ ˙˙

˙˙ wwwœ œ œ œ

ÓÓ

˙≈ œ œ œ

˙




Œ œœ œ œ œ

Œ œ

œ œn œ œŒ œ

œ œ œ œŒ w


Ó ˙ ˙ ˙ ˙˙

˙˙ www

ÓÓ œ œ œ œ


œœ œ œ

œœ

œœ


œ œ œ œ


œœ œ œ


œœ œ œ


œœ œ œ

˙

œ œ œ œ ˙

a) (3:87–88) b) (3:88–89)

c) (3:89–90)

Example 6Type 3.1: Varied bass (and harmony) using Liebster Jesu, wir sind hier,

from Knecht’s Orgelschule (Leipzig, 197–98, 3:83).

{ { {C C C

C C C

&U [etc.]

[etc.]

LH

LH

LH

RH

PedalPedal

Pedal

[etc.]

[etc.]

[etc.] [etc.]

&U

&U

? U ? U ? U

Ó ˙˙

˙˙ ˙ ˙

˙˙˙

˙˙

˙˙

www Ó ˙˙

˙˙ ˙ ˙

˙˙˙

˙˙ ™

˙ œ ww Ó ˙ ˙

˙ ˙ ˙ ˙ ˙ ˙ wwww

Ó ˙ ˙ ˙ ˙ ˙ ˙ ˙ w Ó ˙˙˙ ˙ ˙ ˙ ˙ ˙ ww Ó ˙ ˙ ˙ ˙ ˙ ˙ ˙ www








{™™

™™

C

C

&#

˙ ˙ ˙ ™ œ ˙ ™ œ w ˙ ˙ œ œ w

?#U

#u

˙ ˙ ˙™


˙œJœ ™ ˙œJ

œ ˙ ˙ œ w ˙ ww



œ œ œnœ w

{ {

{

C C

C C

&#

&# U

?# ?#u

&# U

?#

u



˙ œ œ œ Ó ˙ ˙ ˙ ˙˙

˙˙ wwwœ œ œ œ

ÓÓ

˙≈ œ œ œ

˙




Œ œœ œ œ œ

Œ œ

œ œn œ œŒ œ

œ œ œ œŒ w


Ó ˙ ˙ ˙ ˙˙

˙˙ www

ÓÓ œ œ œ œ


œœ œ œ

œœ

œœ


œ œ œ œ


œœ œ œ


œœ œ œ


œœ œ œ

˙

œ œ œ œ ˙

a) (3:87–88) b) (3:88–89)

c) (3:89–90)

Example 7Type 3.2: Varied middle voices and bass using Nun danket alle Gott,


TH

EO

RY

and

PR

AC

TIC

E V

olu

me 4

2 (2

017)

38

Example 8Type 3.3: All voices ornamented,


[etc.]

[etc.]

[etc.]

[etc.]

Example 8. Type 3.3: All voices ornamented, from Knecht’s Orgelschule (Leipzig, 1795–98)

Example 9. Type 4.2: Five or six independent voices, from Knecht’s Orgelschule (Leipzig, 1795–98)

a) O heil’ger Geist, kehr bei uns ein [Wie schön leuchtet der Morgenstern] (3:93–94)

b) Allein Gott in der Höh sey Ehr (3:95–96)

a) Five voices: Ach bleib mit deiner Gnade (3:79)Fünfstimmig.

Sechsstimmig.

Mit obligatem Pedal.


Einfache Melodie zum Singen [”Unornamented melody to sing”]

Unadorned melody in top staff is not in original.

Figurirte Melodie zum Orgelspielen [”Ornamented melody to play on the organ”]

{

{

{

{

C

C

C

C

C

C

C

&bU

&bU

?b

U

&# U

&# U

?#U

&bU U

?bu

#

u

&# U U

?# #

Ó ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙

Ó œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ# œ œ œ œ œ œ œ ˙n

ÓÓ œ œ œ œ œ

Œ ˙œ œ œ œ œ œ œ œœ Œ œ

œ Œ œœ Œ Œ

œ œ# œ œ œœœ˙

Ó ˙ ˙ ˙ ˙ ˙ ˙ ˙ w

®œœœœœ

œœœœœœœœœœœ ™œœœ œ# œœ ™œœœœœ

œœœœœœœœœœœœœœ

œœ œœœR

œœ œ œ œœ œœœœœr œœœœœœœ

œœœ ‰ œœœ

jœœr œœœœœœœ œœœœœœœœ ˙

˙™™™

ÓœœœœJ

‰œœœœj‰ œœœ

œj ‰ ‰œœœn œœœ ‰ ‰

œœœJ

œœœJ

œ œ œ œœ œ œœœœ#J

œœœœœœ œRœœœœœœœœœœ

J‰

œœœœJ

‰œœœJ ‰ ®œœœœœ

œœ˙˙

˙ ˙œ ˙ ˙ œ ˙

œ œ œb œ ™˙ ˙

œnJ˙ ™ ˙ œ ˙ ˙

˙ ˙ ˙ œ ˙ ˙ œ ˙ ˙

˙˙

œœ œ

˙œ

œ

œ œw˙

˙˙

œ œ˙

œ ˙˙

˙

˙˙˙

œ™

˙œ

˙˙

œœ

œ

œ ˙œ œ ˙

˙˙ ˙

˙˙ ˙

œ œ œ˙œ œ œ œ ˙

˙˙

˙œ œ œ œ ˙ ww ™ ˙œ œœ ˙˙˙

˙œ œ œ œ ˙ ˙˙ œ œ ˙

œ œ œ œ œ œ# œ# wœ˙ œ œ œ œ˙œ# œ œ œ ˙ ˙

˙œ œ œ œ w œ œ œ œwœ œ œ œ˙œ œ œ œ ˙

œ œ œ œ ˙˙œ œ œ ˙

˙ ˙˙œ œ œ œ

˙œ œ œ œœ œ œ œ

œœ œ œ

œ œ˙Œœ œ œ

œœ œ œœ

œ œ œ œ ˙œ œ œ œ ˙ ˙˙˙ ˙œœ œ# œ œœ œ œn

b) Six voices: In allen meinen �aten (3:80)

Example 9Type 4.2: Five or six independent voices,


[etc.]

