Clavierübung III of J. S. Bach: Theology in Notes and Numbers, Part 3

Part 1 was published in the October issue of The Diapason, pp. 22–25.

Wir glauben all’ an einen Gott
[We all believe in one God]
(BWV 680–681)
The arrangement of the chorale Wir glauben all’ an einen Gott, the Protestant version of the Credo, opens a series of dramatic chorale preludes in the Clavierübung III. Their themes are built on the minor keys and gravitate around the interval of the fifth.
In this piece the fugal upper voices are contrasted against a melodic line in the bass that occurs seven times. (Example 9) This melody is based on a leap of a fourth followed by a downward move within the octave and displays a structural similarity to the theme of the so-called Dorian Fugue (BWV 538).55 The ostinato motif appears altogether six times in the pedal; once (the sixth appearance) in modified form on the manuals: there only the beginning of the motif appears, repeated three times.
Not just the relationship (6 + 1) in the use of this striking melody is important, but also the fact that its form is changed in the one time it is used on the manuals. Naturally, this begs the question as to the purpose of this change. We have here possibly an allusion to the Old Testament injunction: Six days you shall labor and do all your work, but one day must be reserved for prayer and spiritual needs. From here stem the characteristics of one of the developments: an elevation of the tessitura, the use of only upward leaps, the softening of the harshness of the harmonic minor, and finally the heterolepsis figure used in the upper voices.
The manual voices are developed out of the beginning of the melody of the chorale Wir glauben all’ an einen Gott. The first four notes of this motif in a tonal answer form a musical rhetorical figure, often encountered in the works of Bach, which Boleslav Javorsky called the predestination motif.56 The origin of this motif lies in the chorale melody Was mein Gott will, das g’scheh’ allzeit [What my God wills may always happen] and is usually used by the composer as a culminant, dramatic or recapitulating figure (Fugue in G Minor, BWV 542, Fugue in A Minor, BWV 543, etc.). The whole musical fabric of this chorale prelude is shot through with this predestination motif.
Towards the end of the composition, Bach quotes in the tenor, first in its entirety, the first line of the cantus firmus (bars 89–98). Typically, the subsequent figure in the pedal that accompanies the chorale melody is enlarged, not only in its range (two octaves), but also in the number of notes (to 43—CREDO). One can also hardly describe it as a coincidence that the work has 100 bars: Bach could not have found a better numerological symbol to underscore the idea of “We all believe in one God.”
If we had the task of finding within Bach’s output a work for organ where the dramatic element was more pronounced, we could, paradoxically, hardly do better than choose the small 15-bar manualiter fughetta on the chorale melody Wir glauben all’ an einen Gott in the Clavierübung III. Written in Handelian style,57 it is very chromatic. The traditional double dotting, the richly ornamented musical fabric, the use of characteristic rhetorical figures—tiratas—all combine to sharpen up the harmonic impact of this three-voice fughetta to the highest degree.
The high point of the piece comes in the 12th bar, which results in the interesting proportions of 4:5.58 The density of chords in this bar is a rare example in Bach’s organ works. (Example 10) The diminished seventh on the strong beat contains seven notes. The following diminished seventh from D sharp–C contains six notes, which together makes 13 notes—most certainly another numerological symbol and one that needs no explanation. The impact of the intensive harmonies is strengthened by “talking pauses” and the declamatory answers on the “weak” beats of the bars. The intonations from the introduction (viola da gamba solo) of the aria Es ist vollbracht from the St. John Passion (BWV 245) can be heard in the music. (Example 11)
The descending seconds in Lombardic rhythm, with articulation marks written out in full by the composer (bar 11), the key role of the striking diminished seventh from D sharp–C at the high point of the work, and the key chosen—this is by no means a complete list of the methods the composer has used to create a smooth transition to the subsequent part of the composition.

Vater unser im Himmelreich
[Our Father in Heaven]
(BWV 682–683)
In the extensive arrangement of the chorale melody Vater unser im Himmelreich we encounter an example of a trio that is from time to time expanded to five voices by means of the cantus firmus in canon. This is one of the rare works of Bach full of articulation marks. Thoroughness of articulation shows how important this aspect of organ playing was for the Leipzig cantor.
Already, the choice of key says a great deal about the associative structure of this music. E minor is the key of the opening chorus of the St. Matthew Passion (BWV 244), the Crucifixus from the Mass in B Minor (BWV 232), the Prelude and Fugue for organ (BWV 548), the chorale prelude Da Jesus an dem Kreuze stund (BWV 621) from the Orgelbüchlein, and many other works in which Bach created an atmosphere of grief, sorrow, and misfortune.
The narrative flow of the music in the greater chorale Vater unser im Himmelreich creates an atmosphere of stillness and calm, and invites the hearer to intense prayer. The movement in seconds in Lombardic rhythm59 is akin to the sighs of a humble soul turned towards God. Time moves gently, so as not to disturb the state of intimate prayer.
This composition is literally suffused with thematic symbolism. Allow me to name just a few (following B. Javorsky): the descending third – a symbol of grief; a smooth chromatic movement of 5 to 7 notes – pain; a progression in triplets – fatigue, weariness; a movement along the notes of a first inversion – a symbol of inevitable realization; and so on.
The musical fabric of the composition resembles the tenor aria Wo wird in diesem Jammertale für meinen Geist die Zuflucht sein? [Where will my spirit find its refuge in this vale of tears?] from the cantata Ach, lieben Christen, seid getrost [Ah dear Christians, be comforted] (BWV 114), which Bach completed in Leipzig in 1724. Without a doubt there is an inner connection between the two works. The text of the aria, especially the treatment of the key word “Jammertal” [“vale of tears“ in German] can give the performer the right feeling for the interpretation of the greater chorale prelude Vater unser im Himmelreich.
Another interesting detail of the work is the movement in seconds in Lombardic rhythm in the pedal. This occurs only once in the whole work, at bar 41
(JSBACH), an allusion to the composer’s unseen participation in the prayer to God the Father. (Example 12)
The intricately crafted rhythms of the greater chorale prelude Vater unser im Himmelreich give way in the manual version to flowing linear movement in sextuplets. This sharp contrast has not gone unnoticed by scholars. “As complicated as the rhythms in the large Our-Father prelude may be, so simple is the calm flow of the 16th notes in the manuals version . . .” wrote Christoph Albrecht.60 An interesting explanation for this contrast has been put forward by Albert Clement, who connects the greater chorale prelude with the text of the fourth verse of Luther’s chorale Vater unser im Himmelreich,61 and the smaller prelude with the following verses (5–8). The fourth verse appeals to God’s patience in a time of sorrow, while verses 5–8 speak of trust in His compassion and assistance.62
The placid wave motion of the accompanying voices in the manuals version of the chorale prelude Vater unser im Himmelreich gently prepares us for the stormy motion of the 16th notes in the greater chorale prelude Christ, unser Herr, zum Jordan kam [Christ, our Lord, to Jordan came] as the following section of the Clavierübung III.

Christ, unser Herr, zum Jordan kam [Christ, our Lord, to Jordan came] (BWV 684–685)
The greater chorale prelude Christ, unser Herr, zum Jordan kam presents us once again with something quite out of the ordinary. This is the first occurrence in the whole work of the cantus firmus being transferred to the pedal in a high register. The composer indulges here in musical picture painting: the 16th-note runs produce a sort of perpetuum mobile and create the impression of waves on the Jordan. The music is dominated by an atmosphere of waiting for the miracle of God’s appearance and with it, the forgiveness of sins through the ritual of baptism. (Example 13)
Attempts have been made by various authors to see in the upper voices a dialogue between the Savior and St. John the Baptist,63 a view that I personally do not find very convincing. Built on the symbolic motifs of the Cross and Willingness to Sacrifice,64 the dialogue in the upper voices is often syncopated or transformed into a typical Bachian motion. It does not seem in the least to be associated with the dialogue between God’s Incarnation and His forerunner, but rather serves, as does the stormy motion of the bass, to create a state of what I would call “joyful excitement”—an atmosphere that is typical of many iconographic depictions of the Feast of the Baptism of the Lord.
The appearance of the Holy Trinity—as the Spirit in the form of a dove descending from heaven and as the supernatural light surrounding Christ at His baptism in the waters of the Jordan—is present in this prelude at the deeper level of mystical numerological symbolism. The cantus firmus appears nine times against the three-voiced accompaniment (9×3 = 27), while the total number of bars in the prelude is 81 (27×3).
Each appearance of the cantus firmus is built on a particular number of notes: in four cases it is nine notes, in the other five cases it is eight. And they occur in a strict sequence: 9 + 8 + 9 + 8; 8 + 9 + 8 + 9 + 8. The symbolism of the numbers 3, 9, 27, 81 focuses our attention on the picture of the Holy Trinity, while the number 8 is associated with the heavenly chronos or with the Coming of the Messiah.65
The legitimacy of the numerical proportions in the greater chorale prelude is borne out by the numerological symbolism of the manual fugato in three voices on Christ, unser Herr, zum Jordan kam. The fugato is written in simple triple time and has 27 bars (27×3 = 81). The main theme—the first line of the chorale—occurs three times in the original and three times in the inversion, and each time it is accompanied by a counter-melody based on thematic material in diminution, which forms a kind of canon. (Example 14)
In the opinion of Christoph Albrecht, this is a musical representation of the Gospel words of St. John the Baptist: “He [Jesus] must increase, but I must decrease” (John 3:30).66 It is worth mentioning that the bridges in the fugato (bars 8–10 and 18–20) have an evident three-part structure containing the countersubject (= the diminished theme).
All in all, the composer introduces the theme a total of 14 times (three times the original theme, three times inverted, and eight times diminished).67 The concluding development of the theme in its original form (bass in bar 20) has been slightly altered through the introduction of the Willingness to Sacrifice motif as an anacrusis. This results in interesting proportions for the presentation of the thematic material: 2 + 1 + 3 + 8. It is not difficult to see that these numbers represent a numerical version of the name of the composer (BACH).

Aus tiefer Not schrei’ ich zu dir
[Out of the depths have I cried unto Thee] (BWV 686–687)
The only organ work of Bach written in true six parts with double pedal is the chorale prelude on Psalm 130 (129) Aus tiefer Not schrei’ ich zu dir—a further example of the stile antico in his work. Each verse of this monumental penitential chorale,68 welling up out of the depths of the heart, is introduced in the fugal-like exposition that concludes each time with the cantus firmus in the upper pedal voice. This gives the work, written in the best tradition of J. Pachelbel, the form of an unbroken chain of seven fugues, corresponding to the number of verses of the chorale.
Albert Schweitzer’s attention had already been drawn to the “motif (rhythm) of joy” that first greets one in the initial phrases of the countersubject. As the music develops, this symbolic motif is further elaborated and at the end totally dominates the musical fabric. (Example 15) Schweitzer proposed a dogmatic interpretation for its presence: “Bach . . . is trying to represent the Lutheran doctrine of repentance, according to which all true repentance leads of itself to the joyful certainty of salvation.”69
Schweitzer’s observation is, of course, interesting and not without subtlety, but in my opinion one is dealing here less with joy, but rather with the cleansing power of repentance and the resulting confidence of the penitent in his own future. The motif under consideration conveys just this feeling of confidence.
What motives led Bach to introduce the chorale prelude Aus tiefer Not schrei’ ich zu dir into the Clavierübung III at all? Penance was not a component of the Ordinary of the old Mass, although it had been included in the liturgy in Saxony since 1601. Neither was penance dealt with by Luther in his Great Catechism, although he sometimes mentioned it along with Baptism and the Eucharist as one of the Sacraments. This was apparently the decisive argument for Bach to place two fantasies on Aus tiefer Not schrei’ ich zu dir between the parts relating to Baptism and the Eucharist.
Numerological symbolism plays an important role in both works. As has already been said, the seven fugues that make up this work correspond to each of the seven verses of the chorale. The cantus firmus that crowns each fugue always consists of nine notes, whereas it is interesting to note that it first occurs in the ninth bar. In addition, the length of the cantus firmus from its first to last note always has the same length of eight half-bars.
This changelessness of the cantus firmus, with its connection to the numbers nine, eight, and seven is obviously meant to signify the objective, almost unearthly quality of the beneficial cleansing power that flows over the penitent sinner. An additional indication can be found in the fact that at each occurrence the cantus firmus is first woven into the musical structure only after the completion of the exposition with its five voices. (We recall that the number five symbolizes “sensual Mankind.”)
Our attention is also drawn to the relationship between the number seven (seven verses of the chorale and the seven fugues) and the number five (the five-part musical structure70). These two numbers have an interesting internal proportion: 7:5 = 1.4 (BACH). One could probably regard this as pure chance, were it not that these two numbers occur again within this work. The chorale prelude has 75 bars, where the number 75 is the numerological expression of the word ELEISON (5 + 11 + 5 + 9 + 18 + 14 + 13). The relevance of this cry for mercy in a work dealing with remorse can hardly be doubted.
It is characteristic that the manualiter version of the chorale Aus tiefer Not schrei’ ich zu dir displays the same numerological symbolism as the greater version. A slight change in the rhythmical structure makes the initial motif of the theme correspond to the eighth fugue of the Ariadne Musica Neo-Organoedum Per Viginti by Johann Caspar Ferdinand Fischer (ca. 1660–1746).
Bach’s work impresses us by its architecture. Just as in the first chorale prelude, we encounter an unbroken chain of fugues that treat the seven verses of the chorale one after the other, both in its tonic form and its inversion, where each is brought to a close by the statement of the cantus firmus in the soprano. This results in seven fugues. Six of them are of the same length. The cantus firmus occurs after the fifth bar and lasts for eight bars. But here we encounter an interesting new development: after the cantus firmus has run its course, Bach does not immediately begin with the following fugato, but each time inserts an extra bar as a sort of résumé. Thus the six units have the following structure: 5 + 8 + 1. It is not difficult to see that the résumé thus occurs in the 14th (BACH) bar of the appropriate unit.71
The last and seventh unit differs in its structure from the preceding six, and introduces a proportion that we have already encountered in the greater choral prelude on Credo (6+1). After it has started as all the preceding units (five bars of fugato without the cantus firmus, followed by eight bars with the cantus firmus), this seventh unit has instead of the “Bach résumé” an extension of the second cantus part for a further five bars, resulting in the new proportion of 5 + (8 + 5). It is not difficult to see that this new proportion brings us close to the Golden Rule: 8:5 = 1.6 whereas 13:8 = 1.625. This is not altogether surprising. Thus when the composer understood the combination 6 + 1 as the biblical command to labor for six days, but to keep the seventh as a Sabbath for your God, then it was appropriate that this “special” seventh day be not simply adorned with ordinary music, but be bejewelled with golden tones!

