Brinkman - The Melodic Process in J S Bach Orgelbuchlein - Music Theory Spectrum-1980

The Melodic Process inJohann Sebastian Bach's Orgelbachlein

by Alexander R. Brinkman

Introduction

A number of scholars have briefly addressed the subject ofmotivic derivation in the Orgelbiichlein . They agree that most ofthe preludes in this set are based on recurrent motives, but noone has thoroughly investigated the derivation of the con-trapuntal lines. The following statement by Spitta reflects thepredominant view:

Though the motives of the counterpoint are for the most part indepen-dently devised, in three of these chorales they are evolved out of thefirst line of the tune, and in this way they have an inherent organicconnection with the chorale itself. These three are: "Dies sind dieheilgen zehn Gebot" ... ` `Helft mir Gott's Giite preisen" . . . [and]"Wenn wir in hochsten •othen sein . " 1

Material for this paper was drawn from the author's Ph.D. Dissertation,Johann Sebastian Bach's ` Òrgelbiichlein" : A Computer-Assisted Study of theMelodic Influence of the Cantus Firmus on the Contrapuntal Voices (Ann Arbor:University Microfilms International, 1978) [#7817560]. An abbreviated ver-sion of this paper was read at the International Computer Music Conference(Northwestern Univ., November 1978) .

1 Philipp Spitta, Johann Sebastian Bach, 3 vols., trans. Clara Bell and J.A.Fuller-Maitland (London: Novello & Company, Ltd., 1889, reprint ed., NewYork: Dover Publications, Inc., 1952), 1:600.

Schweitzer also believed that the motives were newly invented,but that they were chosen to reflect the spirit of the text or toilluminate Bach's sentiment about it:

Towards the end of the Weimar period, however, he [Bach] becomesindependent of his masters and produces a type of his own—the choraleprelude of the Orgelbūchlein. In this the melody is used as a cantusfirmus, unaltered and uninterrupted, usually in the uppermost voice;round it plays an independently conceived motive, not derived fromany of the lines of the melody, but prompted by the text of the chorales,and embodying the poetic idea that Bach regarded as characteristic formusic and expressible in musical terms. 2

This point of view has been perpetuated by later authors who didnot reexamine the premise upon which it was based.

The study described in this paper used extensive computer-assisted analysis to test another hypothesis—that much of thecounterpoint is derived from contours of the chorale tunes them-selves. Most scholars acknowledge Bach's derivation ofmotivic material in his fugues and inventions from the subject

2Albert Schweitzer, J.S. Bach, 2 vols., trans. Ernest Newman (Leipzig:Breitkopf and Hartel, 1911, reprint ed., New York: Dover Publications, Inc.,1966), 1:283 — 84.

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Melodic Process in the Orgelbūchlein 47

and countersubject. The melodic process in the chorale pre-ludes, however, is less obvious and not so well understood.Those writers who have noted the use of melodic material fromthe chorale tune in the counterpoint of Bach's chorale preludesusually cite the outline of the tune in peak notes or on strongbeats, or the use of the incipit of the tune in Vorimitation. Thisparody technique, shown in Figure 1, usually occurs in largerchorale preludes such as the 17 Chorales or the large preludes inthe third part of the Clavier- Ubung .

The impetus for this project was Bach's organ setting of AchGott and Herr (BWV 693), in which practically every note ofthe counterpoint is derived from the chorale tune. The processcan be characterized as direct borrowing of melodic contoursfrom the tune. These borrowed contours are transposed, se-quenced, inverted, set to varied rhythms, and woven into atightly-knit fabric that is completely generated by the cantusfirmus. Figure 2 shows the chorale tune Ach Gott and Herr andBach's organ setting. The contours found by the computer aremarked on the music and identified by numerical labels gener-ated by the computer program. Table 1 lists the frequency ofoccurrence for each matching contour and the phrase fromwhich each contour was derived.

Was Ach Gott and Herr an isolated case, or did it illustrate atechnique that might occur in other compositions of the samegenre? Analysis of other preludes produced enough evidence tojustify more intensive research, and eventually the forty-eightorgan chorales of the Orgelbiichlein were chosen for furtherstudy . 3 These preludes are almost all short, and thus ideallysuited to the type of melodic borrowing under consideration. Inaddition, many of the preludes are composed with recurrentmotives that may be related to the chorale tune.

3Forty-five chorale tunes appear in the completed portion of the Orgelbiich-lein. Of these, Liebster Jesu wir Sind hier is set twice, thus most authors refer to45 chorales or 46 preludes in the set. However, Christ ist erstanden has adifferent tune for each of its three stanzas. These are set separately and aretreated as separated preludes in this study.

Table 1. Matching Contours (Prime and Inversion) in Ach Gott andHerr Listed in Decreasing Order of Frequency

Number Pattern Occurrences(Derivation)

31 (phrase 2)21 (phrase 1)14 (phrase 3)10 (*)6 (phrase 5)6 (*)6 (*)4 (*)4 (phrase 6)3 (phrase 4)3 (*)2 (*)2 (*)2 (2,4,6)2 (3,4)1 (5)

14)13)

1)7)

19)3)

16)15)2)

18)9)

17)4)

24)25)28)

+2 +2 +2 —2 —2 —2

—2 —2 —2 +2 —2 —2—2 —2 —2 +2 +2 —3 +2 —2 —2 —2 +2 —2 —2 +2 —2 —2 —2 +2 +2 +2 +2 +3 —2 —2—2 +2 +2 —2 +2 —2 —2 +2 —2 —2 —2 —2 +2 —2 —2+2 +2 —2 +2 —3 +2

*patterns that occur in phrase three but not in any other phrase of the chorale

tune.