[etc.]

[etc.]

[etc.]

Example 8. Type 3.3: All voices ornamented, from Knecht’s Orgelschule (Leipzig, 1795–98)

Example 9. Type 4.2: Five or six independent voices, from Knecht’s Orgelschule (Leipzig, 1795–98)

a) O heil’ger Geist, kehr bei uns ein [Wie schön leuchtet der Morgenstern] (3:93–94)

b) Allein Gott in der Höh sey Ehr (3:95–96)

a) Five voices: Ach bleib mit deiner Gnade (3:79)Fünfstimmig.

Sechsstimmig.



Einfache Melodie zum Singen [”Unornamented melody to sing”]

Unadorned melody in top staff is not in original.

Figurirte Melodie zum Orgelspielen [”Ornamented melody to play on the organ”]

{

{

{

{

C

C

C

C

C

C

C

&bU

&bU

?b

U

&# U

&# U

?#U

&bU U

?bu

#

u

&# U U

?# #

Ó ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙

Ó œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ# œ œ œ œ œ œ œ ˙n

ÓÓ œ œ œ œ œ

Œ ˙œ œ œ œ œ œ œ œœ Œ œ

œ Œ œœ Œ Œ

œ œ# œ œ œœœ˙

Ó ˙ ˙ ˙ ˙ ˙ ˙ ˙ w

®œœœœœ

œœœœœœœœœœœ ™œœœ œ# œœ ™œœœœœ

œœœœœœœœœœœœœœ

œœ œœœR

œœ œ œ œœ œœœœœr œœœœœœœ

œœœ ‰ œœœ

jœœr œœœœœœœ œœœœœœœœ ˙

˙™™™

ÓœœœœJ

‰œœœœj‰ œœœ

œj ‰ ‰œœœn œœœ ‰ ‰

œœœJ

œœœJ

œ œ œ œœ œ œœœœ#J

œœœœœœ œRœœœœœœœœœœ

J‰

œœœœJ

‰œœœJ ‰ ®œœœœœ

œœ˙˙

˙ ˙œ ˙ ˙ œ ˙

œ œ œb œ ™˙ ˙

œnJ˙ ™ ˙ œ ˙ ˙

˙ ˙ ˙ œ ˙ ˙ œ ˙ ˙

˙˙

œœ œ

˙œ

œ

œ œw˙

˙˙

œ œ˙

œ ˙˙

˙

˙˙˙

œ™

˙œ

˙˙

œœ

œ

œ ˙œ œ ˙

˙˙ ˙

˙˙ ˙

œ œ œ˙œ œ œ œ ˙

˙˙

˙œ œ œ œ ˙ ww ™ ˙œ œœ ˙˙˙

˙œ œ œ œ ˙ ˙˙ œ œ ˙

œ œ œ œ œ œ# œ# wœ˙ œ œ œ œ˙œ# œ œ œ ˙ ˙

˙œ œ œ œ w œ œ œ œwœ œ œ œ˙œ œ œ œ ˙

œ œ œ œ ˙˙œ œ œ ˙

˙ ˙˙œ œ œ œ

˙œ œ œ œœ œ œ œ

œœ œ œ

œ œ˙Œœ œ œ

œœ œ œœ

œ œ œ œ ˙œ œ œ œ ˙ ˙˙˙ ˙œœ œ# œ œœ œ œn

b) Six voices: In allen meinen �aten (3:80)


with the simple style of the Sibley Choralbuch, Bach challenged his students to write

increasingly complex realizations that began to imitate the highly ornamented style of

his Choralgesang settings? Two accounts of Bach’s playing and teaching would seem

to suggest the latter. First, in Arnstadt Bach ornamented a chorale melody with such

“strange tones” that he confused the congregation (Wolff 1998, 399)—clearly he was

no stranger to varied harmonizations. Second, according to Johann Gotthilf Ziegler in a

letter dating 1746, Bach advised him to play “not offhand but according to the Affekt of

the words” (ibid., 336). If what Christoph Wolff says is true, that Bach’s genius lay in his

ability to probe “the possible” in the art (2000, 338), then it seems likely that, at least

with some students, Bach would have introduced chorale harmonization techniques

similar to those given by Knecht in order that students’ accompaniments would have

the potential to better reflect the meaning of the text at any given point. That a chorale

harmonization reflect the meaning of the text was also a central point in both Kittel and

Kirnberger’s treatises as well. Thus, the ornamentation techniques in Stage 1 represents

both a pedagogical strategy for beginning composers and a means of textual expression

for advanced organists accompanying congregational singing.

Stage 2: Composing New Basslines and Middle Voices

In the second stage of Bach’s method, students begin composing their own

basslines and middle voices to a given chorale. Whereas Stage 1 addressed texture

and ornamentation, Stage 2 focuses on harmony and simple two-voice counterpoint.

According to Kirnberger, the bassline is written first, and then figures are added

afterward (1982, 284). For this reason, the third section of this article has two parts,

the first of which discusses the process of composing basslines alone, or what I call

“Stage 2a.”

Stage 2a: Composing New Basslines

Example 10 shows Kirnberger’s classification of harmonic types, which I label A,

B, C, and D (Kirnberger 1982, 284–86). All four harmonic types rely on the idea of

chordal inversion to identify the root, which shows Rameau’s influence on Kirnberger.