Jesus Christus unser Heiland
[Jesus Christ our Savior]
(BWV 688–689)
The last two chorale preludes in the Clavierübung III deal with the events surrounding the Last Supper. Viewed from a cultural perspective, the iconography of this subject centers around two key moments. The first is the Transubstantiation of the bread and wine into the Body and Blood of Christ. The second moment concerns the circumstances of Judas’s betrayal.
The greater chorale prelude Jesus Christus unser Heiland is woven out of three voices. The cantus firmus, based on an intonation of fifth, is written out in long notes and appears in the pedal. The lively duet in the upper voices simultaneously spins out the three-note stepwise motif (according to Javorsky, a motif of reconciliation), both in its tonic form and its inversion. (Example 16)
We have already encountered this characteristic method in the Clavierübung III: in the greater chorale prelude on Kyrie, Gott heiliger Geist. Its use with quickened tempi produces a mood of agitation and worried concern. A special feature of the musical language is the frequent use of unprepared dissonances that heighten the sense of drama. Speaking personally, this music always conjures up for me Leonardo da Vinci’s famous Milanese fresco of the Last Supper, where the disciples of Christ, unsettled by his prophecy of betrayal, turn to the Savior with just one question “Surely not I, Lord?” (St. Matthew 26:22).
The cantus firmus appears altogether four times in the pedal as the embodiment of Christ’s serenity and his willingness to drink the Cup of his Passion. Its 44 notes are arranged as a pattern of 10 + 12 + 10 + 12. It would appear that the composer has applied this numerical pattern to emphasize the union of the Old Testament (the Law) and the New Testament (the Testament of Christ). Obviously, it is appropriate to remember at this point that St. Augustine considered the number twelve to be a symbol of the Church of Christ. The universal, catholic character of the Church is portrayed by the numerical symbol 144 (= 12×12). Note that the three-note motif of reconciliation in the manuals occurs exactly this many times in the musical texture of this composition.72
Another mysterious symbol is embedded in the score. When one connects the first and the sixth notes of the first bar, and the second and fifth notes, and the third and fourth notes (d1-d2, f2-f1, e1-e2) with a straight line, one produces a graphic figure which resembles the Greek letters X (Chi) and I (Iota) superimposed on each other. (Example 17)
This figure is the emblem of God made Man (Ιησυ Χριστ – Iesus Christos), and one must assume that the composer intentionally built this motif into the structure of the chorale prelude, a chorale that begins with the words “Jesus Christus unser Heiland” [Jesus Christ our Savior]. Typically this emblem occurs 72 times within the work, something that can hardly be attributed to chance. In accordance with tradition, this symbolic number corresponds to the 72 biblical names of the Lord, 72 biblical angels, the 72 nations of the ancient world, and the 72 disciples that Jesus sent out to preach his gospel. The Old Testament book of Numbers tells of 72 elders who received the gift of prophecy from God (Numbers 11:24, 26).73
The manualiter version of Jesus Christus unser Heiland (an extensive fugal composition in four voices) displays a very interesting feature—the placement of the theme does not match the metrical structure. The use of such a technique in the final chorale work of the Clavierübung III undoubtedly has good reasons. Perhaps Bach wanted to underline that the teachings of Christ have an eternal relevance that is not bound by the confines of physical time.
The theme of this fugue displays a striking structure. It consists of 13 notes74 and is based on two elements, which have a significant structural function in the whole cycle: a leap over a fifth and a stepwise motif over a third. The first notes of the tonal answer replicate exactly the final cadence of the chorale Was mein Gott will, das g’scheh’ allzeit, which (following Javorsky) we have interpreted as a predestination motif. (Example 18)
The countersubject is worked out with a circulatio figure that represents the Cup of Sorrows. The theme occurs 17 times altogether, with the final statement in augmentation. Bach undoubtedly considers the number 17 to be the union of ten and seven, especially as the eleventh statement is introduced by a longer bridge passage. The number ten is associated with the Law of the Old Testament (The Decalogue), while according to Werckmeister, the number seven is the symbol for purity and peace.
Thus one can summarize the conjunction of all these symbols as follows: The predestination from above (predestination motif) and the reconciliation prophesied in the Old Testament (reconciliation motif) through the suffering of Christ on the Cross (the Cup of Sorrows motif) purifies the fallen world (13) and gives it eternal peace and bliss (7).

Four Duets: E minor, F major,
G major, A minor
Scholars agree that the four duets of the Clavierübung III are very difficult indeed to interpret. As Hermann Keller remarked, the duets are “so unique and in part so difficult to understand that one must almost be led to believe that Bach wished to express something very special, but no one has yet found the key to them.”75 And in fact the opinions of the experts concerning both the content and the meaning of these works are indeed very contradictory. Some of them are of the opinion that they should be played during the Eucharist, while others see them as symbolic representation of the four Gospels.76 Albert Schweitzer is most probably the furthest removed from the truth with his opinion that they have only found their way into the Clavierübung III by mistake. He thus underestimates the significance of numerical symbolism within this work. Above all he did not “notice” that with the addition of the four duets the total number of works in the Clavierübung III reached the “cosmic” number of 27.
How does this music present itself?
All four pieces are highly individual and represent the highest achievement within the development of the genre of keyboard music for two voices known as inventions. They display no direct connection to the church chorales, but one is aware that while they have an element of tone painting it would not be illogical to interpret them as representations of the four material elements of this world: fire, air, water, and earth. Indeed, just this sort of interpretation was first suggested by Rudolf Steglich.77
Let us now look at the musical design of the duets.
The duet in E minor (BWV 802) is pure energy. Whole rivers of fire flow in the rapid succession of 32nd notes and the broken line of the syncopated motif recalls tongues of fire. The jagged melisma, the semitone movement within the range of diminished thirds: all reinforce a pervading feeling of tension. An almost pagan cult of fire dominates this music. (Example 19)
The F major duet (BWV 803) is built on the idea of contrast. The sphere of air is represented as a contrast of light and dark elements. The main theme, the embodiment of light, occurs in a major key in both the exposition and the recapitulation. The central part gives the impression of sudden twilight, which shrouds all life and transforms everything into a ghostly world of shadows. The contrast of major and minor suggests conflict—the elements of light struggle to free themselves from the chains of the mythological shadow world. (Example 20)
The G major duet (BWV 804) paints a picture of a body of water sparkling in the rays of the morning sun. Murmuring and iridescent flowing passages stirred by a light breeze create the impression of an unending stream of flowing water, magically calling to us by its freshness and purity. (Example 21) The musical texture of this work shows a high degree of similarity to the aria Von der Welt verlang ich nichts [From the world I nought desire] as the seventh part of the cantata Sehet, welch eine Liebe hat uns der Vater erzeiget [See what love the Father has bestowed on us], 1 John 3:1 (BWV 64). (Example 22)

The duet in A minor (BWV 805) has a different character. Behind the slow unfolding of its ideas, behind the gravity of its utterances one can discern an unbending internal force that holds everything in its thrall and directs all things. The extended, epically expanding theme strives to embrace all earthly things. The rocklike solidity of this musical picture calls to mind the immovable foundation of the earth. (Example 23)
Unlike Rudolf Steglich, Albert Clement suggested another approach. He sees in the duets a connection to the tradition of home prayer.78 In the opinion of this expert, the four duets serve as a musical illustration of the 194th chapter of the book Geistliche Erquick-Stunden Oder Dreyhundert Haus- und Tisch-Andachten79 [Hours of Spiritual Refreshments, or 300 Prayers for Home and Table] by the renowned theologian Heinrich Müller (1631–1675). Entitled “Von vier süßen Dingen” [On Four Sweet Things], this part of Müller’s monograph is devoted to the interpretation of the religious essentials: the Word of God, the Cross, Death and heavenly Bliss.
Let us now look at the structure of the duets in detail (Figure 1). One’s attention is immediately drawn to the emphasized strictness in the handling of the meter and the thematic material in all four duets. This is especially apparent in the first and second duets.
In the third duet, the length of the bridge-passages creates an interesting relationship (Figure 2).
The theme of the fourth duet is exceptionally long (48 notes) and consists of two parts: the first part has 11 notes, while the second contains 37 notes. All three numbers have clear sacred connotations: 11 is the symbol for sin, 37 for the monogram of Christ, and 48 is the numerical equivalent of the abbreviation INRI (Iesus Nazarenus Rex Iudaeorum).80
The first duets contain not only the numbers 11 and 37 but also other numbers that are relevant to the theme of Golgotha: 13 (death), 17 (symbol of spirituality), 31 (the numerical equivalent of PNC as the abbreviation of Pro Nobis Crucifixus). It is remarkable that these are simply different combinations of just three numbers—one, three, and seven—and that 137 is itself the numerical equivalent of DOMINUS DEUS.
It is also noteworthy that the sum of 22 + 15 (first duet) and 18 + 13 (second duet) lead us again to the symbols 37 and 31. Moreover, the combination of the pairs 17 (first duet) and 31 (second duet), as well as the pairs 11 (first duet) and 37 (second duet) both lead to the above-mentioned key number 48. The same number results from the addition of 11, 31 (third duet), and 6 (fourth duet).
It is clear that Bach wove the numerical symbolism into the duets to illustrate the content of these works. The numerology leaves no doubt as to the subject of these works: the music of the duets revolves around the theme of the Passion.
The idea that the four duets in the Clavierübung III symbolize the Cross was first suggested by Gerhard Friedemann.81 His work contained a number of highly original ideas about numerical significance within these pieces, but also many valuable observations concerning the biblical symbolism present in the other sections of the Clavierübung III.
Unfortunately it would be beyond the scope of this article to discuss further in depth the many other interesting details that are to be found in the four duets. So I would like to confine myself to bringing just a few salient points to the attention of the reader. The total number of bars in all four pieces is 369, which is in itself an indication of the association of these works with the Passion.82 The number 16 (4×4), which forms the basis of the A minor duet, is a numerical representation of the Cross. 112 (the sum of the numbers of bars in the E minor and G major duets) is the equivalent of CHRISTUS (3 + 8 + 17 + 9 + 18 + 19 + 20 + 18), and 149 (the number of bars in the F major duet) represents RESURREXIT (17 + 5 + 18 + 20 + 17 + 17 + 5 + 22 + 9 + 19).83
It is difficult to deny the validity of Gerhard Friedmann’s conclusions, based as they are on the analysis of the numerical structure of the duets. But this raises a further question: Is there a connection between, on the one hand, the hidden numerological references to the Cross in the four duets of the Clavierübung III and on the other hand the obvious descriptive character of the music?
Yes, one can indeed find such a connection! It is well known that in earlier times the cross was used as a symbolic representation of the four elements. But with the coming of Christendom, it became an object of adoration and so lost the association with the pagan worship of fire, air, water, and earth.
So now we wish to put ourselves in the shoes of the composer and try to answer the following question: How is it possible to portray musically a Cross, the product of human hands, soaked with the divine Blood of the Savior and transformed by the divine Will into an object of salvation? The answer is obvious. The best way to accomplish this is that chosen by Bach in the four duets of the Clavierübung III.

Prelude and Fugue in E-flat Major
The Prelude and Fugue in E-flat Major forms an overreaching arch that encloses the whole cycle. It is a work on a truly symphonic scale and is in this respect without parallel in the world’s organ literature. Its epic stature is complemented by the vividness and the passion of the musical language.
In both the prelude and the fugue the composer introduces three different musical spheres nevertheless bound together by such characteristics as common key and thematic material. The work is most commonly thought of as being an expression of the Holy Trinity. But no one to date has been able to produce a truly convincing proof for this view. As a result a number of unresolved controversies exist: which part of the fugue, the second or the third part, represents the Holy Spirit, and which Jesus Christ?
The very existence of these controversies should suggest to us that the work has not yet been sufficiently examined. To say nothing of the “echoes” episodes of the prelude, which most experts have associated with the Son of Man. How should we understand this embellished fluttering “in the spirit of the Rococo” to be a picture of the Savior?
In my opinion one should not view this music as one would a picture on a wall.
It is indeed Bach’s purpose to sing the praises of the Triune God, but it is not his intention to paint a musical picture of God. Three parts that are characterized through changes in the musical texture—in both the prelude and the fugue—are always the same God, the One, the Indivisible, the Holy and Consubstantial Trinity.
With what means does the composer accomplish this task? Let us first examine the prelude.

This article will be continued.

Alexander Fiseisky, born in Moscow, graduated with distinction from the Moscow Conservatoire as pianist and organist. He is an organ soloist of the Moscow State Philharmonic Society, head of the organ class at the Russian Gnessins’ Academy of Music in Moscow, and president of the Vladimir Odoyevsky Organ Center. He organized and served as artistic director for organ festivals in Moscow, St. Petersburg, Kiev, and Tallinn, among others. In 1997 he was honored by President Yeltsin with the title ‘Honored Artist of the Russian Federation’. Fiseisky has given concerts in more than 30 countries. In the Bach anniversary year of 2000 he played J. S. Bach’s entire organ works, twice in the context of EXPO 2000 in Hannover, and once in a single day in Düsseldorf as a Bach marathon. Sought after as a juror in international competitions, he has directed seminars and masterclasses in Europe and the USA. He is the dedicatee of numerous compositions, including works by Mikhail Kollontai, Vladimir Ryabov, Milena Aroutyunova, and Walther Erbacher. A musicologist, he has edited anthologies of organ music of Russia and of the Baltics (Bärenreiter-Verlag). He has many recordings to his credit, including the complete organ works of J. S. Bach.

It goes without saying that the primary
task of every performer who wishes to convey the meaning of any given musical work must first be to understand the original intention of the composer. And when the works in question are those of Johann Sebastian Bach, where the invisible thread that should link us to the era in which he lived seems to be irretrievably broken, the task takes on Herculean proportions. The aim of this analysis is to attempt a correct reading of the Clavierübung III—one of the most enigmatic works in the whole literature of the organ.
This work, which was composed at the high point of the composer’s creativity (1739), impresses us by its dimensions alone. It is part of a cycle of works, comprising the Six Partitas (Part 1, composed in 1731, BWV 825–830), the French Ouverture and the Italian Concerto (Part 2, composed in 1735, BWV 831, BWV 971), as well as the Goldberg Variations (Part 4, composed in 1742, BWV 988). And the Clavierübung III itself is also a cyclical work—it consists of 21 chorale preludes and four duets framed by a prelude and a fugue in E-flat major.
Bach certainly accorded the Clavierübung III particular importance. It is no coincidence that this was the first work for organ that he had published in Leipzig. What was Bach’s purpose in writing this work, and what means did he choose to fulfil it?

The history of the composition. The intentions and aims of the composer
The Clavierübung III was written to coincide with the 200th anniversary of Luther’s visit to Leipzig and the festal Whitsun service in St. Thomas Church on the 25th of May 1539, which effectively marked the official recognition of the Reformation in Leipzig. The Clavierübung III consists essentially of arrangements of chorales from the Protestant church service, and in its structure it is reminiscent of Luther’s Catechism, which consists of two parts: the Greater Catechism deals with the principles of faith, while the Lesser Catechism is directed more towards children and the less-educated part of the population. Correspondingly, each chorale melody—with the exception of Allein Gott in der Höh’ sei Ehr’ [Glory be to God alone on high]—is presented in two versions: a greater version which uses all the resources of the organ including the pedals, and a shorter manualiter version.
And indeed, because of its special structure, the Clavierübung III has often in the past been referred to as an “Organ Catechism,” and correspondingly it is usually referred to today as the “Organ Mass.” It is clear that neither of these two names do full justice to the structure of Bach’s composition. Nor do they explain the inclusion of the four duets.
The title of the work is as follows:

Dritter Theil / der / Clavier Übung / bestehend / in / verschiedenen Vorspielen / über die / Catechismus- und andere Gesaenge, / vor die Orgel: / Denen Liebhabern, und besonders denen Kennern / von dergleichen Arbeit, zur Gemüths Ergezung / verfertiget von / Johann Sebastian Bach, / Koenigl[ich] Pohlnischen, und Churfürstl[ich] Saechs[eschen] / Hoff-Compositeur, Capellmeister, und / Directore Chori Musici in Leipzig. / In Verlegung des Authoris.

[Third Part of the Clavierübung consisting of various preludes on the Catechism and other Hymns for the organ: for amateurs, and especially for connoisseurs of such work, for the refreshment of their souls, executed by Johann Sebastian Bach, Royal Polish and Electoral Saxon Court Composer, Capellmeister, and Directore Chori Musici in Leipzig. Published by the author.]

Bach here follows the example of his predecessor at St. Thomas Church, Johann Kuhnau (1660–1722), and modestly calls his work Clavierübung [Keyboard Exercise].2 He thereby encourages us, through diligent practice (Übung in German), to understanding his purpose in writing this work.
Let us accept this invitation.
The first question, even after a cursory look at Bach’s work, is probably “What does it represent in this compositional form? Are we to understand it as a unified dramatic whole or as a collection of diverse pieces for the keyboard?”
Characteristically, the usual concert practice suggests that the Clavierübung III is not seen as an integral work: virtually nobody plays the whole composition in its published form.3 But the question nevertheless remains: Is there really no suggestion of an overall dramatic structure within the work?
An analysis would help us to answer this question. But before we tackle it, we should—even very generally—look at some characteristics of the musical aesthetics and Bach’s particular compositional style during the period when he was working on the Clavierübung III.