Coding the Music

Though a number of viable coding schemes were available tothe analyst, most of these represent in code more informationthan was needed. It is axiomatic that more complex codingsystems increase program complexity and magnify the task ofcoding the music. Consequently it was decided to code contoursdirectly, using a coding scheme that is concise and mnemonic,but still adequate for the projected analysis.



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48 Music Theory Spectrum

Figure 1. Ornamented chorale tunes of the type used in larger choralepreludes

a) Allein Gott in der Hoh' sei Ehr' (BWV 260)

Figure 2. The chorale tune Ach Gott and Herr and Bach's setting fororgan (BWV 693)

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Melodic Process in the Orgelbuchlein 49

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This coding language, which we shall call MELCON (forMELodic CONtour), encodes only that aspect of the musicwhich is the object of this study, i.e. , melodic contour. Noattempt is made to represent rhythm or even actual pitches, andsince we wish to identify melodic motives occurring in differentparts of the diatonic scale, the code does not differentiate thequality of intervals. All seconds are represented by the integer 2,all fourths by 4, and all thirds, whether major, minor, or dimin-ished, by the integer 3. Chromatic inflections of the same pitchare represented by the integer 1. A plus or minus sign precedingthe integer indicates the direction. For purposes of this study,repeated notes and octave skips in either direction are consid-ered equivalent, and each is coded `+0' . During the codingprocess, compound intervals are reduced to simple ones. Theassumption of octave equivalence reduces to ten the symbolsrequired to encode a melody:

+-01234567

Thus, the first phrase of Lob sei dem allmachtigen Gott can berepresented as shown in Figure 3. Other symbols delimit mea-sures, phrases, parts, and pieces in the input stream:

Barlines (not used when coding the cantus firmus)Rests or end of phraseThe end of the cantus firmus or of a partThe end of a composition(The blank character) Separates all other symbols

Figure 3. The first phrase of Lob sei dem allma chtigen Gott in MEL-CON code

An Introduction to the Analytical Method

The computer program partitions each phrase of the choraletune into all possible ordered subsets — from the entire phrasedown to three-note patterns, represented by two intervals. 4 (SeeFigure 4) . A list is made of all of the melodic contours in thechorale and their frequency of occurrence. The list is then sortedin decreasing order by the length of the contours (starting withthe longest pattern) .

As each phrase of the prelude is processed, the slashes (repre-senting barlines) are removed, and the computer creates a paral-lel character string which indicates the number of the measure inwhich each interval occurs. (See Figure 5) . When each pair ofstrings is complete, it is added to a linked list. A linked list is achain of data items or nodes, each of which contains a pointer tothe next data item. 5 In this case the first field for each nodecontains the coded phrase, the second contains the measurenumbers, and the third points to the next phrase in the part. TheHEAD of the list is a pointer to the first phrase in the part. Thelinked list can be processed efficiently, and it is formed with theexact number of nodes needed to store each part, whether thatpart consists of only one or two "phrases" or many.

Pattern matching techniques are used to search each phrase ofthe prelude for melodic patterns derived from the chorale tune.The search begins with the longest contours, since these includethe shorter patterns derived from them. When a match is found,the matching contour is removed from the subject string and thecomputer prints out the pattern along with the part and measurenumber and an identification number. Inversions are found byinterchanging plus and minus signs in the code and repeating thesearch. The computer counts the number of times each contouroccurs in prime and inverted form. The frequency counts for

/RZX6 f

• . . G•

+3 +2 +2 +0 +2 -3 +2

4The computer programs for this project were written in the SNOBOL4 andPL/I programming languages.

5A pointer is the address of the next node in the computer memory.

MF



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Figure 4. Partitioning a chorale phrase Figure 5. Measure numbers in "parallel" character string

[+3 +2 +2 +0 +2 —3 +2] eight-note contour(the phrase)

seven-note contours

six-note contours

five-note contours

four-note contours

+3 +2+2 +2

+2 +0 three-note contours+0 +2

+2 —3—3 +2

N.B. Two-note patterns are accounted for by counting intervals in thechorale tune.

The string —2 —2+2/+3 —4+2/+2+2'becomes

Coded melodic contour : ` —2 —2 +2 +3 —4 +2 +2 +2 'Measure numbers : `01 01 01 02 02 02 03 03 '

each contour are stored, along with other pertinent information,on magnetic tape or disk.

To facilitate comparison of data from different preludes, a listis compiled of all patterns that occur in any of the chorale tunes.This list is sorted by length, and then each sublist is orderedaccording to the numeric values of the coded intervals — fromthe largest descending interval to the largest ascending interval.Printed tables enable the analyst to compare the frequency ofoccurrence of a contour in all preludes that have the contour intheir cantus firmi. A sample of this data is shown in Figure 6.