Type A allows for triads in any inversion from scale degrees one, four, and five, with the

possibility of the dominant chord having a seventh; Type B includes inverted triads on

all diatonic degrees; Type C has inverted triads from degrees one, four, and five of

neighboring keys within one accidental, and especially secondary dominants; and lastly,

Type D includes secondary dominants from remote keys, enharmonic progressions, and

sudden harmonic shifts. Example 11 shows some common types of basslines, a


classification which builds on Susan McCormick’s survey of several multiple-bass

sources (2015, 25). Generally speaking, basslines may be diatonic or chromatic, conjunct

or disjunct, move in parallel or contrary motion to the chorale melody (a feature

Kirnberger emphasizes [1982, 305]), isorhythmic with the chorale or in faster values,

and the bass may have suspensions, pedal points, or may even imitate the chorale. These

factors—not Fuxian species counterpoint, Emanuel Bach’s quote emphasizes—

constitute the student’s introduction to two-voice counterpoint, where the upper voice

is predetermined by the chorale melody, and the student supplies the bassline. Kirnberger

demonstrates how basslines become more smooth and interesting by moving

progressively through Types A, B, C, and D. Thus, there is a pedagogical progression

implied within this four-fold classification, since the basses in Type A lack variety and

become smoother and more interesting with each progressive increase in harmonic

resources. Since Kirnberger was a student of Bach, it is possible Kirnberger’s classification

may represent the use of new ideas borrowed from Rameau to describe a procedure

Kirnberger learned from Bach.

An example from Kittel (Bach’s final and supposedly “star” pupil) demonstrates

how this pedagogical progression may have worked in Bach’s pedagogy. To illustrate,

Kittel’s harmonizations (Example 12) are labeled with Kirnberger’s harmonic types

(Example 10) and bass types (Example 11). Composing the bassline (Stage 2a) is a

H A R M O N Y

Kirnberger’s Types A B C D

Description (all types include chord inversions)

Triads from1, 4, and 5 only

Triads from all diatonic degrees

1, 4, and 5 fromneighboring keys

(especially dominants)

Dominants from remote keys, enharmonic

progressions, and sudden shifts

Example 10. Kirnberger’s harmonic types from The Strict Art of Musical Composition (1982, 284–86)

Example 11. Types of basslines in multiple-bass source of Bach’s pupils (after McCormick 2015, 23)

Diatonic vs. Chromatic (Bass itself)

Conjunct vs. Disjunct

Parallel vs. Contrary to the Chorale

Homorhythmic vs. Faster NCT’s or Leaps

Bass Suspensions

Pedal Point

Imitative of Chorale or Inner Voices

Example 11Types of basslines in multiple-bass source of Bach’s pupils (after McCormick 2015, 23).

H A R M O N Y

Kirnberger’s Types A B C D

Description (all types include chord inversions)

Triads from1, 4, and 5 only

Triads from all diatonic degrees

1, 4, and 5 fromneighboring keys

(especially dominants)

Dominants from remote keys, enharmonic

progressions, and sudden shifts

Example 10. Kirnberger’s harmonic types from The Strict Art of Musical Composition (1982, 284–86)

Example 11. Types of basslines in multiple-bass source of Bach’s pupils (after McCormick 2015, 23)

Diatonic vs. Chromatic (Bass itself)

Conjunct vs. Disjunct

Parallel vs. Contrary to the Chorale

Homorhythmic vs. Faster NCT’s or Leaps

Bass Suspensions

Pedal Point

Imitative of Chorale or Inner Voices

Example 10Kirnberger’s harmonic types from The Strict Art of Musical Composition (1982, 284–86).

Dere

k R

em

eš

– R

econst

ructing E

ighte

enth

-Centu

ry G

erm

an F

igure

d-B

ass

41 Example 12. Kittel’s harmonizations of Jesu meine Freude from Der Angehende Praktische Organist (Erfurt 1808, 1:30–32)

“lacking variety in harmony” [Type A; diatonic; homophonic]

“richer in harmony” [Type C; diatonic; parallel; conjunct]

“good” [Type B; diatonic, parallel; conjunct]

“pure, yet forcedly chromatic”[Type C; chromatic, contrary motion]

“better chromaticism” [Type C; all voices chromatic; parallel; faster values]

“even better” [Type C; pedal point; imitative of A/T; chr. �gures]

[no �gures][no �gures] [no �gures]

“rich in harmony” [Type C; faster values; chromatic bass and �gures]

Chorale:

6 6 6 6 6 6 666 65 5 5

648 74 4

¢2

# #n8

87

7# #

1 2 3 4

5 6 7

{

{

c

c

&b

?b # n #

&bn n

n

n

?b # #n n n n b#

œœœ œœœ œœ# œœ œ œ# ˙ œ œ œ œ œ œ# ˙ œœ œ œ œ œ œ# ˙ œœœ œœœ œœœ œœ œœ œ ˙

œ œ œœ œœ ˙œ ™ œj ˙ œœ œœ œ

œ œœ

œœ

œ ˙

œ œ ˙ œœ œœœ œœ œœ

œœ

œ ˙

œ œ ˙ œ œ œœœ

œœ œœœ ˙

‰œ œœJ

œœ œb œœ œ# œ œ ™ ˙œ#J˙ ‰

œ œœ#J

œœ œn œœ œ# œ œ œ# ˙ œ œœ œœœ œœ# œ œn œ ˙œ œ œ œ œ œ#

#

˙

‰ œj œ œ œ

œœ œ œ

œœ œb œ œ# ˙ ˙

œ œ œ# œn ˙ ‰ œj œ œ# œ œœ œ œ œ œ

œœ œ œ œ ˙ œ œ œ œ# œ œ œœ œ œ

œœœ œ œ œ ˙

œ œ œ ˙

c&b œ œ œ œ ˙ ˙

n

n n

n b b# # # # # # #

“natural bass” [Type C; homophonic; disjunct]

“good bass”[Type C; homophonic]

“more artful bass”[Type C; chromatic bass]

“pure and chromatic bass”[Type C; chromatic upper voices]

“a little too sharp”[Type C; disjunct]

“natural bass”[Type B; disjunct]

“beautiful”[Type B; conjunct]

“clever”[Type B; homophonic]

“harmonic”[Type C; suspensions in all voices]

“chromatic”[Type C; chromatic bass & tenor]

Chorale:

Chorale:

“too foreign to the chorale”[Type C; chromatic]