The theological and philosophical basis of the work of J. S. Bach
Bach’s personal philosophy was heavily influenced by the philosophical ideas and the personality of Martin Luther (1483–1546). Books written by Luther accounted for a quarter of all the books in Bach’s private library. According to the personal inventory that was made after his death, Bach owned two complete editions of the works of Martin Luther in Latin and German, as well as works of his successors: Abraham Calov, Martin Chemnitz, Johannes Olearius, and others.4 The title page of an earlier version of the Clavier-Büchlein für Anna Magdalena Bach5 bears a note giving the title of the work as Anti-Calvinismus by August Pfeiffer, written in Bach’s own hand.
It is well known that Luther was a well-educated musician.6 In contrast to the majority of the reformers in the 16th century, Luther considered music to be a form of divine revelation. In the foreword to Georg Rhau’s anthology Symphoniae iucundae7 he wrote: “In summa: Die edle Musika ist nach Gottes Wort der höchste Schatz auf Erden.“8 [Summing up: Noble music is the greatest treasure on earth next to the Word of God.] He is quoted in the Encomion musices as giving a similar definition: “Musika ist eine schöne, liebliche Gabe Gottes, sie hat mich oft also erweckt und bewegt, daß ich Lust zu predigen gewonnen habe...”9 [One of the finest and noblest gifts of God is music. It has often aroused and moved me so that I have gained a desire to preach . . . ] And in a letter to Ludwig Senfl of 4 October 1530 we find the following lines in his handwriting:
Et plane judico, nec pudet asserere, post theologiam esse nullam artem, quae musicae possit aequari, cum ipsa sola post theologiam id praestet, quod alioqui sola theologia praestat, scilicet quietem et animum laetum…10
[I plainly judge, and do not hesitate to affirm, that except for theology there is no art that could be put on the same level with music, since except for theology, (music) alone produces what otherwise only theology can do, namely, a calm and joyful disposition.11]
Luther’s views were akin to those of Bach. Like the great reformer, Bach saw the world of music and the world of theology as very closely connected.12 A short handwritten treatise concerning figured bass, which Bach wrote while working on the Clavierübung III, is introduced with the following words:
Der Generalbaß ist das vollkommenste Fundament der Music welcher [auf einem Clavier] mit beyden Händen gespielt wird dergestalt das die lincke Hand die vorgeschriebenen Noten spielet die rechte aber Con- und Dissonantien darzu greift damit dieses eine wohlklingende Harmonie gebe zur Ehre Gottes und zulässiger Ergötzung des Gemüths und soll wie aller Music, also auch des General Basses Finis und End Uhrsache anders nicht, als nur zu Gottes Ehre und Recreation des Gemüths seyn. Wo dieses ists keine eigentliche Music sondern ein Teuflisches Geplerr und Geleyr.13
[The thorough-bass is the most perfect foundation of music. It is played with both hands on a keyboard instrument in such a way that the left hand plays the written notes, while the right hand strikes consonances and dissonances, so that this results in full-sounding Harmonie to the Honor of God and the permissible delight of the soul. The ultimate end or final goal of all music, including the thorough-bass, shall be nothing but for the Honor of God and the renewal of the soul. Where these factors are not taken in consideration, there is no true music, rather, devilish bawling and droning.14]

When Bach at the age of 23 left Mühl-hausen, he declared that the Endzweck [ultimate aim] of his creative work would be the regulirte kirchen music zu Gottes Ehren [regulated church music to the glory of God].15
One can further assess the musical and aesthetic views of the composer with the help of his annotations in the margins of a Bible that was published by Abraham Calov (1681–1682) in Wittenberg.16 These marginalia are quite valuable—they allow us to catch a glimpse of the personal views of their writer and open up his world for us.
Already in Exodus, Chapter 15, where the prophetess Miriam sings of the wonderful deeds of God, we can read in Bach’s own hand: “N.B. Erstes Vorspiel auf 2 Chören zur Ehre Gottes zu musiciren.” [N.B.: First prelude for two choirs to be sung to the glory of God.] As a comment on First Chronicles 29, v. 2117 we find the following statement by the composer:

Ein herrlicher Beweiß, daß neben andern Anstalten des Gottesdienstes, besonders auch die Musica von Gottes Geist durch David mit angeordnet worden.
[Splendid proof that, besides other arrangements for worship, music too was instituted through David by the Spirit of God.]18
First Chronicles 26 describes the choosing of musicians for the temple. Bach’s comment: “Dieses Capitel ist das wahre Fundament aller Gott gefälligen Kirchen Music.” [This chapter is the true foundation of all church music pleasing to God.]
And one final quote: Second Chronicles, chapter 5 contains the passage:

. . . it was the duty of the trumpeters and singers to make themselves heard in unison in praise and thanksgiving to the LORD, and when the song was raised, with trumpets and cymbals and other musical instruments, in praise to the LORD “For he is good; for his steadfast love endures for ever,” the house, the house of the LORD, was filled with a cloud, so that the priests could not stand to minister because of the cloud; for the glory of the LORD filled the house of God. (2 Chronicles 5:13–14)19

Bach annotates this text with a remarkable comment that has programmatic significance and shows not only his relationship to the composing, performing, and hearing of music, but also to the activities of a church musician in general: “Bey einer andächtigen Musique ist allezeit Gott mit seiner Gnaden Gegenwart.“ [Where there is devotional music, God with His grace is always present.]
These examples suffice to clarify where we must start if we wish to analyze the works of Johann Sebastian Bach. Albert Schweitzer wrote in his masterful fashion: “Music is an act of worship with Bach… For him, art was religion...”20 The orthodox Lutheran Bach, who was born and raised in Eisenach, Luther’s own town, where the façade of the main church of St. George was decorated with the Protestant motto “A mighty fortress is our God,” transcended in his music the boundaries of confession and creed. “In the last resort, however, Bach’s real religion was not orthodox Lutheranism, but mysticism. In his innermost essence he belongs to the history of German mysticism.”21
This mystical sensitivity to the presence of God and the desire to give witness to Him through music, coupled with his dazzling talent, enabled Bach in his later works to develop an astonishing artistic fusion, the likes of which had not been seen in the world’s cultural history.
In 1747 Bach was admitted to the Societät der musikalischen Wissenschaften [Society of the Musical Sciences], which his one-time pupil, the philosopher and music author Lorenz Christoph Mizler von Koloff (1711–1778), had founded.22 Mizler, a friend of Bach’s, was strongly influenced by Pythagorism and the rational philosophy of both G. W. Leibnitz (1646–1716) and Christian Wolff (1679–1754). He saw music as a mathematical science.23
The very fact that Bach accepted Mizler’s invitation to join the Societät der musikalischen Wissenschaften is in itself significant. The composer obviously sympathized with Pythagoras’s ideas concerning the universe and its perfect harmony: a harmony that, according to the teachings of the ancient philosopher and mathematician, was expressed in numbers,24 and shared the convictions of his progenies.
J. S. Bach became the fourteenth member of the Society after G. F. Telemann (6) and G. F. Handel (11), together with other well-known scholars and philosophers. Following the established tradition, upon joining the Society he contributed a mite of his own. In addition to the Canonic variations on “Vom Himmel hoch, da komm’ ich her” (BWV 769), the composer also donated a portrait of himself to the Society, which had been painted in 1746 by Elias Gottlob Hausmann. A microanalysis of the music manuscript that appears in this painting has been made by Friedrich Smend. The results have thrown light on significant aspects of Bach’s compositional methods, which until the middle of the twentieth century had not attracted much attention by scholars.25
Smend’s publication gave new impetus to investigating numerology in the works of the Cantor of St. Thomas Church in Leipzig.26 It is not without interest that the researchers first found support in the writings of Christian theologians, but later more and more in the works of the ancient philosophers.27

Features of J. S. Bach’s compositional method
Albert Schweitzer defined Bach as a phenomenon in the history of music: “Bach is . . . a terminal point . . . everything merely leads up to him.”28 Indeed the works of the Cantor of St. Thomas make use not only of the fruits of earlier achievements in composition, but they are also the consummation of the most characteristic tendencies in the music of his own time. He makes use of a plethora of past and present expressive techniques and puts them at the disposal of one single goal: the creation of “devotional music.”
So what exactly were the artistic methods used by J. S. Bach as a composer?
Victor Hugo once described Gothic cathedrals as “symphonies in stone.” If we apply this quotation to the works of Bach, we could say that his larger compositions are “Gothic cathedrals” in music. And when one looks more closely at how Bach approached a new composition we can actually find quite close parallels to architecture. One could contrast, for example, Bach’s methods with the processes current in Viennese Classicism. Whereas in the latter period composition proceeded in a “linear” fashion, beginning from the melody in one of the voices, the methods of Bach’s time started from quite a different point. First of all, the composer laid down a concept of the entire work, or—to use the architectural analogy—he created a “ground-plan.” Then he proceeded to fill in the details. An example of this method is provided by the Orgelbüchlein [Little Organ Book] (BWV 599–644).
This working method gave free rein to the composer’s imagination. The proportions of the composition and its “saturation” with both obvious and more hidden details—factors that played an important role in determining the overall sense of the work—could easily be incorporated in the composition from its very beginning. Great importance was attached to Affektenlehre [Doctrine of the Affections], musical-rhetorical figures, and numerology.
Bach was without a doubt a brilliant “musical architect.” There is no room in his works for anything non-essential. He worked in a similar fashion to the architects of the Middle Ages: every detail has its origin in the concept governing the whole. And as with the medieval builders, much of this work remains, even today, shrouded in mystery. There are always new avenues opening up in these seemingly well-known works for new generations of interpreters to explore.
One can of course only penetrate more deeply into this musical architecture of most of Bach’s works if the connection to the words of the chorales used by the composer is taken into account. Johann Gotthilf Ziegler (1688–1747), a pupil of Bach, wrote in 1746: “Herr Capellmeister Bach, who is still living, instructed me when playing hymns, not to treat the melody as if it alone were important, but to play them taking into account the affect of the words.”29
Johann Mattheson (1681–1764) described music as sounding speech. Naturally this form of speech required its own lexicon in the shape of the definite progressions of musical notes bearing the semantic meaning—the motives, or musical-rhetorical figures, as they are called. These were quoted by Bach’s cousin, Johann Gottfried Walther (1684–1748), in his Musicalisches Lexicon [Music Encyclopaedia] (1732) and in the Praecepta der Musicalischen Composition [Principles of Musical Composition] (1708). Another important compositional aspect was the use of rhetorical laws in the construction of the musical structure, so that the composition began to resemble a religious sermon. As already mentioned, the Affektenlehre [Doctrine of the Affections], which depended upon the use of unequal temperament and the resulting different emotional character of the various keys, played an important role in composition,30 as did, surrounded as it was by an air of mystery, numerology with its different levels of meaning.
One of these levels is to be found in allegorical symbolism. Andreas Werckmeister (1645–1706) gave the following meanings to the first eight numbers in Musikalische Paradoxal-Discourse:31 1 – God, unity; 2 – The Word, God the Son; 3 – The Holy Spirit; 4 – The world of angels; 5 – Symbol of Mankind (“sensual Mankind” [Numerus sensualis]); 6 – Third Person of the Godhead (3×2);32 7 – Symbol of purity and peace; 8 – Symbol of wholeness and perfection.
Another level is that of semantic symbolism. For example, the number 7 symbolises the Seven Last Words on the Cross.
A third level is that of cabbalistic symbolism. Each letter of the alphabet stands for a particular number: a = 1, b = 2, c = 3 and so forth. The letters i and j share the number 9, while u and v are both attributed to the number 20. This means that particular combinations of letters each have a corresponding number. For example, the number 14 is the sum of the numerical values of the letters BACH. Thus the number 14 (or similar numbers, such as 140 or 1.4) would be associated with the composer Bach, whose name was assembled from these individual letters.
Numbers were also used as a constructive element, whereby the harmonic proportions of the ratios of simple numbers, which had been known since Pythagoras’s time, were incorporated into the composition. In addition, the proportio divina, the “Golden mean,” was also used. Naturally Bach was a consummate master of all these creative methods and he used them constantly in his compositions. The most obvious example is the Clavierübung III, which occupies a key position among all Bach’s works for the organ.
Let us examine the structure of this composition more closely.

The chorale preludes
The central part of the work under consideration, as Bach’s title-page suggests, is the collection of chorale preludes. This collection covers not only the essential elements of the Protestant liturgy but also of Luther’s Catechism.
Kyrie, Gott Vater in Ewigkeit – Christe, aller Welt Trost – Kyrie, Gott heiliger Geist [Kyrie, God the Father, eternal – Christ, consolation of all the world – Kyrie, God the Holy Spirit] (BWV 669–674)
The triad of the first chorales creates a sense of unity. The models for these autonomous works were certain verses of the Gregorian chorale Kyrie fons bonitatis (10th century),33 which display the characteristic of a refrain. (Example 1) Such a compositional method is seldom found among Bach’s organ works. In the context of Kyrie – Christe – Kyrie it allowed the composer to establish by means of music the essence of the “one and indivisible” Holy Trinity.34
The first motif of the cantus firmus is characterized by a stepwise progression. In the final statement of the cantus firmus (which is the same in all three compositions), note the upwards leap over a fifth. It is perhaps of interest to note that both the stepwise movement on the one hand and the prominent role of the fifth on the other (elements that determine the mood of the first chorales of the Clavierübung III) play an important part in the dramatic construction of the whole work.
The unity of the initial Kyrie – Christe – Kyrie is underlined by the fact that they are written in a single compositional style—the stile antico. Hermann Keller described them as “Orgelmotetten kunst-vollster Art” [The most highly artistic motets for organ].35 The music suggests greatness and quiet strength. The movement of the accompanying voices working out the motifs of the cantus firmus is linear. The cantus firmus, which is kept in longer note values, appears successively in the soprano (Kyrie, Gott Vater in Ewigkeit), in the tenor (Christe, aller Welt Trost), and in the bass (Kyrie, Gott heiliger Geist), and thus symbolizes in similar fashion the three Persons of the Trinity: God the Father, who is above all, who holds all in being; Jesus Christ, the mediator between God and humankind; and the life-giving Holy Spirit.
The epic element appears organically tied to the inner dynamics of the Kyrie – Christe – Kyrie. The contemplative character of the first chorale gives way to a feeling of emotional turbulence in the second chorale. The third chorale is energy-laden, an effect achieved by the introduction of a fifth voice, the acceleration of the musical structure, and the use of chromatics.
The end of the chorale Kyrie, Gott heiliger Geist is quite remarkable: against the backdrop of the final statement of the cantus firmus in the pedals, a tie overflowing with chromatic dissonances appears in the upper voices. These six-and-a-half bars differ quite markedly from all that has gone before. The sound as it were illustrates the text, which at this point contains a plea for mercy. The word eleison is accompanied by an ostinato, which climbs in seconds and by a chromatic figura parrhesia. The music suggests a certain personal involvement. It is significant that one finds the motif BACH in crab motion here (although it appears in other notes), and finally encounters the signature of the composer: CH-BA in the alto of the penultimate bar. (Example 2)
There are altogether 60 bars in the chorale prelude Kyrie, Gott heiliger Geist, which matches Werckmeister’s concept well.36 And there is of course the additional association with the creation of the world (the six days of God’s creative work).37 It is worth mentioning that in the first prelude of the Clavierübung III the numerical symbol for the name Bach already occurs more than once. The subsequent statement of the theme in the chorale Kyrie, Gott Vater in Ewigkeit is not only emphasized by the use of parallel thirds, but also by its extension to 14 notes (the numerical value of the letters BACH).38 And the cantus firmus in the chorale prelude Kyrie, Gott heiliger Geist has a total of 41 notes (JSBACH).
The three manualiter Kyries, each in the form of a small fughetta, all elaborate the opening motif of the appropriate verse of the chorale. Each following chorale begins in the soprano with the last note of the preceding chorale, which serves to underline the inner unity of the three manualiter pieces Kyrie – Christe – Kyrie.
An interesting aspect, which is seldom found within Bach’s organ works, is how the keys of the six pieces we have looked at are related. Each of them has at least two tonal centers. We should not let the key signature with three flats of the greater chorale preludes Kyrie – Christe – Kyrie confuse us: the rules of musical notation would certainly have allowed these preludes to have been written with only two flats. It would appear that the composer intentionally adopted three flats in order to strengthen the association with the Holy Trinity.