The programs described above simulate the manner in whicha human analyst might search for melodic contours in the con-trapuntal voices of the preludes. Patterns related to the cantusfirmus are located and tabulated, but the multitude of overlapp-ing contours within each primary pattern, and those dividedbetween one primary pattern and the next are disregarded. Otherprograms compile a list of all melodic contours in the preludes,whether or not the pattern occurs in the chorale tune. Becausethe number of patterns is large, this list was limited to patternsbetween three and six notes in length. 6 All overlapping patternsare included, and frequency counts for each melodic contour areextremely accurate. Figure 7 illustrates printout from theseprograms. The number between asterisks is the number of

6Even with this length limitation, records were kept of the frequency ofoccurrence of over 7600 contours in each of the forty-eight preludes.

[±3±2±2±0±2-3+2 +2 +0 +2 —3 +2

[±3 +2 +2 +0 +2+2 +2 +0 +2 —3

+2 +0 +2 — 3 +2

ŗ±3±2±2±o+2 +2 +0 +2

+2 +0 +2 — 3+0 +2 —3 +2

+3 +2 +2+2 +2 +0

+2 +0 +2+0 +2 —3

+2 —3 +2



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CHORALE

PATTERNNUMBER

NUMBER

02

2007

5310

1742

37OCCURS IN 4 CHORALE(S) .

OCCURS INCHORALE

2122

0 0 1 10 0 0 02 6 0 21 2 0 1

PRELUDE OCCURRENCEPRIME TOTAL INVERTED P+I


Figure 6. Data summary tables showing pattern-matching frequency for contours from the cantus firmus of each prelude

565) +3 +2 +2 +0 = 5-14708 (I)

CHORALE

PATTERN

OCCURS IN

PRELUDE OCCURRENCENUMBER

NUMBER

CHORALE

PRIME TOTAL INVERTED P+I04

23

1

0

1 0 023

47

1

0

0 0 035

31

1

1

1 0 1OCCURS IN 3 CHORALE(S) .

566) +3 +2 +2 +2 = 5 —14706 (I)

preludes in which the contour occurs. The tables show the totalnumber of occurrences of each contour in each prelude in theOrgelbūchlein . These data will be of primary importance indiscovering which contours may have been borrowed from thecantus firmus and which are merely idiomatic melodic patternsfound frequently in the style.

Interpreting the Data

The first step in the analysis was to mark on the music thematching contours identified by the computer. During the mark-ing process, relationships that seemed important were noted.Matching contours were then compared to see how they relatedto each other. The fact that most patterns are subsets of a longercontour or that many contours are derived from the same phraseof the chorale may be significant. Matching contours werechecked against the data summary tables to see if they occurredin other chorale tunes, and the frequency of occurrence in thetunes and preludes was compared. The second (larger) data



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Figure 7. Tables showing the total number of occurrences of sample contours in the preludes of the Orgelbūchlein

2910) +3 +2 +2 +0 /5-14708 (I)

*4*

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0

2911) +3 +2 +2 +2 /5-14706 (I)

*21*

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0 0 4 0 0 0 0 3 2 6 4 1 1 0 0 0 0 1 0 1 0 0 3 0

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

0 3 0 0 0 1 1 2 0 2 1 0 0 0 2 0 2 2 0 0 0 2 0 2

summary was used to determine the pattern of occurrence in allpreludes.

The musical context in which matching contours occurredwas instrumental in deciding the significance of contour rela-tionships. A melodic pattern that is clearly delineated by theinteraction of other musical parameters is more likely to beperceived as aurally significant than the same contour in acontext in which it is not differentiated from the notes around it.

When a contour from the cantus firmus seemed to be impor-tant in the prelude, the first stanza of the text was examined tosee if the melodic pattern could have been chosen for emphasisbecause of its textual significance. Finally, tables comparinginterval counts for chorale tune and prelude were examined. Itwas thought that a correlation between melodic interval types in

the prelude and cantus firmus might in itself suggest at leastminimal relationship between the two.

Summary of Musical Conclusions

The Chorale Tunes

A brief study of the chorale tunes used in the Orgelbiichleinwas a necessary adjunct to this study. It would be presumptuousto attach any significance to contours related to the cantus firmiwithout first developing some perspective on the melodic styleof the tunes themselves.

Possibly because of their rhythmic simplicity, chorale tunesare often considered a fairly homogeneous body of literature.



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The computer analysis proved that the tunes are quite diverse,both in number of derived contours and in melodic patterncontent. As part of the analysis, all of the melodic contours fromthree notes to the length of the phrase were extracted from eachcantus firmus. The number of distinct melodic contours gener-ated by individual tunes ranged from twenty-seven in Christe,du Lamm Gottes to 197 in Christum wir sollen loben schon. Thenumber of melodic contours derived from a chorale tune isdependent on many factors including form (the number of dis-tinctly different phrases), phrase length, and pattern redundancywithin the phrase.

The contours themselves proved to be surprisingly differen-tiated. The forty-seven tunes generated 1650 different melodiccontours. Table 2 shows that many of these contours are unique:72.7 percent occurred only in one chorale tune, while only .1percent occurred in forty or more of the tunes studied.