6 6 6 6 6 6 6§

§

6 6

6 6 665

65

65

65

6 6 65

5 5 565

55

5 54

44

64

64 n56

4

4¢

2

4 42

7 78 83

3

83 3

¢3

3

43

3 33

7 7

8 7#

8 778 7#

8 7#

8 9 10 11 12

13 14 15 16 17 18

{

{

&b n # n # n b# #b

# n # #

?b

&b # n b

?b

œœœœœ ˙

œ œœ˙œœ œœ

˙˙ œ

œœœœ ˙

œ œœ˙œœ œ ˙œ œ ˙ œœ œœ œ

œœ œœœ ˙œ œ# ˙˙ œœ œnœ œ

œœ œœœ ˙œ œ# ˙˙ œœ

œœ œ

œœ œœœ# œœ œœ

˙˙

œ œ œ œ œ œ ˙˙ œ œ œ œ ˙ œ œb ˙ œn œb ˙

œ œ ˙ ˙b ˙ œ œ# œ œ œ œn œ ˙

œœœ œ œœ œœ œœ# wœ œ ww

œœ œ œœ œ œ

œœ œœ# wœ œ ww œœœ œ œœ œ œœ œ œ wœ œ ww œœ ˙

œ œ œœœœœ#œ

wwœ œ w

œœœœœœ œœœ

œœœ wœ œ œ ˙œ œ œ œ œ œn Œœœ œ œœ œ œ

œœ œœœ# wœœ œœ œ œ Œœ œ Œ

œœ œ œ w

œ œ œ œ wœ œn œ œ# w

œ œ œ œ w œœ œ œœœ œ œ œ œ œ

œœ œ œ# œn œ# œ ˙

&b

&b

œ œn œ œ ˙ ˙#

œ œ œ œ w

œ

Example 12Kittel’s harmonizations of Jesu meine Freude from Der Angehende Praktische Organist (Erfurt 1808, 1:30–32).


separate step from composing the figures and middle voices (Stage 2b) in theory, but

in practice, one assumes that a fluent knowledge of the Rule of the Octave (discussed

below) would mean that the student already knows which figures are implied by a

particular bass scale degree. That is, Stages 2a and 2b are only separate in theory. That

is why Stage 2a is illustrated using Example 12, even though this example includes

middle voices.

Examples 12.1 through 12.7 all ornament the same chorale phrase, shown above in

the single staff. The central point conveyed in these examples is that each harmonization

becomes increasingly more complex, gradually progressing from nearer to Type A in

Kirnberger’s classification to nearer Type C (never reaching Type D, however). That

is, like Knecht, Kittel’s harmonizations transition from more Choralbuch-like to more

Choralgesang-like. The difference is that the “complexity” now focuses on harmonic,

rather than ornamental variety, as in Stage 1. After Example 12.7, the ornamentation

“resets” for the next phrase of the chorale melody in Example 12.8, and Kittel starts

over in a simpler style with the description “natural bass,” meaning diatonic and mostly

triadic. Although Kittel’s path from simple to complex harmony does not traverse

Kirnberger’s four-fold classification (A, B, C, and D) exactly, it is clear that for both

Bach pupils, each chorale phrase functions like a cantus firmus, or stable reference

point, for increasingly complex harmonizations.12

Stage 2b: Adding Figures and Middle Voices

After having composed a bassline, students add figures and middle voices.

Example 13 outlines the most prevalent types of figures in a manner similar to the

bassline types in Example 11. (“N” stands for “neighbor” and “P” for “passing.”)

Examples 14 through 17 come from a very important treatise by David Kellner (1670–

1748) called Treulicher Unterricht (Hamburg 1732). Though Kellner never studied

with Bach, his treatise is relevant to the present article for several reasons. First, Georg

12 Kirnberger, Koch, and Wiedeburg repeatedly refer to the chorale as a cantus firmus (Kirnberger 1982; Koch 1782, 231–374; Wiedeburg 1775). While one tends to associate the term with species counterpoint today, in the eighteenth century it merely referred to a melody—either a Protestant chorale or a Catholic chant.

Diatonic vs. Chromatic

Homophonic vs. Faster non-CT’s (N, P )

Suspensions

Imitative of the Chorale/Each Other

Example 13. Types of �gures (i.e., Middle Voices)

Example 14. Kellner’s �gures for the Rule of the Octave from Treulicher Unterricht (2nd ed. 1737, 31)

{

{

853

643

863

653

853

863

653

853

853

863

´43

853

642

863

643

853

&

?

&

?

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w w w w w w w w

%%%

%%%

%%%# %%

%%%%

%%%

%%% %%%

w w w w w w w w

Hypothetical realization (my own):

Hypothetical realization after Rameau, Traité de l’harmonie, who uses the same �gures (1722, 232):

Example 13Types of figures (i.e., Middle Voices).


Philipp Telemann (1681–1767), godfather to C. P. E. Bach, endorsed the second edition,

showing Kellner’s basic accuracy and an indirect link to the Bach family. Second,

Kellner’s treatise was enormously popular, going through eight editions between

1732 and 1791, the first of which sold 2,000 copies (according to Telemann’s preface).

Such an impressive print run stands in stark contrast to Johann David Heinichen’s

(1683–1729) monumental treatise, Der General-bass in der Composition, which only

had one edition in 1728. But Heinichen is still relevant for us because Bach knew his

treatise, selling copies of it from his home in Leipzig (Leaver and Zager 2017, 18). Yet

Heinichen’s treatise is clearly aimed at the extremely gifted, would-be Kapellmeister,

whereas Kellner’s treatise is intended for less gifted pupils who would take more modest

positions. Because of this difference in intended audience, Kellner’s treatise is more

representative of the average level of knowledge that most eighteenth-century German

keyboard players possessed. Bach’s more famous pupils tend to be remembered, but one

should keep in mind that he had a constant stream of students of varied abilities. This is

all to say that one should not discount Kellner as a window into Bach’s musical culture

merely because Kellner’s treatise is aimed at less talented students. Besides, Kellner

borrows heavily from Heinichen anyway. In sum, Kellner’s basic accuracy, popularity,

introductory level, and his connection to Heinichen and Telemann justify his inclusion

here, even though Kellner was not a Bach student.13

Examples 14 through 17 provide the most important figures in Kellner’s treatise.

All are taken from the second edition (1737) because this is the one Telemann endorsed.