Allein Gott in der Höh’ sei Ehr’
[Glory be to God alone on high] (BWV 675–677)
A special feature of the following section of the Clavierübung III is the fact that it has three different preludes on the chorale Allein Gott in der Höh’ sei Ehr’—the Protestant version of the Gloria in excelsis from the Gregorian Mass for Easter Sunday. An explanation for this phenomenon must be sought in the text of the chorale itself,39 as it sings the praises of the Holy Trinity. Correspondingly, Bach includes three preludes here, each of which is a very individually elaborated piece in three-part texture.
In the first prelude, elegant and rhythmical canon-like outer voices surround the cantus firmus in the alto. The next prelude is executed as a trio sonata with pedal obligato. The cantus firmus appears from time to time in one or other of the voices of this exquisite trio and blends with the natural flow of the music.40 The last chorale prelude is a small fugato in the manner of an Italian versetto, based on the first notes of the cantus firmus.41 All in all, these three versions of the angel’s praise Allein Gott in der Höh’ sei Ehr’ create a feeling of incorporality and immateriality, convincing us by their clarity and purity, and creating an impression of harmony and perfection.
In this section of the Clavierübung III there is a small, at first glance insignificant, compositional detail that is, however, very interesting when seen from the perspective of the dramatic construction of the whole. The keys of the chorale preludes—F major, G major, and A major—form an ascending motif that is the basis for all three preludes on Allein Gott in der Höh’ sei Ehr’. The composer must assuredly have chosen this sequence of keys with the aim of thus uniting the whole cycle. Numerology reveals another interesting aspect—the numerical values of F, G, and A (6 +7 + 1) comes to 14, the same value as BACH.

Dies sind die heil’gen zehn Gebot’ [These are the holy Ten Commandments] (BWV 678–679)
Following the lead of Luther’s Catechism, Bach now begins an extensive section of the Clavierübung III with arrangements of the Gregorian chorale on an Old Testament theme, Dies sind die heil’gen zehn Gebot’.42 This is the last pair of chorales in a major key for the remainder of the cycle and the only time that Bach uses the same key for two consecutive compositions—Mixolydian G major, which is one of the purest keys in unequal temperament. It is significant that in both the Orgelbüchlein and in Cantata 77, the chorale melody Dies sind die heil’gen zehn Gebot’ is also written in this key.
The greater chorale prelude is developed as a composition for five voices, with the cantus firmus appearing a total of five times as a canon in the tenor. Thus it appears ten times in all, symbolizing an obedient response to the Law.43
The beginning of the prelude is wonderful: over a pedalpoint we hear, emerging out of the stillness, the motif of three descending notes, which we encountered earlier in the piece, worked out as a canon in the upper voices. The measured diatonic motion, the prepared suspensions, the surrounding motifs, and the ascending triads—these are just some of the musical means the composer has used to create a world of unspoiled purity, order, and harmony, in which the unsullied inhabitants of Paradise were at home before the Fall. (Example 3)
A change in character occurs in the fifth bar44 with the introduction of a figura suspirans45 and a motif of ‘falling seconds’, supplemented by a descending chromatic figura parrhesia motif in the alto. (Example 4)
Now the music is dominated by grief, sorrow, and misfortune.46 A change occurs once more in the sixth bar with the introduction of a figura kyklosis or figura circulatio in the alto47 (Example 5), which enriches the fabric with its new nuances. Thus with the help of symbolic motifs that are organically woven into the very fabric of the music, the composer brings us closer to the meaning of the chorale.
The First Commandment, which Luther in his Great Catechism deems to be the most important, is interpreted in the second verse of the chorale:

Ich bin allein dein Gott, der Herr,
kein Götter sollst du haben mehr,
du sollst mir ganz vertrauen dich,
von Herzens Grund lieben mich,
Kyrieleis.

[I alone am your God, your Lord,
No other Gods shall you have,
You shall put your whole trust in me,
Love me from the depth of your heart.
Kyrieleis.]

There is much evidence that precisely these lines were the starting point for Bach’s plan for the whole composition.
It is interesting to note that where the text speaks of “the love of God that comes out of the depths of the heart,” Bach interrupts the cantus firmus (bars 48–50) and increases the number of repetitions from ten to twelve. The motivation for this change can best be seen as an attempt to create a connection between the Old and New Testaments, whose interpreters in the new Christian congregations were the twelve Apostles. And Bach will follow the same intention to connect, through the symbolic comparison of the numbers ten and twelve, the Mosaic Law and the teachings of Jesus again in the Eucharist part, the conclusion of the chorale prelude section of the Clavierübung III.
It is well known that in the New Testament the Commandment of Love takes on decisive significance: “Jesus answered . . . you shall love the Lord your God with all your heart, and with all your soul, and with all your mind, and with all your strength” (Mark 12:30). The composer underlines the importance of this commandment with the help of special methods that are introduced at key points. When the word Herz [Heart] appears in the chorale text, Bach highlights it (in bars 46-47) with two groups of 16th notes, and when the words lieben mich [love me] appear in bars 51–52, he uses the heterolepsis, a musical rhetorical figure that creates the effect of two being united in one.48 Thus the composer uses musical means to portray the tangible content of the text. (Example 6)
Numerology plays an especially important role in the chorale prelude Dies sind die heil’gen zehn Gebot’.49 The chorale prelude has 60 bars (corresponding to the six days of creation). A pause first appears in the pedal after 37 notes, which can be seen as the Labarum, or Chi-Ro Christogram.50 The next pause comes after 60 further notes (another apparent reference to the creation of the cosmos). The subsequent melodic structure of the pedal line up to the pedalpoint in bar 29, which creates the illusion of a reprise, contains 47 notes. In the first bar, after the pause (bar 21), we encounter a leap of two octaves in the pedal, covering the entire range of the pedal, which is very unusual. (Example 7)
It is well known that Bach often referred to the Psalter, as did Luther in his Catechism. Psalm 47:2 states: “For the LORD, the Most High, is awesome, a great king over all the earth.” The text of the cantus firmus quoted at the point of the two octave leap is: Kein Götter sollst du haben mehr [No other Gods shall you have]. Michael Radulescu suggests that we should see the leap as an original “musical comment” by the composer, which, though hidden behind the abstract numerological symbolism, is to be understood as a distinct statement: “I am larger than life, I am your King.”51
The subsequent phrase in the pedal contains 147 notes. When Luther in his Catechism explains the meaning of the Ten Commandments, he quotes Psalm 147:11: “But the LORD takes pleasure in those who fear him, in those who hope in his steadfast love.” By introducing the number 147 into his chorale prelude Dies sind die heil’gen zehn Gebot’, Bach is underlining the actuality of the psalmist’s words quoted by Luther for the theme of the Decalogue.
The final notes of the cantus firmus in the second tenor are accompanied by a descending counterpoint in the first tenor, beginning with a chromatic figura parrhesia, which contains 12 notes (bars 57–60). The last phrase in the pedal consists of 14 notes (BACH), which is preceded by two short phrases of five notes each.
After all the above we can concur with those experts who suggest that the basic idea behind this work is love for the Creator.52 Additional confirmation for the correctness of this view is the number 315, which is the sum of all notes in the pedal. Albrecht Clement considers this number to be the numerical expression of the phrase Du sollt Gott, deinen Herren, lieben. [Literally: “You should love God, your Lord” as a direct rendering of the Luther Bible’s translation of Mark 12:30.]53
Characteristically, Bach introduces this summons in the title of Cantata 77, whose opening chorus is built upon the theme of the chorale prelude Dies sind die heil’gen zehn Gebot’, viz.

Du sollt Gott deinen Herren lieben
24 + 73 + 59 + 49 + 65 + 45 = 315

The manual fughetta on the chorale Dies sind die heil’gen zehn Gebot’, written in the form of a gigue, is also dominated by the number 10, although it also contains other interesting numerical allusions.
First of all, it is a four-voice fughetta and the theme is presented ten times (4×10 = 40). The same relationship can be seen in the exposition of the fughetta: ten bars of four dotted eighth notes (10×4 = 40). The theme runs for ten beats. Thus we see the same relationship in the exposition: 10×4 = 40. The theme in the second exposition is presented in inversion and in a shortened form (six beats). The relationship is correspondingly 6×4 = 24. And finally, the last two stretti quotations of the theme (bars 32–35) give us the relationship 8×2 = 16, as the theme here is eight beats long. It is not difficult to see that the addition of 24 and 16 results in the key number 40, which is apparently a reference to the Jewish people’s forty years of wandering in the wilderness before being given the stone tablets with the Decalogue.
The theme has a most interesting structure. It consists of two parts: the main melody of the chorale emerging from a repeated ostinato note and its leaps (six beats), and stepwise motifs over a fifth (four beats). (Example 8) Christoph Albrecht described the theme figuratively as a musical picture of a “raised warning forefinger.”54 But numerology allows us to find deeper connotation in it. The second part of the theme contains 14 notes (BACH). One could consider this as a mere coincidence, were it not that we meet the melody with this numerical symbol again at other central formative points in this little piece.
This second part of the melody occurs as a theme in its own right in the 41st beat of the fughetta (JSBACH), where it fills out the eleventh bar at the junction between the two expositions. Again, this melody is consistently developed in the 14 bars that separate the two concluding quotations of the theme from the second exposition. And we would finally add that the number 14 is underlined by the sum total of all the beats in this chorale prelude: they all add up to 140.
Without a doubt it would be the very height of negligence for a performer who is looking for an authentic interpretation to ignore the manifold recurrence in the composition of the name of its creator. The composer of the manual version of Dies sind die heil’gen zehn Gebot’ obviously had definite reasons for weaving his name again and again into the musical fabric of the work.
Let us boldly assume that in this work Bach wishes to embody the idea of the divine Commandments as the cornerstone of his own life. The tenfold repeated theme of the chorale Dies sind die heil’gen zehn Gebot’ and the numerical symbol 40 harbor the idea of the Commandments. Their importance for Bach personally is attested to by the composer’s repeated use of the symbol 14.

This article will be continued.

Robert August is director of music/organist at First Presbyterian Church of Fort Worth, Texas. Previously he was assistant university organist and choirmaster at The Memorial Church at Harvard University, during doctoral studies at the New England Conservatory of Music. A native of the Netherlands, he has an extensive background in historical performance. August has served as carillonneur at Brigham Young University, and as organist and conductor at churches in the Netherlands and the United States. In addition to collaboration with artists such as Yo-Yo Ma, Christopher Hogwood, and Simon Carrington, he has performed in Europe and the United States as a solo artist and accompanist, including tours and CD recordings with the Harvard University Choir and the Harvard Baroque Chamber Orchestra. Robert and his wife, flutist Dolores August, often collaborate on modern and period instruments.

This is a work that has occupied
me for the whole of the previous year in an effort to make it worthy of the lofty name it bears. It is also a work which, I believe, is likely to outlive my other creations the longest.”1 This was Schumann’s description of the Six Fugues on the Name of BACH, op. 60, in a letter to his publisher, after completion of the final fugue. Schumann took great care and pride in the six fugues, but his prediction could not have been more off target as the fugues are rarely performed anymore. Rather, they have become the topic of ongoing discussions about Schumann’s mental state in relation to the quality of his output.
The notion that the Six Fugues on the Name of BACH are of lesser quality than the majority of Schumann’s oeuvre seems to be based on largely subjective analyses. Such subjectivism is not uncommon in art and music, as is evident in Albert Schweitzer’s discussion of J.S. Bach’s Passacaglia in C Minor, BWV 582: “He [Bach] saw clearly, however, that on the whole the incoherency of this kind of work was not suitable to the greatest organ music, and he ventures upon the experiment only with this colossal theme.”2 In Schweitzer’s opinion, the Passacaglia was a compositional failure that did not compare to Bach’s other organ works.
Robert Schumann was of a different opinion: “After a pause, these [organ compositions] were followed by the Passecaille in C Minor (with 21 variations, intertwined so ingeniously that one can never cease to be amazed) admirably handled in the choice of registers by Mendelssohn.”3 Schweitzer’s and Schumann’s remarks, published roughly sixty years apart, could not be more contradictory.
Why is it that the Passacaglia can render such opposing views, especially by two men known for their deep respect and understanding of Bach’s music?4 With regard to Schweitzer, we cannot be sure if his comments were the result of a somewhat subjective analysis, but he undoubtedly would not have published his findings unless he believed them to be correct.5 Schumann’s opposing remarks are fascinating as well. They not only provide us with his opinion of the Passacaglia but also unveil his often-overlooked understanding of the organ.
Tragically, Schumann’s organ works, the Six Fugues on the Name of BACH, op. 60, have often been deemed ‘unworthy’ and are repeatedly criticized or, perhaps worse, omitted from Schumann biographies. Op. 60 is systematically neglected and misinterpreted, often as a result of careless research. It is undoubtedly the most disputed cycle Schumann ever composed. Despite a number of favorable articles, a flow of negative writings remains consistent.6 Numerous articles on the six fugues are based on flawed research and, in some cases, pre-existing articles. Biographers often use Schumann’s mental condition to explain the lack of quality in the six fugues, conveniently ignoring the fact that Schumann produced some of his best works during the same period, including the Symphony in C Major and the Piano Concerto in A Minor.7

A musical cure
A general misconception of Schumann’s organ works seems to have carried well into the 20th and 21st centuries, as several of even the most recent Schumann biographers merely reference the fugues rather than opening up a dialogue or deeper discussion. Schumann’s organ works are neglected in several “comprehensive” Schumann biographies. Alan Walker, e.g., speaks favorably of the 1845/46 compositions in general, but omits op. 60 altogether.8 George Dadelsen describes the six fugues as “appallingly monotonous” while trying to compete with Bach’s Art of Fugue.9 Other biographers carelessly mislabel op. 60; Marcel Brion describes the Four Fugues on the name of Bach, op. 72,10 while John Worthen writes: “In April he began writing his Six Fugues for Organ on B-A-C-H (op. 60), a sequence interrupted only by the arrival of a rented pedal-piano which allowed him to write works for keyboard and pedal which did not require an organ.”11 Schumann, in fact, did not interrupt his fugal writing. Instead, a pedal attachment for the piano was hired to practice organ.12 Eric Jensen makes a similar mistake: “Schumann rented a pedal piano—a piano fitted with pedals for the feet like an organ—in order to become familiar with the technique involved.”13
Although Schumann was by no means an accomplished organist like Mendelssohn, he did have a deep understanding of the instrument, as is evident in numerous sources.14 Robert Schauffler claims that the fugues were mere play: “To Schumann at the height of his career, such exercises [contrapuntal studies] were mere play. While diverting him, they used up so little of his true creative power that, with the approach of warm weather, he was able to throw himself into making two of his chief masterpieces: the Piano Concerto and the C Major Symphony.”15 Schauffler continues:

Schumann must have felt in his bones that fugal writing was not in his line; for not until 1839 did he compose his first published attempt, that unsuccessful experiment, the Fughette, op. 32, no. 4. He gave out nothing more of the sort until the nervous collapse of 1845, during which he wrote works that look passing strange in a catalogue of his music.16

After a short description of Schumann’s contrapuntal works of 1845, Schauffler writes:

The composer’s nervous collapse had been aggravated by the too intense labor and excitement of his years of song, symphony, and chamber music. One suspects that when, as he wrote Mendelssohn on July 17th, 1845, ‘an onslaught of terrifying thoughts’ had brought him to try his hand at fugal writing, very much as we of today would cajole a nervous invalid into doing crossword puzzles, to take his mind from his troubles. The very fact that Schumann’s intensely subjective nature made it almost impossible for him to give of his best in this formal, objective style allowed him to play with these contrapuntal forms without expending too much energy.17
Peter Ostwald too, believes that the contrapuntal works of 1845 were exercises to improve the composer’s mental condition:

Despite his physical and psychological complaints, Schumann was beginning to do some composing again, but it was mainly the sort of counterpoint exercises he had relied on, as a way of settling his mind, during earlier depressive episodes. He rented a special musical instrument, called a pedal piano, that “has an extra set of strings and hammers, making it easier to play fugues, and worked on Bach for a while.”18

While Ostwald does not stand alone in his opinion of Schumann’s mental state in relation to the compositions of the contrapuntal year of 1845, one cannot but wonder why they, in particular the organ works, have methodically been deemed inferior. Ostwald also writes:

Before the trip with Clara, in August 1845, Schumann had composed several fugues based on the name BACH, and he published an impressive amount of contrapuntal work later that year and the next. The six BACH Fugues in particular must have required enormous concentration, since not only are they based on a musical relationship between Bach’s name and the notes of each fugue subject, but they also incorporate an intricate mathematical system, the so-called Bach numbers, which Bach himself had used to provide cohesion in his contrapuntal work.19

With all due respect to Mr. Ostwald, his findings are based on pre-existing, flawed research. Though Schumann indeed incorporated certain Baroque principles in his organ works, Peterson’s attempt to attribute “Bach numbers” to the fugues holds no ground. Similar misguided assumptions have been applied to Bach’s music as well, claiming for example, that Bach had left clues in his music in regards to his own date of death.20 Despite his intrigue with Bach numbers, Peterson’s opinion of the fugues as a whole is less than favorable: “Schumann’s fugal writing seems, in spite of his studies, to have been a contrivance which he discarded when he felt hampered by it, even in a work entitled ‘fugue’.”21 Stephen Walsh provides us with a similar statement: “Even in the finest passages of op. 60 one is aware of a certain impersonal quality about the writing.”22
A recent biography by John Worthen reads: “This [study of counterpoint] was, after all, a musical cure; one that involved creating music on the page, after the enforced dry period of the autumn of 1844.”23 Worthen continues with some blatant assumptions:
Such music insisted on structure and pattern, rather than on the harnessing and expression of emotion and melody which had made the work on Faust so exhausting. The fugal music could be worked out logically and tunefully, within its own very narrow confines. Its very limitations offered freedom from excitement.24
What Worthen exactly means by ‘tunefully’ remains uncertain. As an analysis of the fugues will demonstrate, his claim that the fugues are confined or free from excitement could not be farther removed from the truth. Worthen’s next statement too, is completely false: “At any rate, the ‘quiet’ neo-Baroque music that engaged Schumann in the spring and early summer of 1845 may have been a rather narrowly focused sequence of works to occupy the composer of the Finale zu Faust, but it had served the purpose of getting him back into composing.”25 As we will see in the following discussion, the perception of Schumann’s contrapuntal studies as mere therapeutic tools has remained a common yet flawed assumption for over a century.