The Preludes: Melodic Influence of the Cantus Firmus on theContrapuntal Voices

Every prelude in the Orgelbiichlein is unique in its develop-ment of melodic and motivic ideas from the cantus firmus. Thefollowing summary is a synthesis of trends based on a carefulanalysis of all forty-eight preludes. The examples chosen toillustrate various conclusions are representative but not exhaus-tive. In many instances, the problem was not finding an exampleto illustrate a particular point, but deciding which example touse.

Derivation of Contours

Spitta recognized the melodic influence of the cantus firmusin only three preludes; in each of these, the recurrent motive isderived from the incipit of the first phrase of the chorale tune.While the incipit is the most obvious type of melodic derivation,it is not the only source of motivic material in the Orgelbiichlein .Important contours are often related to distinctive portions of the

Table 2. Distribution of Contours by Number of Chorale Tunes inWhich Each Contour Occurs

Number of Tunes inWhich Contour occurs

Number ofContours

Pecentage ofTotal Numberof Contours

40 or more30 or more20 or more10 or more5 or more4 or more3 or more2 or more

1 only

28

2554

122165256451

1199

.1%

.51.53.37.4

10.015.527.3

72.7

middle or end of phrases, and melodic derivation is not limitedto the first phrase of the tune. For example, the recurrent motivein Christ ist erstanden is derived from the unusual cadenceformula that concludes the second and fourth phrases. Figure 8shows the derivation of this contour. The contours labeled 31and 37 permeate the entire prelude.? Note that contour 37, thelower-auxiliary figure, is also the incipit of the first phrase of the

?The numeric labels used to identify contours were generated by the computerprogram for each prelude. Thus the same number may be used for differentcontours in other examples. Note that in many examples the entire texture willnot be shown—only the pertinent parts. When parts are omitted, numbers placedto the left of each staff will indicate which parts are shown.



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Figure 8. Derivation of recurrent contour from phrase 2 of Christ isterstanden (first stanza)

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chorale tune. It is not uncommon for a motive to be related totwo or more phrases.

Many contours other than the primary recurrent motive arerelated to the cantus firmus. Contours derived from an entirephrase or from a phrase without , the first and/or last note dooccur, although shorter contours are more common. In Figure 9,a contour from the middle of the second phrase of Wir dankendir, Herr Jesu Christ is imitated in the alto and tenor.

When Bach used an unusual variant of a phrase, contourswere sometimes derived from the more common version. Jesumeine Freude illustrates this point. In the Orgelbiichlein setting,Bach used an older version of the tune with a simpler setting of

the second, fifth, and eighth phrases (see Figure 10). Bachprobably used the earlier version of the tune in order to maintainthe tonic harmony for the first two beats of measures 5 and 15 inthe prelude, but the distinctive contours in the contrapuntalvoices are derived from the more familiar variant of the chorale.

The Function of Related Contours

Traditional contrapuntal terms, such as imitation and Vorimi-tation, are sometimes inadequate to describe the motivic activityin the Orgelbiichlein . While the function of related contours isnot always clear-cut, a useful distinction can be made depending



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Figure 10. Derivation and use of distinctive contours in Jesu, meineFreude from common version of phrases 2, 5, and 8

phrase 2,4 (Orgelbiichlein) phrase 8 (Orgelblichlein)

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on the location of the contour relative to the phrase from which itis derived. Most occurrences of related contous can be classifiedas recurrent, anticipative, concurrent, imitative, or reminiscent.

Recurrent contours are usually stated in the beginning of theprelude and pervade the contrapuntal fabric to the end. Thesecontours, usually accompanied by a characteristic rhythmicmotive, are perceived as the primary motive in the prelude.Figure 8 (above) illustrated a recurrent contour in Christ isterstanden.

Contours are anticipative when they precede the occurrencein the phrase of derivation. When the temporal proximity isclose, the phenomenon resembles Vorimitation in larger pre-ludes. But since there are few interludes between phrases, theanticipative contour frequently accompanies the phrase preced-ing the phrase to which it is related.

Imitative contours occur just after the contour from whichthey were derived. Unlike the traditional concept of imitation,the imitated contour may be any part of the phrase and is notlimited to the incipit. Figure 11 illustrates anticipation andimitation in a passage from Christ lag in Todesbanden. Thedistinctive contour of the beginning of the sixth phrase is antici-pated and then imitated in the alto voice. The statement ofpattern 19 in measure 12 is the beginning of what could beconsidered an embellished statement of the contour of the entirephrase; contour 54 in the alto uses the same pitch classes (exceptfor the C-sharp) as the incipit.

A contour is concurrent if it occurs simultaneously with theportion of a phrase from which it is derived. Since the derivedcontour usually occurs in rhythmic diminution, concurrent con-tours often begin after and end before the related contour in thecantus firmus (Figure 12) . In canons, the result sometimesresembles a stretto, with the derived motive appearing betweenentries of the related contours in the dux and comes. Figure 13shows two of these strettos in Hilf Gott dass mir's gelinge. Ineach case, the diminution is the only occurrence of the contourin the tenor voice in the entire prelude.