Example 14 is Kellner’s Rule of the Octave, which assigns normative figures to each

bass degree in ascending and descending conjunct motion.14 The Rule of the Octave is

the basic point of departure for harmonizing unfigured basses, but of course basslines

do not always move by step and are not always this consonant. Kellner says that some

variety (i.e., leaps) comes through chordal inversion [Umkehrung or Verkehrung], as

shown in Example 15. According to Kellner, the unprepared dissonant bass note F

at Example 15c is justified through an inversion of the parts in Examples 15a and

15b.15 Unlike Kirnberger, Kellner’s (and Heinichen’s) understanding of inversion exists

13 The first English translation of Kellner is forthcoming with a modern edition of the Sibley Choralbuch (Leaver and Remeš, eds. 2018).

14 The figures are Kellner’s; the ascending harmonization is borrowed from Rameau, but it corresponds exactly to Kellner’s figures.

15 Kellner writes, “Those who are not fully educated in this matter are confused, and ask ‘From where does this unprepared dissonance [at Example 15c] come?’ because, for all they know, this is the only way such an inversion may be allowed. The following example [Example 15] serves to explain this matter. At (c), the second note [bass note F] represents an inversion of the parts that had occurred in the second chords of (a) and (b)” (1737, 40). “Diejenigen, so in dieser Sache keinen vollkommenen Unterricht haben, verwundern sich, woher


independently from Rameau’s fundamental bass theory—for Kellner, and indeed, most

Germans in the first half of the eighteenth century, inversion simply means a swapping

of parts, without reference to a generative root. Thus, as Example 15 demonstrates, the

Rule of the Octave may also determine the implied harmony of leaping basslines, even

when they involve unprepared dissonances.16

dann diese unpræparirte Dissonanz entstehe? daher können sie allhie begreiffen, daß eine sothane Verkehrung der Stimmen es zulasse. Nachgeseztes Exempel kan die Sache mehr erläutern. An statt der zweyten Note so wohl bey (a) als auch (b) findet man bey (c) die Umkehrung auch bey der zweiten Note.”

16 Kellner writes that “While it may often seem that, in modern compositions, composers omit preparations when they are forced to do so, in reality, this arises from the inversion [Verwechselung] of voices, because, at the moment of the dissonance, the bass trades places with an upper voice, a topic which was already mentioned in certain places [in this treatise]” (1737, 89). “Indessen scheinet es offt in den modernen Compositionen, als wann

Diatonic vs. Chromatic

Homophonic vs. Faster non-CT’s (N, P )

Suspensions

Imitative of the Chorale/Each Other

Example 13. Types of �gures (i.e., Middle Voices)

Example 14. Kellner’s �gures for the Rule of the Octave from Treulicher Unterricht (2nd ed. 1737, 31)

{

{

853

643

863

653

853

863

653

853

853

863

´43

853

642

863

643

853

&

?

&

?

%%%

%%% %%%

%%%

%%%

%%%

%%%

%%%

w w w w w w w w

%%%

%%%

%%%# %%

%%%%

%%%

%%% %%%

w w w w w w w w

Hypothetical realization (my own):

Hypothetical realization after Rameau, Traité de l’harmonie, who uses the same �gures (1722, 232):

Example 14Kellner’s figures for the Rule of the Octave from Treulicher Unterricht (2nd ed. 1737, 31).

Example 15. Kellner on chord inversion (2nd ed. 1737, 40)

(a) (b) (c)

[ ]6

643

65!

642

? ˙ œ œ ˙ œ œ ˙ œ œ

s 8t

8e

7 w 7e

6e

6y

6w

8t

8t6

6®2

6

6r

5ib2

5 - 6

aug. 5th

aug. 6th

dim. 4th

5 b

baug. 2nd

¢

4

4 - 3

4e

5w

4w

9u -[ 8y

9y

9r9 - 8

9

7 - 6

7

7y

6

6

6r --[ 5e

6 - 56t

3

3

5

5w

5e5

3

5e3

¢e

8e

8e8

3

8e

7rs

The most common [abbreviated] signatures

The required voices to be added

Example 16. Kellner’s tables of signatures (2nd ed. 1737, 28)

Example 15Kellner on chord inversion (2nd ed. 1737, 40).


Example 16 reproduces Kellner’s two tables of signatures, in which he gives

all the most common abbreviated figures on the left, and the required intervals to be

added on the right. Such a concise reference of available figures would be very useful for

harmonizing an unfigured bassline. But Kellner’s most useful and enduring contribution

to figured bass pedagogy is shown in Example 17. Whereas the Rule of the Octave in

Example 14 focuses mostly on consonance, the two tables in Example 17 summarize

Kellner’s conception of dissonance. These tables outline a method for adding dissonant

figures to an unfigured bassline in the clearest manner of any source known to the

present author. The tables are essentially a digest of Heinichen’s chapter on unfigured

basses (1728, 2:725–768). Indeed, that Wiedeburg referenced these tables fifty years

after its publication is an indication of their lasting pedagogical value (1765–75, 3:2).

As in the Rule of the Octave, the first parameter in Example 17 is the scale degree

of the bass note, listed in the left-hand column. The second parameter is the type of

die Componisten, da, wo es nothwendig erfordert wird, die Præparation nicht observiret: Solches aber entstehet nur aus der Verwechselung der Partien, weil bey der Dissonanz die Baß-Note in die Ober-Stimme, und eine von den Ober-Stimmen in den Baß gesezt werden, wovon an einigen Orten schon vorher Erwehnung gethan.”

Example 15. Kellner on chord inversion (2nd ed. 1737, 40)

(a) (b) (c)

[ ]6

643

65!