Schumann and Bach
An aversion to the organ works is routinely linked to Schumann’s mental illness, while some scholars maintain that Schumann simply was not a real contrapuntist, and that his knowledge of counterpoint was quite moderate. Though the number of unfavorable commentaries seems perhaps overwhelming, it is interesting to make the comparison with—at least as many—complimentary testimonials. Schumann’s studies in counterpoint commenced well before composing the six fugues. The numerous entries in the diaries and household books depict Schumann as a prodigious student of Bach works and contrapuntal techniques (see Appendix 1). Schumann seems to have taken a natural liking to Bach’s music, perhaps enhanced by the Bach revival of the early 19th century. Leon Plantinga writes:
He [Schumann] subscribed to a rather deterministic view of history in which a central tradition in music could be expected to develop in certain orderly and predictable ways. For him this tradition, for all practical purposes, had its beginning in Bach, the first in a series of monumental composers whose personal contributions comprised the locus of an inevitable line of progress leading to his own time. This line extended through Beethoven and Schubert to Schumann’s own contemporaries.26
This ‘extended line’ manifests itself in the organ fugues as Schumann reaches back to older forms while engaging in a new kind of fugal writing. Though Schumann was not the first composer to incorporate the famous BACH theme, the Six Fugues on the Name of BACH comprise the first significant cycle of organ works of its kind, soon to be followed by Liszt, Reger, and many more. For Schumann, studies in the Art of Fugue were crucial in the genesis of the organ fugues. As Gerhard Weinberger writes:
The overall conception, the thematic material and the extremely high quality of the writing all derive from Bach; this fugue cycle represents the end of a developmental phase which culminated in Schumann’s study of Bach’s music (the six fugues may be viewed directly as modeled in the Art of Fugue) and of the fugue per se.27
Weinberger continues: “Nevertheless, the fugues are by no means derivative stylistic copies, but effective ‘character fugues’ in the romantic vein.”28 An interesting detail is the fact that Schumann, despite his admiration of Bach, deemed the Art of Fugue too intellectual. His view in this matter may be explained by his famous quote:
The best fugue will always be the one that the public takes for a Strauss waltz; in other words, a fugue where the structural underpinnings are no more visible than the roots that nourish the flower. Thus a reasonably knowledgeable music-lover once took a Bach fugue for a Chopin etude—to the credit of both! Thus, too, one could play for many a maiden the last part of one of the Mendelssohn fugues and call it one of the Lieder ohne Worte. The charm and tenderness of the figures are such that she would never be reminded of churches and fugues.29
This last comment is fascinating. “Never be reminded of churches” is a telling statement that says a lot about the Zeitgeist, since churches and fugues are so strongly connected here, and in such a harsh way.
Schumann’s interest in the organ was steeped in a deep admiration for Bach. In the April 1842 issue of the Neue Zeitschrift für Musik he wrote: “ . . . At our next meeting, a volume of well-executed fugues would please us more than another one full of sketches. At this royal instrument, the composer must have learned the value of clearly defined artistic form, such as that given to us by Bach in the largest as well as smallest works.”30 Three years earlier Schumann wrote: “But it is only at his organ that he [Bach] appears to be at his most sublime, most audacious, in his own element. Here he knows neither limits nor goal and works for centuries to come.”31 Schumann’s organ fugues, thus, are not a byproduct of mental exercises. They are carefully crafted works, based on a long tradition.
Approaching fugal composition from a new (Romantic) perspective, Schumann felt that he had created works that were truly unique. Like Bach himself, Schumann united the old and new, resulting in six spectacular character pieces. After all, according to Schumann, “Most of Bach’s fugues are character pieces of the highest kind; in part truly poetic creations,”32 and Schumann’s fugues were no different. In the diaries Schumann refers to Bach’s compositions repeatedly. He seemed to be concerned with preserving and reviving Bach’s legacy, which, according to Hans T. David, “. . . by invoking the name of Bach again and again, helped gain for Bach’s work a secure place in the minds of educated musicians.”33 In addition to the Bach legacy, Schumann was concerned with preserving his own legacy. His preferred medium in this—the fugue—is easily explained by his lifelong admiration of Bach’s keyboard fugues. Charles Rosen gives a second reason for Schumann’s choice: “In the nineteenth century, the fugue had become a demonstration of conventional mastery, a proof of craftsmanship. Besides competing with Beethoven, Schumann conforms to the standard pattern of fugue laid down by Cherubini.”34
In addition to Bach’s keyboard fugues, at least two more sources play an important role in Schumann’s contrapuntal output: Marpurg’s Abhandlung von der Fuge (1753) and Cherubini’s Cours de Contrepoint et de Fugue (1835). Federhofer and Nauhaus write:

The composer’s concern with counterpoint began during his ‘apprenticeship’ with Heinrich Dorn (1804-1892) in the years 1831/32, and bore its first fruits in his exercise books. Schumann subsequently turned his attention to F.W. Marpurg’s Abhandlung von der Fuge [Treatise on Fugue], parts of which he studied again, albeit reluctantly, in the autumn of 1837, along with Bach’s Well-Tempered Clavier. This independent study is reflected, in an artistically transmuted form, in the book of Fugengeschichten [Fugal matters] (November 1837) which is at present held at the Robert Schumann Haus in Zwickau.35
According to the Haushaltbücher, the Schumanns’ studies of Cherubini’s treatise commenced April 6, 1845, the same month Robert finished the first two organ fugues. Cours de Contrepoint et de Fugue is largely based on Bach works and clearly serves as a point of departure for Schumann’s organ fugues. Two and a half weeks later, on April 24, Clara describes the rented pedal board for their piano: “. . . we obtained on hire a pedal to be attached below the pianoforte, and from this we received great pleasure. Our chief object was to practice organ playing.”36 Both Robert and Clara enjoyed the organ, but it seems that the intent was to study organ rather than becoming concert organists like Mendelssohn. Clara by then was a renowned concert pianist, while Robert had given up keyboard playing some fifteen years earlier, due to his numb finger.
A combination of counterpoint studies, a deep admiration for Bach, and a great appreciation for the organ finally resulted in the counterpoint episodes of 1845. In regards to Schumann’s organ compositions, Joachim Draheim writes, “The exceptional importance and originality of these fugues were long insufficiently appreciated, although they belong to the very few truly distinctive organ compositions from the first half of the 19th century, together with Mendelssohn’s Organ Sonatas, op. 65, to which they owe certain impulses.”37 Besides generating an artistic legacy, Schumann may have anticipated commercial success from his contrapuntal output; works for pedal piano were hardly available, and Schumann made sure he was among the first to write for the instrument, ensuring a ‘head start’ in any possible financial gain. The six fugues were, like Mendelssohn’s organ sonatas, among the very few serious organ compositions of their time, and the first large cycle of organ fugues on the name of BACH. And as Schumann himself points out, the organ fugues can also easily be performed on piano (four hands). Schumann cleverly published opp. 56, 58 and 60 as works for pedal piano or organ, most likely to enhance sales. However, the Six Fugues on the Name of BACH lacked (financial) success, and remain Schumann’s only attempt at organ composition. Schumann, however, was very pleased with his contrapuntal endeavors. A letter of 8 February 1847 to his friend Carl Ferdinand Becker illustrates Schumann’s satisfaction with the six fugues: “I have never polished and worked so long on any composition of mine as on this one in order to make it worthy of the illustrious name which it bears.”38

Mendelssohn
Like Mendelssohn, Schumann favored a modern fugal type steeped in the Bach tradition, yet combined with a poetic flavor. As Plantinga points out: “It was the particular genius of Mendelssohn, Schumann said, to show that successful fugues could still be written in a style that was fresh and yet faithful to its Bachian and Handelian models; these fugues hold to the form of Bach, he felt, though their melody marks them as modern.”39 Already a famous conductor, composer and organist, Mendelssohn wrote his Three Preludes and Fugues, op. 37 in 1836–37. Later, in 1844–45, he wrote the Six Sonatas, op. 65. As Klaus-Peter Richter points out, the motivic resemblances between Mendelssohn’s and Schumann’s organ works are more than obvious.40 In reference to Mendelssohn’s fugues of the six sonatas,41 Schumann writes: “I do not wish to indulge in blind praise, and I know perfectly well that Bach made fugues of quite a different sort. But if he were to rise from the grave today, he would, I am sure—having delivered himself of some opinions about the state of music in general—rejoice to find at least flowers where he had planted giant-limbed oak forests.”42
Mendelssohn’s organ works were well received by critics43 and may have generated Schumann’s contrapuntal aspirations, though Schumann may have chosen a slightly different path to avoid comparison with Mendelssohn’s compositions; in addition to writing the Six Fugues on the Name of BACH he wrote a set of canons and sketches for the pedal piano.44 Schumann hoped to be among the first to publish works for this relatively new instrument, ensuring financial and artistic gain. Including the piano as an optional instrument for performance of the fugues, sketches, and canons aided Schumann in several ways; it bypassed the archaic reputation of the organ while marketing the music for the most widely used keyboard instrument of that time. An advertisement in the Neue Zeitschrift für Musik states:

Some Studies and Sketches for the pianoforte with pedal will shortly be published from Robert Schumann. We would like to remind our readers that in our opinion, when once this combining of instruments finds general acceptance, performers will have the opportunity not only to return to the earlier art and bring classical organ works into private homes, but also discover many different uses for the pedal piano and accomplish new effects.45

Alas, the pedal piano never became the widely used instrument Schumann was hoping for, and none of the contrapuntal studies of 1845 were a financial success.

Schumann and the organ
The rise of the Enlightenment caused a great shift in the use of instruments in churches, the court, and at home. The new, galant style called for instruments capable of immediate and subtle changes in timbre and dynamics; hence, the piano became the new keyboard instrument of choice. The organ, as Schumann wrote, reminded people of “churches and fugues,” and was considered an archaic and static instrument. Despite its tainted status, Schumann proceeded to compose for the instrument, a decision that may be partially attributed to a long tradition; many post-Renaissance composers wrote larger works to preserve their name in history. Several of Bach’s sacred compositions, for example, were simply too long to be included in church services.46 Similarly, Mendelssohn, Brahms, and Schumann were not employed by the church, yet their output includes a large quantity of sacred works.47
Scholars have often blamed Schumann’s limited knowledge of the organ for the so-called poor quality of the organ works. However, Schumann knew the organ well, and his understanding of the instrument was in fact greater than most of his contemporaries. Russell Stinson recently uncovered an important document in regards to Schumann’s perception of Bach, as well as the organ. The Clara Schumann Bach Book offers a detailed list of Bach keyboard works from Schumann’s library and contains numerous detailed markings (corrections, registrations, etc.) in Schumann’s hand (see Appendices 2 and 3 on page 26).
The source is very specific and provides us with a list of Bach’s keyboard works that Schumann owned before the contrapuntal year of 1845. In one particular example Stinson points out: “In the case of the Clavierübung setting of ‘Vater unser, im Himmelreich,’ Schumann bracketed every phrase of the canon on the chorale melody, similar to how he analyzed fugues from the Well-Tempered Clavier.”48 The Vater unser chorale prelude is a compositional tour de force and one of Bach’s most complex organ works. Based on the many markings, this work must have had a great impact on Schumann. Schumann also corrected typographical errors and gave detailed descriptions about the use of stops, manual changes, as well as pitch designation, all of which demonstrate more than basic knowledge of the organ.49 As Stinson points out:
Just consider how Schumann annotated, from Part 3 of the Clavierübung, the manualiter setting of “Aus tiefer Not schrei ich zu dir,” a work in which Bach subjects each phrase of the chorale tune to a complex fugal exposition before stating the melody in augmentation in the soprano voice. Following Bach’s constant use of inversion and stretto, Schumann bracketed, in addition to each phrase of the chorale proper, every one of the roughly forty fugal statements.50

The Clara Schumann Bach Book is an invaluable source, and for once and for all does away with the general misconception of Schumann’s limited knowledge of the organ. The evidence in Schumann’s personal library discloses both his interest and knowledge of Bach, the organ and counterpoint.

A new approach
Schumann was known to compose rather fast, but it took him from April to November to write the fugues. In the Diaries, Schumann writes:

I used to write most, practically all of my shorter pieces in [the heat of] inspiration; many compositions [were completed] with unbelievable swiftness, for instance, my First Symphony in B-flat Major [was written] in four days, as was a Liederkreis of twenty pieces [Dichterliebe]; the Peri too was composed in a relatively short time. Only from the year 1845 on, when I began to invent and work out everything in my head, did a completely new manner of composing begin to develop.51

This new manner of composing resulted in works that were based on a thorough, perhaps more intellectual approach. Schumann’s keyboard compositions of 1845 are often said to be more objective than his earlier compositions.52 That in itself is a subjective statement, and should be taken with a grain of salt. Traits of the younger Schumann can be found in any of the collections written in 1845, but they also expose a maturing composer. These are indeed contrapuntal works based on models by Bach, Marpurg, and Cherubini, but Schumann remained true to himself as a person and artist by combining the new with the old. The fugues exhibit a blend of sentiment (third fugue), restriction (fifth fugue), and excitement (second and sixth fugues). Schumann, as Weinberger says, “demonstrates the highest skill in contrapuntal writing, using all sorts of complicated polyphony culminating in the concluding double fugue. But at the same time he produced expressive compositions which he himself termed character pieces, but in the strict style.”53 Charles Rosen was right when he wrote, “Throughout his short musical life, Schumann produced his most striking works not by developing and extending Classical procedures and forms, but by subverting them, sometimes undermining their functions and even making them momentarily unintelligible.”54
The six fugues remain among the most unique works in the organ repertoire, and Schumann was well aware that these compositions differed from his earlier output. Having given up his old habit of composing at the piano, Schumann felt liberated. Daverio sheds more light on Schumann’s new manner of composing: “. . . it is perhaps better understood as a logical outgrowth of his approach to large-scale instrumental composition in the earlier 1840s rather than as a radical break.”55 Scholars have maintained the notion that Schumann’s oeuvre reflects several distinctly different compositional periods. Daverio’s opposing view, however, “explains” the six fugues in a nutshell:

Perhaps Schumann intermingled ‘subjective’ and ‘objective’ qualities throughout his career, but with varying degrees of emphasis, a hypothesis implying that the passage from a ‘subjective’ to an ‘objective’ phase was hardly abrupt. To insist on a hard and fast demarcation of style-periods in time is to miss the point, namely, that Schumann’s oeuvre unfolds in a series of sometimes parallel and sometimes overlapping phases. The products of his imagination may thus be viewed as points where divergent or complementary trends intersect.56

Von Wasilewski agrees with this view, pointing out the combination of strict form and a Romantic, poetic spirit:
Of the two sets of fugues (ops. 72 and 60), the latter, consisting of six fugues on the name of Bach, is of extraordinary merit. The first five fugues especially display so firm and masterly a treatment of the most difficult forms of art, that Schumann might from these alone lay claim to the title of a profound contrapuntist. They show variety of plastic power with four notes only. The tone of feeling varies in all six pieces, and is always poetic, which, in connection with a command of form, is the main point in composition. These are serious character pieces.57
Though the Canons and Sketches display a more intimate, subjective side of Schumann, the six fugues demonstrate a stronger balance between head (Eusebius) and heart (Florestan). Daverio’s and Von Wasilewski’s points of view are supported by the great variety of character in Schumann’s mid-1840s compositions.