Related contours are reminiscent if they follow the phrase ofderivation after some elapsed time. These occurrences may bemelodically motivated, or Bach may be forming some associa-tion between the texts of the two phrases. In a number ofpreludes, contours from earlier phrases accompany the lastphrase, resulting in a kind of "closing summary" of the choraletune. Figure 14 shows possible references to the incipits ofphrases 2, 3, and 4 in the last two measures of In dich hab ichgehoffet, Herr. Contour 84 occurs only twice in the prelude —once in the cantus firmus and once in the tenor in measure 10.

Treatment of Related Contours

The most common references to the cantus firmus are of thegeneric contours represented by MELCON interval succes-sions. They are related to the cantus firmus by contour, but notby specific intervals. The relationship can be compared to thetransformation of a motive in a sequence as it passes throughdifferent portions of the diatonic scale. Related contours occurmost frequently in prime and inverted form, but retrograde andretrograde inversion forms were found also.

Once a recurrent motive has been well established, it may bevaried by interval expansion or contraction. The cadential con-tour that was noted previously in the first stanza of Christ isterstanden (Figure 8) continues to play an important role in thesecond stanza (see Figure 15). In this stanza the descending thirdis frequently expanded to a fourth. The resulting contour couldalso be interpreted as the original contour with an interpolatednote.

When Bach varies the cantus firmus, the unvaried contouroften occurs in diminution in close proximity to the variant. This"proximate correction" may be anticipative, concurrent, orimitative. Figure 16 shows an example from Es ist das Heil unskommen her. We can be fairly certain that the tune used for thelast phrase is anomalous, since it differs from at least five otherBach settings .The incipit of the common version of the phrase



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Melodic Process in the Orgelbiichlein 59

Figure 11. Christ lag in Todesbanden: the incipit of phrase 6 anticipates and imitates the cantus firmus

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Figure 16. "Proximate corrections" to variant of cantus firmus in Esist das Heil uns kommen her



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(contour 47) occurs in the tenor concurrently with the variedsetting in the soprano. Although the distinctive contour of theend of the phrase does not occur in the soprano, it occurs fivetimes in the accompanying counterpoint. The contours markedX(73) are derived from contour 73 by the expansion of theperfect fourth to a perfect fifth. The inversion of contour 72 inthe alto is also shown.

A similar technique is sometimes used when the addition ofpassing tones obscures distinctive contours in the cantus firmus.The most persistent recurrent motive in Herr Jesu Christ, dichzu uns wend' is derived from the triadic incipit of the first phraseof the chorale tune. This contour (pattern 54) occurs a total offorty-two times in this prelude in inverted form—more than inany other. The sixteen prime form occurrences are exceeded inonly two other preludes studied. Figure 17 shows a number ofoccurrences of this contour in the beginning of the prelude. The

frequency count for this contour would be considerably greaterif arpeggiated first and second-inversion triads had been countedas variants of pattern 54. (These are marked in broken bracketsin the example) . This example also shows the imitation of thefirst phrase in the bass and the inversion of contour 40 in the alto.The bass imitation of the cantus firmus continues for eachsuccessive phrase.

Contours that occur explicitly are sometimes extended ineither or both directions in peak notes or longer notes in thecontrapuntal line. The result is a paraphrase of longer contoursor entire phrases (see Figure 11, alto) . In Christus, der uns Seligmacht, the process is so systematic that it could be termed"progressive interpolation." In the alto and tenor, the amountof interpolation is tied to the time lapse in the imitation. InFigure 18 the notes outlining the contour of the second phraseare marked X, and the interpolated notes are parenthesized. At

Figure 17. Derivation of the recurrent contour from the incipit of HerrJesu Christ, dich zu uns wend'

a) phrase 1 54

a . • i •

40b) mm. 1-2

'x 40 54 'x x

x

s-54 —^ (54 -.^ 54

^ r— 54 --i1(40) r

54 _

t t

^54-,

^

phrase 1



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ff•20

5959b) m. I

59 interpolationinterP

a) phrase 2 59

phrase 2 paraphrase.c) mm. 2-3 x x x

e) mm. 23-25

interpolation

2

3

x x x x x xd) mm. 4-6

• •hrasex x x x

20

9: tt=

x interpolation• phrase 2 par

x x 0:(1..t"phrase 2

x x x

phrase 2xx

59 interpolation


(b) only the incipit of the phrase is used, and the contour isimitated after one beat. At (c) the incipit is imitated after twobeats, and three sixteenth notes are interpolated into the contour.At (d) the incipit is imitated after four beats and two and a half

beats are interpolated between the beginning and end of thecontour. Figure 18c shows the same basic contour in the sopranoat the codetta, where four beats are interpolated into the contour.Here the contour occurs at the original pitch level. Note that in

Figure 18. "Progressive interpolation" in alto and tenor of Christus,der uns selig macht



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Hal - le - lu

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jah!


most of these passages, portions of the interpolated contours canalso be related to the second phrase.