642

? ˙ œ œ ˙ œ œ ˙ œ œ

s 8t

8e

7 w 7e

6e

6y

6w

8t

8t6

6®2

6

6r

5ib2

5 - 6

aug. 5th

aug. 6th

dim. 4th

5 b

baug. 2nd

¢

4

4 - 3

4e

5w

4w

9u -[ 8y

9y

9r9 - 8

9

7 - 6

7

7y

6

6

6r --[ 5e

6 - 56t

3

3

5

5w

5e5

3

5e3

¢e

8e

8e8

3

8e

7rs

The most common [abbreviated] signatures

The required voices to be added

Example 16. Kellner’s tables of signatures (2nd ed. 1737, 28)

Example 16Kellner’s tables of signatures (2nd ed. 1737, 28).


bass motion: either ascending or descending, and either conjunct or disjunct. The four

columns to the right show how the available dissonant figures depend on the type of

bass motion: first, for ascending stepwise motion; next, for descending stepwise motion;

then, for either ascending or descending stepwise motion; and finally, in the far right

Example 17. Kellner’s tables of available dissonances (2nd ed. 1737, 96–97)

MAJOR KEYS

MINOR KEYS

s s s

dim. 7th*

aug. 5th

5 b

5

§ t

¢

7

7

7

7

9b

b

§ t b

6 t b b

b

b

b n

6rs

6rs

6rs

6®s 6®d

7rs

6rd

6®d

5rs 6rs

6rd

§rd

§rd

[TYPE OF BASS MOTION]

BASS SCALE DEGREEIN [STEPWISE] ASCENDING

ONLY

IN [STEPWISE] DESCENDING

ONLY

IN [STEPWISE] ASCENDING

OR DESCENDING

THESE FIGURES DO NOT REFLECT [STEPWISE] ASCENDING OR

DESCENDING MOTION [i.e. LEAPS]

2

3

4

5

6

7

[TYPE OF BASS MOTION]

BASS SCALE DEGREEIN [STEPWISE] ASCENDING

ONLY

IN [STEPWISE] DESCENDING

ONLY

IN [STEPWISE] ASCENDING

OR DESCENDING

THESE FIGURES DO NOT REFLECT [STEPWISE] ASCENDING OR

DESCENDING MOTION [i.e. LEAPS]

1

2

3

4

5

6raised

loweredaug. 2nd aug. 6th

7raised bdim. 4th, 5

dim. 7th

lowered

1

*

*

*When scale degree four in the bass is raised a semitone.

7 9

7

7

9

7

5 r -e2 w

5rs 6rs5 w

5 r -e

6 r -[ 5e

6 r -[ 5e 7 y 7 t 6r 5r -e 7 9

9

7

7

9

7 9

9

9

7rs 75 r -e 6 r -[ 5e 9

7 9

5 r - 6 r -[ 5 7 y 7 t 6r 5r - 7 9

[ ]

n[ ]

Example 17Kellner’s tables of available dissonances (2nd ed. 1737, 96–97).


column, for leaps, which has the most available dissonances.17 In sum, Examples 14

through 17 represent the essentials of a very popular method for training eighteenth-

century German students to figure an unfigured bassline. In fact, these examples likely

represent a base level of knowledge that many students were familiar with. And since

Example 17, in particular, is a refinement of many of Heinichen’s ideas, and because

Telemann (godfather to Emanuel Bach) endorsed the second edition of Kellner, it is all

the more likely that J. S. Bach may have used similar methods with his own students

and conceived of this process in a similar way. If Bach’s students were to use a method

similar to Example 17, their task would be simplified because the chorale melody is

always given. That is, a given soprano note restricts the choice of figure for a given bass

note, simplifying the harmonization process.

Kittel and Kirnberger, two of Bach’s students, provide the best models for how

Stage 2 of Bach’s pedagogical method works in practice. Multiple-bass chorales figure

prominently in both of their pedagogical methods, and they both claim their methods come

from Bach, at least in part.18 Example 18 is from a manuscript attributed to Kittel (1791).

The chorale is given at the top, followed by eight basslines. Each chorale phrase is labeled

in brackets using Kirnberger’s harmonic types (Example 10) and the bassline descriptions

(Example 11), just as in Example 12.

The most notable feature of these eight basslines is that they begin in the homophonic

Choralbuch style and end in an ornamented Choralgesang style. This is more due to a

gradual acceleration of surface rhythm (from half notes to quarter notes) than due to a

progression through Kirnberger’s harmonic Types A–D, even though the last harmonization

does use all Type C. At this point it must be emphasized that while the Choralgesang style

is usually used for voices, it need not be. Basslines six and seven in Example 18 are indeed

ornamented, but the leaps resemble a more active, instrumental style than flowing, vocal

style. Still, the overall trend exhibited in the eight basslines is toward smaller note values,

more tonicizations, and more suspensions. These factors are in keeping with the description

of the Choralgesang style given in the first part of this article.

17 Example 17 includes only one chromatic alteration: the raised fourth degree. The same occurs in Wiedeburg’s table for harmonizing chorales (1765–75, 3:359). Wiedeburg dedicates two chapters to chorale harmonization and includes a chorale with one hundred basses (1765–75, 3:504–534)! I discuss Wiedeburg in greater depth in my forthcoming dissertation, which addresses the compositional pedagogy of Bach and his contemporaries.

18 Kittel claimed that his teaching was framed “entirely according to Bachian principles” (McCormick 2015, i). Kirnberger also claimed his ideas were rooted in those of J. S. Bach: “His [J. S. Bach’s] method is the best because he proceeds step by step from the simplest to the most difficult, whereby even the step to fugue itself is no more difficult than any other step. For this reason, I consider the method of Johann Sebastian Bach to be the only and best one” (Kirnberger 1986, 75). Admittedly, this comment was made in the context of evaluating counterpoint treatises, not chorale harmonization.

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MU

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BA

SSE

Sm

ore

Cho

ralb

uch

styl

em

ore

Cho

ralg

esan

g st

yle

21 CHORALE (four phrases)

[Type C; homophonic; diatonic] [Type A; homophonic; diatonic] [Type B; homophonic; diatonic][Type C; homophonic; diatonic]

[Type C; homophonic; diatonic]

[Type C; homophonic; diatonic]

[Type C; homophonic; diatonic; conjunct]

[Type C; bass suspension]

[ ]

[Type C; bass suspension]

[Type C; conjunct; chromatic]

[Type B; disjunct]

[Type C; disjunct; upper suspensions]

[Type B; faster values]

[Type B; faster values; conjunct] [Type C; faster values]

[Type C; faster values] [Type C; faster values; suspensions] [Type C; faster values] [Type C; faster values]

[Type C; faster values]

[Type C; faster values; suspensions] [Type C; faster values; suspensions]

[Type C; faster values; upper suspension]

[Type C; faster values; suspensions]

(imitation)

[Type C; disjunct; upper suspensions] [Type C; conjunct; upper suspensions]

[Type C] [Type C] [Type B; conjunct]

[Type C; conjunct; chromatic]

[Type B; diatonic; conjunct] [Type B; diatonic; conjunct]

3 4

{

°

¢

™™

™™

™™

™™

™™

™™

™™

™™

™™

1.