Six Fugues on the Name of BACH
Schumann’s Six Fugues on the Name of BACH are the product of a carefully planned blueprint. Modeled after Bach’s examples, one might expect various Baroque elements in these pieces. Indeed, the fugues were conceived as a set of six, similar to many of Bach’s cycles (including many of his organ works).58 Such systematic arrangement of cycles containing six pieces was common in the Baroque era and, as Piet Kee points out, is rooted in numerology that goes back as far as Pythagoras.59 The use of number symbolism in music diminished substantially after the rise of the age of the Enlightenment, and despite Schumann’s use of ciphers (on several occasions) there is no evidence that points to the composer’s knowledge or intentional use of number symbolism. Schumann’s fugues, however, do reveal a consistent observance of the Golden Ratio. This number (0.6180339887…) is found in nature, music and art.60 Schumann’s knowledge of the Golden Ratio is not recorded anywhere, but based on the many examples found in his and his contemporaries’ music, it seems plausible that he was familiar with the concept. The use of the Golden Ratio though, so closely related to nature, seems to have prevailed through the Romantic period into our time.61 A close examination of the Six Fugues on the Name of BACH unveils Golden Ratio (G.R.) proportions (often multiple times) in each of the six fugues. These examples are often found within a measure of the exact G.R. When applying the G.R. to the number of measures in each fugue we see the following outcome:
Fugue I. The first fugue totals 64 measures. When we apply the G.R. to these 64 measures, we come to 64 x 0.61 = 39, or measure 39. This measure contains two consecutive subject entries in the pedals. A ‘reversed’ G.R. (counting 39 measures from the end) is found in m. 25, located between two more subject entries (the second being a false entry) in the pedals. NB: this fugue only contains two such double-pedal entries, each clearly defined by the Golden Ratio. In addition, the apex (c3) is reached first in m. 40 (one measure after G.R measure 39).62
Fugue II. The second fugue is 174 measures long; 174 x 0.61 = 106. In m. 106 new material is presented (ascending octaves/scales). A reversed G.R. leads us to m. 68, where the subject appears in the pedals (in its entirety) for the first time. Like several Bach compositions, this fugue contains Golden Ratios within Golden Ratios. The second fugue can be separated into three separate divisions: At m. 74 we see a clear separation in the music; there is a sudden dynamic change (from forte to piano), while the texture changes from chordal homophony to strict polyphony with the BACH motive in stretto. An inverted G.R. within that section highlights m. 29, where the exposition is stirred up by a repeat of the subject in the alto voice. This entry starts on B-flat, similar to the very first entry (slightly modified for harmonic purposes), but then suddenly shifts from a dux to a comes entity; the first four notes of the subject appear in dux form, while the remainder of the entry is presented in comes fashion. It is the only fugue in the cycle where Schumann applied (uniform) dynamic markings to each voice entry in the exposition, as to point out the exposition’s irregularity. Federhofer and Nauhaus point out that “. . . Schumann probably regarded the treatment of the ‘comes’ (different in each case) as depending on the character of the subject.”63 Mm. 75–121 mark the second division of the fugue, totaling 47 measures; 47 x 0.61 = 29 = m. 102, which is marked marcato while presenting new material. The fugue’s third division comprises mm. 123–174, totaling 53 measures. This section contains a reversed G.R. (counting 32 backwards) at m. 143. The score reveals a significant change in m. 143 as the music changes from a thin, three-part polyphonic to a full, chordal and homophonic texture.
Fugue III. The third fugue is the shortest one of the cycle, counting only 59 measures; 59 x 0.61 = 36. The G.R. is found in m. 36, where the music moves to the sub-mediant, E-flat major. A reversed G.R. points to m. 23; the end of the exposition. This five-voice fugue does not combine all five voices until close to the end, after the third (and final) pedal entry. Schumann uses the pedals to single out the Golden Ratio.
Fugue IV. The fourth fugue is 116 measures long; 116 x 0.61 = 71. M. 72 is marked fortissimo, the loudest dynamic marking in the fugue. Here the music also has a strong sense of forward motion (see endnote 64). The drastic change at m. 72 divides the piece into two sections. The second division, totaling 45 measures, unveils one more reversed G.R. at m. 92, where the music changes from a homophonic to a polyphonic texture.
Fugue V. The fifth fugue in the cycle totals 124 measures; 124 x 0.61 = 76, the beginning of the pedal tone F. When looking at that first section separately (mm. 1–76), we find yet another striking place; 76 x 0.61 = 46; in m. 46 the subject appears in the middle voice, while the BACH theme (in sustained note values) are presented—in stretto—in the bass and soprano voices. NB: this is the only time the BACH theme is played in the pedals. The fugue’s second part (mm. 76–124) contains one more G.R.; 49 (number of remaining measures) x 0.61 = 30, which appears exactly at the pedal point in m. 104. Additionally, the original subject appears in retrograde.
Fugue VI. 155 x 0.61 = 95. Measure 95 presents a clear statement of the subject in the pedals. A reversed Golden Ratio (95 from the end, rather than the beginning) leads us to m. 60. Schumann writes a clear break in the music at measure 59, immediately before introducing the second subject of this double fugue; the fugue’s two sections are separated by a quarter note rest and a double bar line, as well as a dynamic increase (più f). In addition, Schumann writes lebhafter (livelier). When we apply the G.R. formula to the first part of the fugue (the first 58 measures) we come to 58 x 0.61 = 35. One measure earlier the subject is first introduced in the relative minor key (G minor). Similar Golden Ratio divisions are found in the second part of the fugue (97 measures long): 97 x 0.61 = 59 (m. 117). In m. 116, just one measure earlier, Schumann clearly defines the break in the music after two (!) four-measure pedal points, when the BACH motive is re-introduced—this time in block chords. A reversed G.R. is found at mm. 95/96. In m. 95, after a three-measure pedal point, the fugue’s first subject appears first in the second part of the (double) fugue. Other changes involve a dynamic increase and the introduction of both subjects simultaneously.
The number of Golden Ratios in Schumann’s fugues is overwhelming, yet the question remains if they were intentionally ‘placed’ or if they are a mere compositional byproduct. Schumann’s organ compositions are an unusual blend of styles, which could easily generate an over-analytical approach. Peterson’s and van Houten’s previously mentioned findings are prime examples of such “determined research,” and one needs to be careful not to attribute music’s every single detail to a genius mind. In regards to Golden Ratio, perhaps the truth lies somewhere in the middle. Regardless of Schumann’s intentions, the number of G.R.s is remarkable and cannot be denied.

Styles
Schumann’s organization of the cycle reveals a fascinating blend of Baroque and Romantic principles. Burkhard Meischein points out the cycle’s sonata-like layout:
Fugue 1: Slow introduction
Fugue 2: Faster section
Fugues 3 and 4: Cantabile, slower section
Fugue 5: Scherzo
Fugue 6: Exciting, intensely growing finale64

Interestingly, Schumann’s Classic outline is not unlike Bach’s symmetrical organization of larger collections.65 Notice, for example, the symmetry in time signature, tempo, dynamics and texture (see Appendix 4).
The six fugues are based on the famous BACH theme that Bach himself had used in the final (incomplete) fugue of The Art of Fugue. As Daverio points out, “Though all the fugues incorporate the BACH theme, some of them use this theme merely as a starting point for a larger subject (see the subject of the second and fifth fugues).”66 Stinson discusses the many motivic similarities between Schumann’s opp. 56 and 60 and Bach’s organ works. The second fugue on BACH, for example, has occasionally been ridiculed for its elongated subject, but is analogous to BWV 575, which was published by Schumann in the Neue Zeitschrift für Musik in February 1839.67 In Abhandlung von der Fuge, Marpurg discusses the proper treatment of fugue subjects:
I myself once heard him [Bach], when during my stay in Leipzig I was discussing with him certain matters concerning the fugue, pronounce the works of an old and hardworking contrapuntist dry and wooden, and certain fugues by a more modern and no less great contrapuntist—that is the form in which they are arranged for clavier—pedantic; the first because the composer stuck continuously to his principal subject, without any change; and the second because, at least in the fugues under discussion, he had not shown enough fire to reanimate the theme by interludes.68
While some of the subjects are indeed rather lengthy, Schumann seems to adhere to Bach’s examples, avoiding redundant (complete) repeats of fugue subjects. Similarly, rather than following conventional compositional techniques, Schumann used existing forms as a starting point for a more modern idiom. Thus, the amalgamation of old and new techniques generated compositions that were (and still are) anomalies in the organ repertoire, and may in part explain their unfortunate fate. A closer examination of the fugues reveals some very interesting patterns:
Fugue I. The first fugue initially follows the conventional exposition pattern, as each of the voices is introduced in the right order. However, when the fifth voice is introduced in m.12 (in the pedals), the alto part drops out, leaving a four-part texture before finishing the exposition. In fact, the five voices never appear together in contrapuntal passages. Schumann, undoubtedly aware of this atypical approach, applied the idiosyncrasy in five of the six fugues (the fifth being the exception). Throughout the cycle, both the core subject (the BACH motive) and the complete subjects appear in many different forms. Klaus Jürgen Sachs points out the repeatedly changing order of emphasized notes of the BACH motive.69 In the first fugue, for example, the motive appears straightforward in four half notes, with B-flat and C being the emphasized notes (B-flat and C appear on beats one and three in a 4/2 time signature). In m. 5 the same motive is presented in the alto voice, starting on the second beat rather than the first. This metrical displacement is typical of Schumann and is employed throughout the cycle.
Fugue II. In the second fugue we see a continuation of metrical shifts; starting in m. 3, the running sixteenth notes suggest a duple (2/4) rhythm in a 3/4 time signature. In m. 48 the first fugue’s subject is introduced in the pedals, combined with the second fugue’s main subject in the manuals. Schumann takes great liberty in the intervallic relationship between the first and second parts of the subject. The first part of the subject (BACH) starts on B-flat, while the second part (continuous sixteenth notes) follows at the sixth, on G.
This relationship remains consistent until m. 30, where Schumann separates the two motives by abandoning the intervallic connection. The two motives still appear together throughout the fugue, but the second part of the subject (its starting pitch) is modified for harmonic purposes.70
Fugue III. The third fugue appears to be a double fugue, but the second subject is never fully developed. Derived from the main subject, it might be conceived as a melodically and rhythmically weak countersubject. ‘Undermining’ the second subject may have been intentional, as Schumann’s focus seems to be mainly on the principal subject. Whereas the first two fugues were written in the key of B-flat major, the third is written in G minor. Bound by the initial BACH motive (centered around B-flat), Schumann may have used the countersubject as a means to establish the fugue’s tonality. This thought also explains the countersubject’s lack of development, as Schumann’s focus is on the principal subject. Of the six fugues, the third maintains the strictest counterpoint throughout, and never resorts to a homophonic texture.Fugue IV. In the fourth fugue Schumann for the first time deviates from the established BACH motive. Though still citing the same motive, the notes are ordered in a new manner, incorporating the interval of a sixth. There are a number of similarities between the fourth fugue and Schumann’s second symphony, which was written 1845–1846. The symphony’s Adagio exhibits chromatic elements similar to the BACH motive used in the six fugues,71 and even incorporates a (semi) exposition, starting at m. 62, using two subjects. The Adagio’s harmonic progression of m. 82 also appears in m. 100 of the fugue. Schumann must have been fond of the chord progression, repeating it several times (consecutively) in both pieces. Like the fugue, the Adagio reveals a striking G.R. (130 measures x 0.61 = 80) at m. 82, where the music—marked by a double bar line—suddenly shifts from C minor to C major.
Fugue V. The fifth fugue, the scherzo of the cycle, maintains a strictly polyphonic texture. The independent voice leading, combined with fast-moving eighth notes, makes for some daring harmonies. Similar writing is found in the second Duetto of Bach’s Clavierübung III, of which Schumann owned a copy. Schumann again takes some liberties in the exposition, as the fourth entry of the exposition starts on E-flat rather than F. In addition, the pedal entry consists of two short, repeated motives rather than the entire subject.
Fugue VI. Schumann ends the cycle with a majestic, five-part double fugue. Simultaneous use of duple and triple meter, combined with a gradual buildup of tension and grandeur, creates a strong sense of completion. Stinson claims that the fugue is based on Bach’s Fugue in E-flat Major, BWV 552, pointing out the similarities between the two fugues.72 Schumann, however, once again deviates from the Bach models and moves towards a thinner texture before the end of the exposition. In the second exposition (starting at m. 59), Schumann’s approach is unconventional too, but not without reason. As the second theme is introduced, Schumann holds off on the expected pedal entry of m. 67. Instead, he omits the pedals until much later, in m. 92, where a three-measure pedal point adds gradual tension, leading to the first pedal statement of the fugue’s first subject. As the pedals introduce the first subject, the second subject is played in the manuals, thus combining the fugue’s two themes. Towards the end of the fugue, starting at m. 116, the fugue shifts suddenly from a polyphonic to a homophonic texture. Daverio points out the motivic resemblance in Schumann’s second symphony: “Culminating in a chordal peroration on the B-A-C-H theme, the fugue’s coda at the same time prefigures a climactic passage in the Final (mm. 343ff.) of the second symphony.”73 Just like the first fugue, the final fugue concludes with a coda. In the first fugue, at m. 34, Schumann indicated: “gradually faster and louder.” In the final fugue he specified: “Moderate, gradually faster.” While a thinning in the texture of the first fugue’s coda seems to suggest a sudden quieting down of the music, the sixth fugue’s coda undoubtedly calls for full organ, ending the cycle in a grand, majestic manner.

Schumann and the pedal piano
As discussed earlier, Schumann’s main purpose for hiring a pedalboard was to practice playing the organ. He found, however, that the pedal piano had much potential and that it might develop as an independent instrument. It seems plausible, then, that Schumann’s output of 1845 was conceived for pedal piano, organ, or both. Though opp. 56 and 58 are clearly written for the pedal piano (Studies for the Pedal Piano and Sketches for the Pedal Piano, respectively), there seems to be a discrepancy in regards to op. 60, which is labeled Six Fugues on the Name of B-A-C-H without any further specification in regards to the instrument of choice. The cover of the 1986 Henle Urtext edition of opp. 56, 58 and 60 reads Works for Organ or Pedal Piano without any further specification. In its preface, Gerhard Weinberger explains that in the first publication op. 60 is referred to as an organ work.
Interestingly, in the 2006 Schott edition the three cycles are published as Schumann Organ Works. In the preface, the editor, internationally renowned organist Jean Guillou, writes: “Schumann composed these masterpieces as a pianist and he wrote them for the piano, allowing for the possibility that they might be performed on the organ, but not really envisaging the precise manner in which an organist might ‘translate’ them for the instrument.”74 Guillou’s edition provides the performer with registration and tempo markings that go well beyond the original. As useful as a performer’s edition may seem, one needs to keep in mind that such is the interpretation of one person, and one needs to be mindful of the composer’s intentions. Notwithstanding the usefulness of such an edition, Guillou seems to have overlooked a most important issue; unlike the Studies and Sketches, the Six Fugues on the Name of BACH were written for the organ, not for the piano.
In the preface of the Henle edition Weinberger explains that the first edition refers to the six fugues as organ works.75 As we will see, the fugues are stylistically quite different than the other cycles. They lack, for example, the very pianistic approach, as found in the second and third canonic studies. Also, there is a drastic difference in the use of dynamics. Rather than the pianistic crescendos and decrescendos of opp. 56 and 58 (see the beginning of the fourth sketch), Schumann employs practical dynamic changes, easily realized through registration or manual changes.76 A compelling piece of evidence lies in the treatment of pedal points; Schumann frequently employs pedal points in both the piano and organ cycles. In the piano cycles Schumann repeats the pedal points every so often to ensure a continuous sounding of the bass note. Pedal points are never sustained longer than two measures.77 In the organ fugues Schumann writes pedal points for as long as twelve measures.78 Also, unlike opp. 56 and 58, op. 60 never exceeds the compass of the typical German Baroque organ, which may give us an idea of Schumann’s favored organ type. Hermann J. Busch points out that Mendelssohn preferred older organ types. For his first performance of the Six Sonatas for Organ, Mendelssohn chose an older instrument (Franz and Johann Michael II Stumm, 1779), while a modern instrument (a large Walcker organ) was available.79 Mendelssohn’s influence on Schumann as a composer and organist suggests that Schumann too may have favored older organ types, as is evidenced in Schumann’s comments in the diaries.80 Busch also points out that the majority of the organs known to Schumann were from the 18th century. These instruments were generally not equipped with a swell box. Crescendos therefore were realized by manual changes and/or adding stops.