In a few cases the recurrent motive is itself an elaboration ofthe basic structure of a phrase from the cantus firmus. The mostimportant recurrent contour in Christ lag in Todesbanden can beanalyzed as an ornamented descending scale line with the struc-ture shown in Figure 19a. This descending line is related to thecontour of the last phrase—the setting of the word "hallelujah."Although a truncated version of the contour is used throughoutthe prelude, the full five-note descent occurs primarily in thebass and only at important structural positions in the prelude. Itoccurs at the beginning of the first (repeated) section, at thebeginning of the second section, and at the end, concurrently

with the unornamented statement in the soprano (Figure19c – e) . The entire contour occurs in the tenor at the end of thefirst phrase. Here the exact pitch classes of the last phrase areembellished—almost as if Bach were answering the text "Christlag in Todesbanden" (Christ lay in death's grip) and "Der istwieder erstanden" (He is risen again) with "Hallelujah!"(Figure 190.

The embellishment of the descending scale creates a sequen-tial pattern that can be analyzed as overlapping statements ofcontours 65 or 67. Pattern 65 (— 3 +2) occurs a total of eighty-five times in this prelude, almost twice as often as in any other,while pattern 67 (+2 —3) occurs a total of 110 times, 31 percentmore than in any other prelude in the Orgelbiichlein . Figures

Figure 19. Derivation of the recurrent contour in Christ lag in Todes-banden

a) structure b) phrase 8 40

c) m. 1 40 x x x x d) m. 9 40

x

. • •- .011=1I• ICI= ME MI aIIIINK /11L4M.IK 111MINOI/ NI III

4

e) mm. 15-16 40

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40 f) m. 2

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40 x xx x x

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62b) mm. 9-10 40

_. I11161

--:7---M1,717b) m. 1-216

Lobt Gott, ihr Christen, allzugleicha) phrase 4 , 39

aa

a•a w •

Vom Himmel hoch, da komm' ich hera) phrase 1 40 62r r

n.n

Es ist das Heil uns kommen hera) phrase 6 , 66

n

54 ,n


20a— c show the derivation of these contours from phrases 2, 4,6, and 7; Figure 20d shows the application of the patterns in theanalysis of the embellished descending scale line.

Occasionally, contiguous statements of contours result indistorted references to phrases, with the end of the contourshifted relative to the beginning, or with one section inverted(see Figure 21). In other instances the juxtaposition of contours

in two different voices suggests a complete statement of a phrase(Figure 22) .

Octave transfer within contours was also found. The octaveshift frequently occurs on repeated notes and is most common inthe bass. In Figure 23 the incipit of the first phrase of Christ isterstanden (second stanza) is imitated in the tenor and bass. Eachstatement of contour 42 involves octave displacement, and eachis in progressively shorter durations.

Figure 20. Embellishment of basic structure from Figure 19a related tophrases 2, 4, 6, and 7

a) phrase 2,4 65r 67 b) phrase 6 67

n

• .1, •

c) phrase 7

i

67

n

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d) m. 165

6565

• IV aa •

67 67 67

67

Figure 21. "Distorted" references to phrases resulting from contigu-ous statements of contours



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Figure 22. Juxtaposition of contours in alto and soporano suggestcomplete statement of phrase in Das alte Jahr vergangen ist

b) m. 7

1 !b^ • ^ 6

56 0

•

When derived contours are not particularly distinctive, theyare often carefully delineated in the counterpoint. In Figure 24the inversionally related contours derived from the first andfourth phrases of Vom Himmel hoch are set off by leaps andchanges in the rhythmic flow.

Even distinctive contours are sometimes difficult to see whenthey are buried in the counterpoint. The alto voice of Ich ruf zudir, Herr Jesu Christ is a mosaic of motivic reference. Most ofthe important motives are derived from the first two phrases ofthe cantus firmus, and a number of these are quite rare (seeFigure 25) . Contours 13 and 27 do not occur in any other prelude

Figure 23. Octave displacement of repeated note in imitation of incipitof Christ ist erstanden, second stanza

mm. 1-3 42

( i(phrase 1)

J P^

42

4

3 LLL.

9.

•

s

Figure 24. A common pattern set off by rhythm and contour in VomHimmel hoch, da komm' ich her

a) phrase 1 44 b) phrase 4 55

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74r ^c) mm. 1-8

i (30)66d) mm. 11-14 13

74 5172b) phrase 247

a) phrase 1 67

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Figure 25. Derivation of contours in alto of Ich ruf zu dir Herr Jesu

Christ. Contours 13 and 27 are unique to this prelude

13

in the entire Orgelbiichlein. In this prelude contour 13 occursthree times and 27 occurs five. Contours 46, 47, and 67 have ahigher frequency of occurrence in this prelude than in any other.

Embellishment

Bach's ornamentation frequently utilizes diminutions of con-tours from the phrase being set, or of important contours fromsome other phrase. In Nun komm' der Heiden Heiland, theembellishment of the first phrase is derived by inversion fromthe first five notes of the incipit (see Figure 26) . Part of thisfigure then becomes the primary recurrent motive in the prelude(see Figure 26c and d) .

The most important discoveries about embellishment, how-ever, were made in the ornamental chorales: Das alte Jahrvergangen ist; 0 Mensch, bewein' dein' Siinde gross; and Wennwir in hochsten Nothen sein. In these it was common to find

diminutions of contours from the chorale tune in the expressiveornamentation of the cantus firmus. Several of these contoursoccur at the same pitch level as in the cantus firmus and at thecorrect relative position (beginning, middle, or end of thephrase) . References to contours from phrases other than the onebeing set were found also.