2.

3.

4.

5.

6.

7.

8.

´ 6 6 4 3 6 6 6 4 3 6 6 4 # 6 6 6 48

37

83

24

6 ´ 6 64

53

6 6 48

37

6 6 64

6 4 # 6 64

53

6 6 65

8 7

6 65

8 7 6 5 5 ´ 35

42

6 43§

6 42

6 4 37

42

6 6 65

7#

4 3 65§

4 3 - 6 48

37

83

6 6 6 4 3 4 6 6 6 4 3 53

43

6 6 6 6 4 # 65

53

53

6 65

8 7 83

6 8 7 7 ´ 4 3 6 65

9 8 4 3 64 3

9 8 48

37

42

6 43

6 4 # 43

4 3 64 3

5 6 48

37

83

53

6 6 4 3 6 65 4

53

--5 6 4

837

83

83

--

6 43

4 3 52

--

7#

42

6 65

53

6 7 6 48

37

83

7 ´ 6 6 4 3 8 7 6 6 6 6465

42

6 48

37

83

53

6 42

6 436 ´ 4 # 6 7

§53

53

6 65

8 7

65 6 6 4 3 - 6 65986 6

453

52

--9 6 6

58 7 5

364

6 53

42

3 65

9 8 53

64

- 6 6 9 3 65

8 7

&# U U U U

?#

?#

?#

?#

?#

?#

?#

?#

˙ ˙ ˙ ˙ ˙ ˙ w ˙ ˙ ˙ ˙ ˙ ˙ w w ˙ ˙ ˙ ˙ ˙ œ œ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ w w

˙ ˙ ˙ ˙ ˙ œ œ w ˙ ˙ ˙ ˙ ˙ ˙ w w˙ ˙ ˙ ˙ ˙

˙ w ˙ ˙ ˙ ˙ ˙ ˙ w w

˙w ˙ ˙ ˙ w ˙ ˙ ˙ ˙ ˙ ˙ w w ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ w

˙ ˙ ˙ ˙ ˙# ˙ wn ˙ ˙n ˙ ˙ ˙ œ œ w w ˙ ˙ ˙ ˙

#

˙ ˙ w˙ ˙ ˙ ™ œ ˙ ˙ w w

˙ ˙ ˙ ˙ ˙œ œ w ˙ ˙ ˙ ˙ ˙ ˙ w w ˙ ˙ ˙ ˙ ˙ ™ œ w ˙ ˙ œ œ ˙ ˙ ˙ ˙ ˙ w

˙ œ œ ˙ ˙ ˙˙ w ˙ ˙ ˙ ˙ ˙ ˙ w w ˙ ˙ ˙ ˙ ˙ ˙ w ˙ ˙ ˙ ˙ ˙ ˙ w w

˙ œ œ œ œ ˙ ˙ œ œ w œœœ œ ˙ ™ œ˙ ˙ w w œ

œ œ œ œ˙ œ ˙ ˙ ˙

˙œ œœ œn œœœ œ œ œ ˙ ˙ w w

˙ ˙ œœŒ œ œ œ œ œ w ˙ œ œ œ œ œ œ˙ œ œ w w ˙ ˙ ˙ œ œ œ œ ˙ w œ œœ œ œ œ œ œ œ

œ ˙ ˙ ˙ ˙ w

˙#

Original Key: G Major#

œ œn œ œ œ œ œœœœ

œ w œ œn

n

n

n

n

3n

œ œ œ œœ˙ ™ œ# œ

œ ˙ ˙ w œ œ# œ œ œ œ w ˙# ˙˙

œn œ œ œn œ œ ˙ ˙# œ œ œ œ ˙ w

Example 18. Kittel’s multiple basses for Liebster Jesu wir sind hier from 25 Chorale... (ms., Erfurt, 1791)

Example 18Kittel’s multiple basses for Liebster Jesu wir sind hier from 25 Chorale... (ms., Erfurt, 1791).


Example 19 by Kirnberger exhibits the same overall trend from the Choralbuch

style to the Choralgesang style, but in a different way than Kittel. Whereas Kittel used more

varied rhythms and more conservative harmonies (never reaching Type D), Kirnberger’s

settings remain in half notes throughout and become much more chromatic.19 For

example, consider the last two basslines—Type D in Kirnberger’s classification. Given the

criticisms of the complexity of Bach’s vocal chorales quoted above, it seems likely that

this level of chromaticism would not usually be appropriate for organ accompaniment of

congregational singing, which was Kittel’s primary goal. Rather, Kirnberger is testing how

far he can take the chromaticism as a compositional exercise. Thus, Kittel and Kirnberger’s

different approaches to multiple-bass harmonization are the result of their different goals:

Kittel is training organists to accompany congregations, while Kirnberger is training

composers. For this reason (and as a rhetorical appeals to copia, or abundance), Kirnberger

is adamant that countless variations are possible beyond the twenty-six harmonizations

he gives.20 Therefore, it seems that Stage 2 in Bach’s pedagogy was designed to explore

the full range of harmonic resources and ornamental possibilities with the chorale melody

held constant as a cantus firmus. Such a pedagogical strategy would be especially fitting

for a composer like Bach, whose explorations of “the possible” in nearly every genre and

style of his day still move and fascinate listeners three centuries later.

Summary and Conclusion

Leaver’s recent reassessment of the Sibley Choralbuch suggests the existence

of two distinct styles of chorale harmonization in Bach’s pedagogy—the Choralbuch

style and the Choralgesang style. I argue that Bach’s two-stage method described by C.