Schumann the organist
It is obvious that Schumann took great pride in the six fugues. Rooted in a long tradition, stemming from his primary example, Bach, Schumann felt that he had contributed an important work that could stand the test of time. As Larry Todd points out: “Thus, Bach was memorialized in Schumann’s penchant for learned counterpoint, culminating in that erudite fugal compendium for organ, the Six Fugues on BACH, Op. 60 (1845).”81 How ironic then, that the cycle he had worked on for so long was received with such little approval. Perhaps Schumann would have been more successful if he, like Mendelssohn, had written organ sonatas rather than fugues. Rejcha perhaps explains the early 19th-century Zeitgeist best, saying “Since Handel and Corelli’s time, everything in music has changed two or three times, both in inner, as well as outer form. Only the fugue remains unaltered; and therefore—nobody wants to hear one.”82 Schumann, who “maintained with equal conviction that slavish imitation of older models was to be avoided,”83 must have thought that his organ works were indeed a breath of fresh air, as he expected them to outlive his other creations the longest.84 Notwithstanding their unfortunate fate, Schumann masterfully combined the old with the new. As Heinrich Reimann writes:

. . . the best proof of how deeply Schumann had penetrated, in thought and feeling, into the spirit of the Old Master. Everywhere the fundamental contrapuntal principles of Sebastian Bach are recognizable. They rise up like mighty pillars; but the luxuriant tendrils, leaves, and blossoms of a romantic spirit twine about them, partly concealing the mighty edifice, partly enlivening it by splendour of colour and varied contrast and bringing it nearer to modern taste. The most obvious proofs of this are:—The second fugue with the characteristic Schumann rhythmic displacement (2/4 time in triple rhythm); the fifth, with its subject on quite modern lines; and the last, with its romantically treated counter-subject.85

Though Schumann is perhaps remembered foremost as a composer of homophonic music, it is no coincidence that, as Nauhaus and Federhofer point out, Werner Krützfeld used two examples of Schumann’s Kreisleriana in Die Musik in Geschichte und Gegenwart as examples of counterpoint.86 The Six Fugues on the Name of BACH mark an artistic high point in Schumann’s career, and one can only hope that these erudite compositions will eventually become part of the standard repertoire. A deeper understanding will perhaps spark a renewed interest in these wonderful pieces.

Margaret Sandresky is a graduate of Salem Academy and College with a major in organ performance. She earned a master’s degree in composition with a minor in organ at the Eastman School of Music, and later received a Fulbright Grant for the study of organ with Helmut Walcha at the Hochschule für Musik in Frankfurt am Main, Germany. She has held positions at the Oberlin Conservatory of Music, the University of Texas at Austin, the North Carolina School of the Arts, and at Salem College where she is Emeritus Professor of Music. Her articles have been published in The Journal of Music Theory, Music Theory Spectrum, The American Liszt Society Journal, Ars Organi, and The American Organist. Her seven volumes of organ music are published by Wayne Leupold Editions, and her anthems are published by Paraclete Press. In 2004, she received the Distinguished Composer award given at the AGO convention in Los Angeles, and in 2006 was honored by St. Andrews College with the Sam Ragan Award for distinguished service to the Arts in North Carolina.

In the summer of 1829, after an extended journey through the British Isles with his friend Klingemann, the twenty-year-old Felix Mendelssohn Bartholdy completed his trip with a visit in Wales, where he made sketches, now lost, of the piece he intended to present to his “dear little sister,” Fanny, as a special gift for her wedding to William Hensel on October 3.1
Back in London, he met with an accident on September 17, seriously injuring his leg when he was hit by a light horse-drawn vehicle he called a “stupid little gig.”2 On September 25, he wrote his mother that he had “thought of a splendid idea” for Fanny’s wedding piece, but now he wouldn’t be able to present it until after the wedding.3 By November 6, he wrote his father that he had been laid up in bed for five weeks, was just going out for his first drive, and could almost walk without crutches.4
It was during this time that he completed the proposed piece for Fanny’s wedding. Since the final working manuscript is either lost or in private hands, the only available music is a sketch, now in the Bodleian Library. It is written on two staves, the bottom staff mostly blank, the top staff outlining the melody and briefly indicating the harmony.5 This is unmistakably the same material that appears as the opening and closing sections of Mendelssohn’s Sonata III. Many years later, when he was assembling material for the organ sonatas, he inserted between the sections two fugues with the chorale Aus tiefer Noth schrei ich zu dir (“In deep need I cry to thee”) as a cantus firmus.
The outer sections form two strong A-major homophonic pillars surrounding the two inner fugues in A minor, which, by means of their dark chromatics, jagged rhythms and tumbling 16th notes, seem contrastingly very dark and stormy. In each fugue, after the exposition for four voices in the manuals is completed, the chorale melody is introduced in the pedal as a fifth voice.
The second movement that closes the work is a simple song form. The two movements must have been conceived together, since they are dated August 9 and 17, 1844, probably while he was still vacationing in Bad Soden near Frankfurt, where his wife’s family lived. The use of this particular chorale, its stark contrast to the A-major sections, and why it is spread over the two fully developed fugues are questions that are discussed in the following paragraphs.
Mendelssohn was only seven years old when his wealthy and cultivated Jewish parents had their children baptized at the Neue Kirche in Berlin. In these early years, the music and worship of the Lutheran Church must have had a profound influence on him, for his use of Lutheran chorales as well as his interest in the organ and his dazzling performances on that instrument testify to an enduring love for this music throughout his life. By the time he was twelve, he was studying Bach fugues and writing one of his own as shown in the following charming note to his teacher, August Wilhelm Bach.

Berlin, the third day of the lovely month of May, 1821.
What does the sexton say, my dear Herr Bach? Can we play this afternoon? Or is there a wedding? or a confirmation . . . Greetings to the Prelude and Fugue in G Minor. I am presently sweating over an organ fugue, which will come forth into the world within the next few days. My heartfelt greetings to all the principal (sic) pipes, yours faithful (sic),
F. Mendelssohn6

Aus tiefer Noth
Mendelssohn showed an early interest in “Aus tiefer Noth” by composing a cantata on the chorale in 1830, a year after his English journey. Then on his travels in 1831, he must have been particularly interested when he found a copy of the Sebastian Bach organ chorale prelude on the same melody.
He wrote the following to his sister, Fanny, on her birthday, November 14, 1831, from Frankfurt am Main:

Oh my dear little sister and musician . . . I want to give you one of the unbelievingly [sic] moving Seb. Bach organ pieces which I just got to know here . . . Now play this chorale with Beckchen [another sister] . . . and think of me. . . . NB. The chorale is with double pedal.
Bach composed only one chorale prelude with double pedal, so Mendelssohn must be referring to Bach’s setting of “Aus tiefer Noth.”7
The chorale itself, composed by Martin Luther in 1523–4, was the first one for which Luther wrote both words and music. (Example 1) The previous year he had composed his first melody, to the poem “Ein neues Lied wir heben an,” after two young martyrs were immolated in Brussels, Belgium. “Aus tiefer Noth” stems from the same time.8 Luther’s poem is taken from Psalm 130, De Profundis, a psalm of redemption. Since metrical translations in English hymnals, by their very nature, cannot be specific, the following is my literal translation and, though awkward, may be helpful in grasping Luther’s meaning.

Verse I
Aus tiefer Noth schrei ich zu dir,
Herr Gott, erhör mein Rufen.
Dein gnädig Ohren kehr zu mir,
und meiner Bitt sie offen;
denn so du willst das sehen an
was Sünd und Unrecht ist getan,
wer kann, Herr, vor dir bleiben?

In deepest need I cry to thee,
Lord give ear to my cry.
Thy gracious ear incline to me,
And to my plea be open;
Then as you are sure to watch,
What sin and lawlessness is done,
Who can, Lord, stand before you?

Verse V
Ob bei uns ist der Sünden viel,
bei Gott ist viel mehr Gnade;
sein Hand zu helfen hat kein Ziel,
wie gross auch sei der Schade.
Er ist allein der gute Hirt
der Israel erlösen wird
aus seinen Sünden allen.9

Though by us there be many sins,
By God is much more grace.
His hand will help us without fail,
However great the peril.
He is alone the shepherd good,
Who will release Israel
From all her sins.

Bach’s chorale prelude is found in his Clavier Übung Part III in the section of Catechism chorales, and represents the sacrament of confession and forgiveness, known in the Lutheran Church as the Office of the Keys. It is the form for the confession and absolution of sin and derives its name from Matthew 16:19 and John 20:21–23.10
Mendelssohn’s early cantata on “Aus tiefer Noth,” op. 23, no. 1, published in 1832, takes its pattern and style from the cantatas of J. S. Bach. It is in five movements, one movement for each verse of the five verses of text. The first and last verses are set in a simple chorale harmonization, the second and fourth are a fugue and a chorale prelude with introduction, and the middle movement is for three solo voices with chorus and organ. Although “Aus tiefer Noth” is in the Phrygian mode, the cantata is firmly in F minor, and the cadences avoid any trace of the Phrygian in their strong tonality. The contrapuntal writing is a perfect model of 18th-century counterpoint.

The fugues of Sonata III
In the later Sonata III, the Phrygian character of the chorale is retained. (Example 2) Here Mendelssohn presents the chorale in the pedal transposed to A minor, inserting a B-flat before the A at the proper cadence points; and at the close of the second phrase (mm. 46–47), he uses a Phrygian cadence harmonizing the B-flat to A pedal as IV/6 to V in D minor. On the other hand, where this phrase is repeated in the second fugue, the B-flat to A is harmonized in the key of G minor as I/6 to VII/6 (mm. 69–70) and is not at a cadential point in the overall work. However, the final cadence (m. 92) is Phrygian, IV/6 to V/9, and introduces a long pedalpoint leading into the pedal cadenza.
The expositions of the two fugues illustrate two different aspects of Mendelssohn’s fugal writing. (Example 3) In the first fugue, the exposition (m. 24) follows traditional fugal procedure. Scale steps 5–6 at the beginning of the subject are answered by scale steps 1–3 (m. 28). The order of entry is bass, tenor, alto, soprano. After the exposition, the chorale enters in the pedal, overlapping the last measure of the answer. The chorale is split between the two fugues. Phrase one, phrase two, and the repetition of phrase one are presented in the first fugue, and the fugue closes with a half cadence in A minor, composed of a Neapolitan sixth chord going to a dominant ninth followed by a five-measure pedalpoint.
It is worth noting that because Mendelssohn decided to make his two fugue subjects compatible as invertible counterpoint and to bring them together near the end of the second fugue, he designed them both on the same vertical sonority, the V/vii7. (Example 4) Thus it was convenient to divide his cantus firmus between the fugues at a point where the dominant could function in both places, with the result that he did not follow the rhyme scheme of the text or the form of the chorale, which is abab-ccd, but split it after the repetition of the second phrase, aba-bccd. (See Example 2.)
In contrast to the scholarly correctness of the first fugue, Mendelssohn seems to have designed the second one with Romantic fervor, avoiding scholarly constraints and directing the performer to play with gradually more and more animation. The A-minor subject beginning on scale steps 5-6-5 (m. 58) and outlining a dominant/diminished area, tumbles down in 16th notes to C-sharp, throwing it into the subdominant key of D minor by means of this chromaticism. One remembers here that in the old modal system, D really would have been the dominant of the Phrygian on A. These events present two problems for the tonal system, solved traditionally by answering scale steps 5-6-5 with 1-3-2 and by returning the modulating subject to the proper key in the answer. Mendelssohn does neither.
Since the modulating pitch, C-sharp, is the very last note of the tenor subject, whose proper tonal answer, 1-3-2 in the alto, would force a cross relation between the C-sharp and a C-natural, the situation requires deft and imaginative treatment. (See Example 3.) Mendelssohn gives the alto a real answer (m. 60). However, in order to halt the continuous modulation of subject and answer and not stray too far from the main key, he ends his real answer by writing an F-natural instead of F-sharp, thus preparing for the third entry of the subject in the soprano and remaining in D minor. Here, one may be surprised to hear a tonal subject, scale steps 1-3-2 in D minor (m. 62); but the subject, placed now in the highest voice, sounds exciting, overarching, overreaching, and not like a misplaced answer. The fourth entry in the bass (m. 64) is then a real answer to a tonal subject; and this upside down arrangement ending in D minor effectively prepares the two measures of chromatic secondary dominant-seventh chords leading from the exposition to the entrance in the pedal of the fourth phrase of the chorale, where he is heading temporarily for F minor.

The outer sections of Sonata III
Under analysis, the principal thematic material in the opening and closing sections of the sonata seems drawn from the opening phrase of the chorale, whose first interval of a descending perfect fifth from E to A appears, now in the key of A major and filled in stepwise, as the opening gesture of the main theme. (Example 5) This “filled in” fifth dominates Mendelssohn’s thinking here, for it occurs some twenty times during the course of this section. The same pitches also appear in measure two of the second movement. Again, in the first phrase of the chorale, the ascending leap of a fifth moving up a half step to the sixth degree of the scale may be interpreted as the interval of a sixth appearing in several places throughout the sonata. First, it occurs between measures one and two of the opening theme; second, it appears twice at the recapitulation in the pedal from low C-sharp to A and then up to F-sharp. Finally, it appears as the first two pitches of the second movement. The chorale provides one other motive. Compare the scale steps 5-6-5 in the first two measures of the chorale to the subjects of each fugue.
Such an analysis, then, shows that the entire movement, and in a broader sense the entire work, can be viewed as evolving from one theme, that of the chorale, and not from separate ideas. This coincidence presents a conundrum: did Mendelssohn either consciously or unconsciously have the “Aus tiefer Noth” chorale in his head during the closing weeks of his English journey, and turn it into a joyful bridal piece by filling in the melodic skeleton and changing the mode? Then years later, did he decide to expand Fanny’s piece into the Sonata III? This would explain the juxtaposition of seemingly disparate parts, the wedding piece, the chorale, and the fugues. But why put them together?

Why “Aus tiefer Noth”?
One answer may lie in the important significance the music of Mendelssohn’s faith had in his life. For example, in the top right-hand corner of many pieces he wrote “Hilf du mir” or “H.d.m.” (“Help thou me”) before he began work. According to my Evangelisches Gesangbuch, “Aus tiefer Noth” is the chorale for the week of the eleventh Sunday after Trinity.11 Mendelssohn, in his letter of April 14, 1829 from Hamburg, where he made a visit before embarking on his first trip to England, wrote that he couldn’t comment on theatre and music in that city since everything was closed during Holy Week there.12 That would place the eleventh Sunday after Trinity near August 25, just the time when he was in Wales, where he wrote a long letter to his father that day from Llangollen, in which said he had “done a little composing.”13 These documents show how he could have decided to use the chorale for that week as the basis for a triumphant expression of joy celebrating Fanny’s marriage. Years later, as he assembled the sonatas, remembering the relation of the chorale to Fanny’s piece, he added two fugues over the same chorale.
Why two fugues rather than just one? Could it be that Mendelssohn was thinking of the two fugues as a memory of the two young martyrs who influenced Martin Luther’s first complete chorale, “Aus tiefer Noth”??