Figure 27 is an analysis of the embellishment of the firstphrase of Wenn wir in hochsten Nothen sein. Contours 45, 60,and 49 are of special interest because they occur in diminution atthe same pitch level as in the cantus firmus and at a position thatcorresponds to the portion of the phrase from which the contourwas derived. Thus, contour 45, derived from the incipit, occursin diminution in the embellishment of the beginning of thephrase, while contour 49, the last four notes of the phrase,occurs in diminution at the very end of the phrase. Also note theinversion of pattern 8 in the beginning of the embellishment.Pattern 8 is the contour of the entire first phrase less the first and



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49 62r-------,


Figure 26. Derivation of embellishment and recurrent contour from theinversion of the incipit of Nun komm' der Heiden Heiland

a) phrase 1 10

Figure 27. "Diminutions" in the embellishment of the cantus firmusin Wenn wir in hochsten Nothen sein

a) phrase 1 t g --

62—' 49—

45

58

6045 lx x x x 1(58) 1(60) I (60) 1(60)r .r _.._ i ^--- `_^ r---., 45

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last notes. Contour I(23), shown at the end of the example, is theinversion of the first six notes of the third phrase.

Figure 28 shows the embellishment of the second phrase. Asin the first phrase, the contour of the beginning and end of thephrase occur in diminution at the correct pitch level and in thecorrect relative position. Contour 14 is the entire fourth phrase,except the last note, at the correct pitch level. Similar relation-ships can be found in phrases 3 and 4.

Intervallic Similarities

Although the melodic style of the preludes is not nearly socircumscribed as that of the chorale tunes, there are someinteresting parallels between them. The order of frequency(calculated as a percentage of the total number of intervals) foreach generic interval type is the same for the preludes as it is forthe chorale tunes. In both cases seconds occur most frequently,followed by thirds, repeated notes (including octave leaps),fourths, and fifths. In the preludes, these intervals are followedin frequency by sixths, chromatic inflections, and sevenths.

In some instances, the interval-count tables for individualpreludes show a correlation between the frequency of occur-rence of certain intervals in a prelude and its cantus firmus. The

interval type most frequently reflected in the preludes was therepeated note (+0) . High incidence of repeated notes occurs inboth cantus firmus and parts in Gelobet seist du, Jesu Christ;Herr Gott, nun schleuss den Himmel auf; Liebster Jesu wir sindhier; and Dies sind die Heil'gen zehn Gebot' . A correlation wasalso found for other interval types. In particular, the disjunctmotion in Vater unser im Himmelreich and In dich hab' ichgehoffet, Herr are clearly reflected in the counterpoint, as aredescending seconds in Vom Himmel kam der Engel Schaar. Inother cases, high incidence of certain intervals reflect an impor-tant portion of the chorale tune. For example, the use of thetriadic incipit of Herr Jesu Christ, dich zu uns wend' as theprimary recurrent motive results in the highest incidence ofmelodic thirds in the Orgelbiichlein .

Rhythm

The fact that the computer input code and programs did notdeal with rhythm is not an indication that this aspect of the musicwas considered unimportant, only that its inclusion would beunnecessary and even detrimental to the study of melodic con-tours. While marking contours on the music, the author notedthat matching contours often recur in the same rhythmic pattern.

Figure 28



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This is not surprising, since the recurrent motives in the preludeare rhythmic as well as melodic. On many occasions, therhythmic parameter was instrumental in deciding which of sev-eral possible interpretations of a melodic line was correct.

In a number of cases, the rhythmic setting of the cantus firmusis reflected in the rhythm of matching contours. In Christus, deruns selig macht, the settings of phrases 2, 4, and 5 all begin witha syncopation, which also occurs in diminution in every instanceof the primary recurrent motive (see Figure 18) . Figure 29shows that the agogic accent from the peak of the first phrase inBach's four-part setting of Christum wir sollen loben schon isreflected in the rhythmic setting of the contour in the counter-point of the prelude.

Textual Implications

In many preludes the chorale phrase that generated the mostmatching contours seemed to set a key phrase of the hymn. Thusthe first phrase (the title of the chorale) generated the mostmatching contours in Dies sind die heil' gen zehn Gebot' and inWir danken dir, Herr Jesu Christ. Table 3 shows the distributionof matching contours relative to the phrase of derivation in Lobsei dem allmeichtigen Gott. The primary motive in the bass wasderived from the third phrase, as were most of the more signifi-cant matching contours . 8 This phrase sets the text "gesandt denallerliebsten Sohn" (sent His most beloved Son) . Figure 30shows the derivation of the primary motive and its use in the bassof the prelude.

When beginning this project, the author thought that recurrentmotives might have been chosen for their textual associations.In a few pieces, this does seem to be the case. One example,from In dich hab' ich gehoffet, Herr, is shown in Figure 31. Inthis prelude contour 80 (-4 +2) matched six times as often as

8 Significance is determined by the number of pattern matches, the length ofthe contour, and the "degree of uniqueness" of the pattern.