P. E. Bach bridges between the two types of realization. In Stage 1, which addressed

texture, Types 1, 2, and 4.1 belong to the homophonic Choralbuch style, whereas

Types 3 and 4.2 belong to the ornamented Choralgesang style. In Stage 2, which

addresses harmony and simple outer-voice counterpoint, realizations in the Choralbuch

style tend to use harmonic Types A and B because these are diatonic. In contrast, the

Choralgesang style tends to use Types C and D because these are more chromatic. The

chorale remains a cantus firmus, or fixed point of reference throughout both stages.

Eventually the restriction of the chorale framework was discarded and Bach’s lessons

19 The quoted descriptions in Example 19 are Kirnberger’s; the bracketed text is mine.

20 He writes that “We cannot help being amazed at the variety that harmony offers. The harmonies that could be used with this melody are not at all exhausted by these twenty-six basses. If one now considers that at least as many melodies can be written to each of these basses, that each melody can be changed again in countless ways by florid counterpoint—what wealth, what diversity!” (Kirnberger 1982, 305–6).

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more C

horalbuch stylem

ore Choralgesang style

Example 19. Kirnberger’s multiple basses (selection from 26 total) from The Strict Art (1982 [1771–91], 300–305)Ach Gott und Herr, wie gross und schwer sind mein be - gang - ne Sün - den

CHORALE:

2”Natural” [Type C; disjunct]

”Greater variety”[Type C; disjunct]

“Foreign Dominants” [Type C; mostly conj.]

“Contrary motion”[Type C]

“Parallel motion”[Type C]

[Type C; conjunct;very chromatic]

[Type C; conjunct; little chromaticism]

[Type C; chromatic; contrary motion]

“Contrary motion”[Type C/D;very chromatic]

“Canonic Imitation”

[Type D; disjunct]

[Type D; conjunct]

{

°

¢

1.

2.

3.

8.

12.

14.

16.

17.

18.

20.

24.

26.

§ 6 6 6 6 § 6 4 § 6

§ 6 y 6 §65 § 5

65

r2 ´ 6

5 6r2 6

65

65 y

64

r2 6

42 ´ m ´ 6

I2

65 y

m 2 6 2 6 m 7 § 754

7e 7

7§ 6 6

65 6 6 6 y 6

54

R2 6 y

6 7 2 6 7 5 6 § 7 Y 6

mRC

6B

4C N 7 C m 7 § 6

65 2 6 y

7 § 6 7 y 6r2 6

65 §

7§

4§2 6 2 6 7 6 6

465 2

65

§4

§4

§42 6 6§

6 6 2 n 42 6 6 6 6

65 § !

42 m

831

-42

753 5

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m5

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53 y

C

C

C

C

C

C

C

C

C

C

C

C

C

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?bb

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?bb

?bb

?bb

?bb

?bb

?bb

?bb

˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ w ˙ ˙

˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ œ œ w ˙ ˙

˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙˙ ˙ œ œ ˙ ˙ ˙ ˙ ˙ ˙

˙ ˙ ˙# ˙ ˙ ˙ ˙ ˙ ˙# ˙ ˙ ˙ ˙ ˙n ˙# ˙ ˙

˙ ˙ ˙ ˙ ˙b ˙ ˙ ˙ ˙n ˙ ˙ ˙n ˙ ˙ ˙n ˙ ˙

˙ ˙ ˙n ˙b ˙ ˙b ˙ ˙ ˙ ˙ ˙n ˙ ˙n ˙ ˙# ˙ ˙#

˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙n ˙ ˙ ˙ ˙ ˙

˙ ˙ ˙ ˙ ˙b ˙ ˙ ˙ ˙n ˙ ˙ ˙ ˙ w ˙ ˙

˙n ˙ ˙ ˙ ˙b ˙ ˙# ˙b˙n ˙ ˙n ˙ ˙ w ˙ ˙

˙ ˙n ˙ ˙b ˙n ˙ ˙ ˙b ˙ ˙n ˙ ˙ ˙ ˙ ˙ ˙ ˙

Ó Ó˙ ˙ ˙b ˙ ˙ ˙ ˙n ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙

˙ ˙ ˙n ˙ ˙b ˙ ˙b ˙b ˙ ˙n ˙ ˙n ˙ ˙n ˙ ˙b ˙b

Ó ˙ ˙n ˙ ˙ ˙ ˙ ˙b ˙ ˙ ˙ ˙n ˙# ˙ ˙˙ ˙b

4 6 8M

ULT

IPLE BASSES

Example 19Kirnberger’s multiple basses (selection from 26 total) from The Strict Art (1982 [1771–91], 300–305).


would then address fugal composition. But even here the pupil was not completely

untethered, because the conceptual framework of figured bass had been internalized

and likely continued to inform the composition of free, contrapuntally oriented works.

That is, upper voices were still determined primarily by the bass scale degree in both

harmonically and contrapuntally oriented genres.

Bach’s ordering of topics—figured bass, chorale harmonization, fugue—implies

that he viewed an understanding of figured bass as a prerequisite to the study of fugue.21

And since Bach was training composers, it seems likely that his pedagogical method

would reflect his own compositional outlook. Although one often associates figured

bass more with harmony than with counterpoint today, the pedagogical method

reconstructed in this article (and, indeed, the early seventeenth-century origins of

figured bass) suggest that one should view thoroughbass as equally capable of describing

vertical and horizontal dimensions of music. These findings suggest two directions for

the future: first, an increased reliance on figured bass and bass-degree-oriented thinking

in analyses of contrapuntal genres; and second, a more consistent emphasis on figured

bass and the Rule of the Octave in music theory pedagogy, regardless of whether one is

teaching “harmony” or “counterpoint.”22 Like Bach’s method, where the chorale was a

musical cantus firmus for realizations that bridge from homophony to ornamentation,

so should figured bass act as a conceptual cantus firmus—a theoretical bridge between

harmonic and contrapuntal modes of thought.

21 McCormick (2015, 246) and Renwick (2001, 1–8) also describe a pedagogical progression from figured bass to fugue in connection with J. S. Bach.

22 The strict division between “harmony” and “counterpoint” which became so prevalent in the Paris Conservatory in the nineteenth-century (and largely characterizes present-day thought) was foreign to the eighteenth century.


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