Table 3. Pattern Matches by Phrase in Lob sei dem allm ā chtigen Gott

Phrase

1234

No. of Patterns No. of Matches

10161913

58507424

any other contour. This motive corresponds to the setting of thewords "Hab' ich" (I have) in the first line of the chorale: "Indich hab' ich gehoffet, Herr" (In Thee have I placed my hope,Lord) . If the assumption of textual significance of the motive iscorrect, this prelude may contain one of the greatest affirmationsof faith in the Orgelbiichlein: contour 80 occurs a total ofthirty-seven times in prime form — almost twice as often as inany other prelude. Figure 31 shows the derivation of the contourand its use in the first phrase of the prelude. Note that the altoand tenor begin with the contour on the same pitch classes as inthe cantus firmus (marked with heavy brackets) . The contourmarked X(80) is derived from pattern 80 by the expansion of thefourth to a fifth. This variant of the primary motive occurs a totalof fourteen times in the prelude, more frequently than in anyother.

Unfortunately, Figure 31 is not typical. More often than not,related contours break into the middle of words and phrases inawkward places, a fact that does not support the hypothesis thatthe motives are directly related to the text.



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Figure 29. An agogic accent from Bach's four-part setting of Christumwir sollen loben schon reflected in counterpoint of prelude

a) phrase 3 from Bach's four-part setting86

Figure 30. Derivation and use of recurrent contour in bass of Lob seidem allmiichtigen Gott

a) phrase 3

44

• • a • i

b) mm. 1-2. Bass sequence 44 44 44 44

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80a) phrase 1

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Figure 31. The recurrent contour in In dich hab' ich gehoffet, Herr

An Evaluation of the Research Method

During the course of this study, forty-eight preludes andchorale tunes were coded for computer input and a number ofcomputer programs were developed. The computer programsgenerated several thousand pages of print-out and tens ofthousands of data records on punched cards, computer tape, anddisk. How successful was this method of analysis? What waslearned that could not have been learned, perhaps with lesseffort, by a more traditional approach?

The contour-seeking program described earlier was not de-signed to find all contours related to the cantus firmus, but tolocate those contours that were most likely to have musical

significance. The program found many contours that are notimportant along with those that are. During the course of theanalysis the author made many judgments concerning the signif-icance of each contour. Decisions were based both on themusical context and on data comparing the frequency of occur-rence of the contour in other preludes. The process of siftingthrough the data and evaluating each pattern's musical contextforced the analyst to weigh many possibilities that otherwisemight not have been considered. This led to the discovery ofmelodic relationships that would be difficult to find by a lessrigorous approach. Still, it is conceivable that most melodic



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relationships could have been discovered by persistent manualanalysis. Thus the computer could be considered a luxury ratherthan a necessity during this phase of the study.

However, the computer did provide this study with an addeddimension. This was the ability to gain an overview of themelodic contour content of the entire Orgelbiichlein and tocompare occurrences of any contour in each of the preludes.Thus, it was possible to ascertain that some contours that wererelated to the cantus firmus were unique in certain preludes, orthat they occurred with high frequency relative to the frequencyin other preludes. This information provided the analyst with aperspective that would have been impossible without data pro-vided by the computer.

Closing Remarks and Speculations

Two important issues have not been addressed in this paperbecause no definitive answers can be given. These are: 1) howmany of these melodic relationships can one hear? and 2) wasBach aware of these relationships while composing the pieces?

The first question could be answered, only half in jest, byanother: How well do you hear? What one hears depends partlyon innate and developed ability and partly on knowing what tolisten for. One might suppose that the reason these melodicrelationships were not discovered earlier was because they arenot aurally obvious. Most are not particularly difficult to hearonce you know that they are there, although trying to hear themall at once is a real challenge.

It seems probable that the use of contours from the cantusfirmus, like numerical symbolism, was one of those hiddenaspects of Bach's art in which he took such delight. 9 If this is thecase, it suggests some interesting conclusions regarding Bach's

9An interesting discussion of numerical symbolism can be found in KarlGeiringer's Symbolism in the Music of Bach (Washington: The Library ofCongress, 1956), pp. 10-14.

method of composition. It is unlikely that many of the moresubtle references to the cantus firmus would be made whileimprovising. The implicaton is that Bach probably workedmany of these pieces out on paper rather than at the keyboard.

While there is no way to know Bach's thought processeswhile writing these pieces, it is interesting to speculate on thesecond question— were these melodic relationships put in themusic intentionally? In the most obvious cases there is noquestion that they were. In other instances the process may havebeen subconscious or even accidental. It makes little differencewhether Bach intentionally used contours from the cantusfirmus or whether the process was subconscious: the phenome-non is part of these pieces—the evidence is in the music. Weshould not be surprised to find that this melodic device, which isso much a part of Bach's other contrapuntal forms, is found alsoin the chorale preludes. These pieces would be remarkable formany reasons if there were no relationships between cantusfirmus and parts. That they do exst reminds us once again thatBach was a consummate artist whose skill and genius permeateeven the smallest details of his work. by guest on January 31, 2014


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Brinkman - The Melodic Process in J S Bach Orgelbuchlein - Music Theory Spectrum-1980