Olga Savitskaya was born in Minsk (Belarus) and earned a Ph.D. with a specialty in musicology at the Belarusian State Conservatory, where she is now assistant professor and music theory chair. A member of the Belarusian Union of Composers, she lectures on harmony, form and analysis, and polyphony. Her research interests include instrumental music of baroque period, Belarusian symphonic music, and modern composition techniques. Her publications include many books and articles.

The end of the 17th century through the beginning of the 18th century was a period of development for the trio sonata and its two varieties: sonata da chiesa and sonata da camera. Being formed in the works of Corelli, “the typical form of a church sonata of four contrasting parts: Grave (homophonic or imitative, C), Allegro (treated fugally, C), Adagio (homophonic, 3/2), Allegro or Presto (treated fugally or homophonic, C or 3/2)”1 appeared to be one of the most universal and flexible formulas of musical-logical development of the large instrumental concept in the baroque period. Influenced by the principles of the cyclic organization of the church sonata, the structure of the violin solo sonata and the concerto grosso evolved. Thus, the musical-historical phenomenon of the church sonata appears in the combination of two aspects: 1) as a genre during the 17th and early 18th centuries, moving from the bounds of church music into the sphere of secular concert music; 2) as a type of the baroque large instrumental form whose organizational principles (primarily crystallized in the genre of a church trio sonata) were adapted and developed at the end of the 17th century through the first half of the 18th century.
The highest achievements in this sonata form are connected to the prominent masters—Corelli, Purcell, Couperin, Biber, Buxtehude, Bach, and Handel, etc.—whose works in many aspects have defined both the character of the baroque era as a whole, and the national and regional schools that developed in this period. The Italian sonata, embodied in the sonatas of Corelli, undoubtedly had a great influence on composers throughout Europe. But much more notable is finding the “national appearance” of the sonata in England, France, and Germany.
One of the high points in the history of this genre is seen in the 14 trio sonatas for violin, viola da gamba and harpsichord of Dieterich Buxtehude, which were quite original when they were published in 1696.
The main features of Buxtehude’s sonatas are their general structure and non-specific number of movements, from three to seven. The sonata movements are mainly differentiated by tempo, style and degree of independence. The fantasy style of composition abounds in unexpected changes of rhythm, contrasted with strict fugues, improvisational interludes, and juxtapositions of different manners of writing. And though the contrast of polyphony and homophony as one of the basic traits of the sonata da chiesa retains its significance, fugues do not always take the central place. All this testifies to the fact that trio sonatas by Buxtehude are oriented not so much to the Corelli pattern, but to the German tradition of violin writing, where the principle of free thematic development and improvisational character of performing fuses with compositional techniques.
The fugues included in each of Buxtehude’s 14 sonatas are very different, ingenious, and exhibit the individual style of the composer, as well as a definite stage of evolution of this polyphonic form prior to the art of Bach.
The instrumental ensemble fugues reveal one of the bright sides of the complex, many-sided Buxtehude fugal style, which includes also his organ and vocal compositions. As V. Protopopov noted, their typical features are “vividness of themes, ease of motion, and a lack of concentrated philosophical musical images . . .”2 As a rule, the fugal subjects of trio sonatas are rather extensive, intonationally expressive, and based on the structure of core-development. The elements of dance music and style-intonation figures representing performing technique of stringed instruments give a special shape to them.
Two-voice fugues predominate, where the theme is expressed by solo instruments; the basso continuo functions as accompaniment (op. 1: no. 1 Presto, no. 3 Allegro, no. 5 Vivace, no. 6 Allegro; op. 2: no. 2 Allegro, no. 4 Allegro I, no. 5 Allegro I). However, three-voice fugues in which the harpsichord participates in concertante alongside the two soloists (op. 1: no. 1 Allegro; op. 2: no. 2 Vivace, no. 6 Vivace, Poco Presto, no. 7 Allegro) are also frequently used. In some cases three-voice fugues are used only in the exposition, subsequently replaced by two-voice fugues with accompaniment (op. 2: no. 1 Allegro).
According to the tradition of pre-Bach fugues, in Buxtehude’s trio sonatas the tonic-dominant alternation of subjects is mainly a result of the interchange of expositions and counter-expositions that becomes the basic structural characteristic. However, even in rather small and “simple” fugues, expansion of the texture and attention to the architectonical aspect of composition is obvious. An essential role belongs to episodes.
As an example we shall give the scheme of the three-voice fugue of the Sonata in F Major, op. 2, no. 7, Allegro I (Example 1). At the same time in trio sonatas of Buxtehude, fugues having two or three parts are also frequent. Such are the two-voice fugues of sonatas in C Major (op. 1, no. 5), E Minor (op. 1, no. 7), and A Minor (op. 1, no. 3).
All these examples show a definite development: from a fugue as the combination of expositions and counter-expositions by means of episodes to three-part fugue with functional differentiation of sections and exceeding the limits of tonic-dominant relations through modulation. Such development, which looks forward toward Bach’s fugues (especially chamber-instrumental), is not, however, the single one for Buxtehude.
The unrestrained imagination of the baroque artist and the aspiration to the new and unusual are manifested also in the interpretation of a fugue, resulting in expansion and complication of its structure and assimilation of the elements of other genres and forms. The structure and organizational logic of these Buxtehude fugues are not repeated, but as a whole one can see a similarity to his organ works, the successive line from which leads to grandiose Bach organ fugues. Let us examine specific examples.

Sonata in G Major (op. 1, no. 2)
Its structure emphasizes a cyclic three-part form, while the weakened role of polyphony and significant role of dance themes testify to the effect of an instrumental concerto. The principle of composition “in mixto genere” (in a mixed form) is in part I, the result of synthesis of two forms: a complex double fugue with a joint exposition and the concerto form.
Lively dance themes do not contrast but supplement each other in free development when complementary rhythms underline the linear independence of the voices, with homophonic duplication of the melodic motives in tenths and thirds. Development of themes in exposition and counter-exposition, which constitute a fugue itself, is divided by the episodes based on the new material in the manner of the homophonic ritornellos of the violin concerto. (Example 2)
In essence, in this work, and in the entire cycle, not only interaction of various musical forms takes place but also the more complicated synthesis of “the old” and “the new” genres: the church sonata, which has reached its full maturity, and the young instrumental concerto, which rapidly developed in Europe at the end of the 17th century.

Sonata in B Major (op. 1, no. 4)
Another combination features the interaction of a fugue and basso ostinato. In the Sonata in B Major (op. 1, no. 4) the element of ostinato seems “to be splashed out” outside of 32 variations of part I by subordinating a final fugue. In its middle section Buxtehude, being the master of musical rhetoric, specially combines two principles of organization—fugue and ostinato. At first the brief fugal subject is stated by the solo instruments. Then it dissolves in figurations, and its function in the thematic process temporarily transfers to the basso ostinato. The final section again affirms the fugue, but a reminiscence of the basso ostinato returns in the last bars of the coda.
The ostinato principle takes a special place in Buxtehude’s compositional technique. The German master’s adherence to ostinato seems to be consistent even against the background of its pervasive occurrence in music of the 17th century (perhaps only Purcell can be compared with him in this respect). Buxtehude makes use of basso ostinato in organ compositions: Chaconnes in C Minor (BuxWV 159), E Minor (BuxWV 160), Passacaglia in D Minor (BuxWV 161), Preludes in C Major (BuxWV 137) and G Minor (BuxWV 149); and in the cantatas Jesu dulcis memoria (BuxWV 57), Laudate pueri (BuxWV 69), Liebster, meine Seele saget (BuxWV 70), etc.
In the 14 trio sonatas, basso ostinato is almost as necessary as fugue (the ostinato is absent only in two sonatas). Its various forms can be divided into two groups—the less numerous so-called arias for basso-ostinato (Strophenbas arie), and the basic group, consisting of basso-ostinato forms of passacaglia type.
Basso ostinato is employed in lively (op. 2, no. 3 Vivace) and slow (op. 2, no. 3 Andante), outside (op. 2, no. 6 Allegro) and middle (op. 1, no. 1 Andante) movements. In some sonatas (op. 1, no. 4; op. 2, no. 5), the basso ostinato principle appears to be the predominant compositional idea and is implemented under different tempo and texture conditions.
A variety of basso ostinato uses derives from the character and structure of ostinato themes and the whole ostinato layer of basso continuo, thematic peculiarities of the high voices, structural-semantic interaction of the ostinato and upper voices, and, lastly, inclination to this or that type of composition—closed, precisely structured or free, and contrasting-compound.
At the same time all of these serve as the concentrated expression of the musical thinking of the composer. Thus, a fugue and a basso ostinato are the dominant constants of Buxtehude’s trio sonatas. The presence of a fugue is proof of observance of the major genre standards of sonata da chiesa, whereas the constancy and skilfulness of use of basso ostinato in the greater extent reflect the individual principles typical of Buxtehude’s style, which was based on the North-German tradition.

Other elements in Buxtehude’s trio sonatas
Other movements illustrate an extremely wide spectrum of genre, composition, and textural-timbral combinations. It is difficult and hardly reasonable to generalize the principles of cyclic organization in Buxtehude’s sonatas. The architectonics of any of them do not repeat exactly in any other, and each composition demands analysis of its individual logic. Besides a fugue and ostinato variations, these are small, without reprise, strophic, general and mixed forms. Among genre prototypes and patterns one finds the jig, chaconne, “echo,” chorale prelude, dialogue, toccata, “signal trumpet,” etc. The “formulas of imagination” acquire special significance, these indispensable attributes of improvisational style—passages, recitatives, arpeggio—creating, according to M. Lobanova, the “illusory, imaginary disorder” or the “intense pathetic development.”3 The sonatas combine genres, styles, affects and rhetorical figures.
In this “game of senses” the important role belongs to the thematic ties within the cycle. Strictly speaking, such ties characterize the sonata da chiesa, with its origins in the mono-thematic, multi-part canzona. But that sequence and ingenuity with which the thematic unity is realized in the sonatas of Buxtehude testifies that its role by no means is restricted to ensuring formal compositional integrity but acquires a distinct symbolic sense. Here it is reasonable to appeal to one of the central concepts of the baroque poetics being defined as the “witty conception.” The delicate, veiled differentiation of the themes in different parts of the cycle acts as a manifestation of baroque “wit,” whose purpose seems to display the obvious or hidden similarity, in what seemed to be on the surface, completely unrelated.

Sonata in C Major (op. 1, no. 5)
One of the instances is the Sonata in C Major, op. 1, no. 5. In this four-part cycle the first and the final fugues symmetrically frame the contrasting middle parts—an aria of a solo violin with a bass, and an ensemble jig (Vivace–Violino Solo; Allegro–Largo; Allegro–Adagio; Allegro).
Fugues are connected tonally. The source of their common material is the initial subject. Their motives and submotives, like the elements of a mosaic, are easily combined and rearranged to form new thematic configurations. The initial sections and the end of the final fugue are especially distinguished, serving to express a rhetorical idea of “connection,” the “concatenation” known under the name of symploce, or repetition (see Example 3).
The middle parts are also connected thematically: the motive of the second strophe of the aria with bass is unexpectedly “recalled” in the theme Allegro (Example 4). Finally, all thematic material of the sonata reveals as its basis a uniform intonational pulse, active, exclamatory (exclamatio) fourth (fifth) interval motion, a sort of the “intonational monad” as an indivisible core encompassing the whole world in it.

Sonata in A Minor (op. 1, no. 3)
The other example of thematic ties is found in the Sonata in A minor, op. 1, no. 3. The general idea is disclosed gradually, from movement to movement, revealing a semantic potential concealed within it.
In the melodic lines of the Adagio gradual downward motion (f-e-d-c-b-a-g#-a) covering a diatonic hexachord with adjoining introductory material is “summarized” by compact expressive formula saltus duriusculus (f-g#-a) (see Example 5a). Both elements are marked also in the themes of the Allegro: in the capacity of one of the motives of the fugue subject (hexachord by parallel sixths) and as the hidden voice of counter-subject (f-e-d-c-g#-a) (Example 5b). Further, the diatonic hexachord (including that which has been expressed by parallel sixths) becomes the thematic basis of the Vivace. Supplemented up to heptatonic, it is continuously exhibited in different voices, like a migrating cantus firmus in a chorale prelude (similar to its textual coincidence with the final phrase of Buxtehude’s organ chorale variations Wie schön leuchtet der Morgenstern, BuxWV 223) (Example 5c). Descending scale-like motion is retained in the finale (Presto), but already against a background, not in the parts of melodic instruments but in the basso continuo. The most characteristic baroque style figure—passus duriusculus, appearing in slow modulation binding sections (Lento, Largo) as ascending and descending pieces of a chromatic scale—is brought to the forefront. Only in the final Lento is the semantic orientation of the general thematic process “explained.” The descending chromatic motion, trebled by imitations that embrace all verticals of the ensemble compass and saturated with rhetorical figures of grief (catabasis, passus duriusculus, catachresis, parrhesia), closes the sonata. (Example 5d)

Conclusion
Dieterich Buxtehude’s trio sonatas are among the high points in the history of the genre. Standing out against the background of the rich tradition of ensemble music at the end of the 17th–beginning of the 18th century, they testify to the exclusive originality of the North German model of the baroque sonata. Created in the period of, probably, the greatest “purity” of the style, the sonatas of Buxtehude embody the baroque world image itself—which has lost its Renaissance integrity, being woven of “incongruous combinations” of contrasts opening into infinity by the kaleidoscopic unsteadiness of existence and at the same time blessed by the supreme harmony of all-reconciling unanimity. ■

J.S. Bach's Prefatory Message and Implications

Introduction

In an earlier article devoted to Bach's last printed composition, the presumably authentic title was established.1 The conventional reading in all printed editions was Die Kunst der Fuge; however, the correct version would read Die Kunst der Fuga. Amongst other observations, this spelling renders the title's gematrial sum as 158, identical to the result when converting the composer's full name Johann Sebastian Bach. An earlier article indicated numerous allusions to the system "wohltemperirt" within the composition.2 In order to demonstrate here the essential notion of the unitas in baroque music theory,3 in both spellings the title's 15=7+1+7 letters are centered upon the letter T=19--the number of intervals closing the circle in tuning.4 Further to the title, the first printed edition of the composition contains a short preface comprising seven lines, called Nachricht. Thanks to a remarkable booklet of great originality and richness of ideas by Vincent Dequevauviller,5 my attention was drawn to this message. Following my study devoted to the title itself, the purpose of the present article is to scrutinize that message more profoundly and interpret the outcome. Finally, new aspects as to how many bars, ideally, the unfinished fugue would comprise, are presented.

The preface to the first edition, 1751

Die Kunst der Fuga had two early editions in rapid succession, the first one 1751 and the following one already in 1752. These editions carry different messages as preface. The text published with the first edition of Die Kunst der Fuga, is shown in Figure 1 and below.

Nachricht

Der selige Herr Verfasser dieses Werkes wurde durch seine Augenkrankheit und den kurz darauf erfolgten Tod ausserstande gesetzet, die letzte Fuge, wo er sich bey Anbringung des dritten Satzes namentlich zu erkennen giebet, zu Ende zu bringen; man hat dahero die Freunde seiner Muse durch Mittheilung des am Ende beygefuegten vierstimmig ausgearbeiteten Kirchenchorals, den der selige Mann in seiner Blindheit einem seiner Freunde aus dem Stegereif in die Feder dictiret hat, schadlos halten wollen.

Preface

The late author of this work, due to his eye disease and his death occurring shortly afterwards, was rendered incapable to terminate the last fugue wherein he identifies himself by his name upon composing the third section; therefore one wished to compensate the friends of his muse by communicating the church chorale set in four parts and adjoined at the end which the late author, in his blindness, dictated into the pen of a friend in spontaneous improvisation.

As concerns this text, Dequevauviller argues, that--contrary to appearance and expectation--it had been written and prepared in advance by J. S. Bach himself! Thus, one might wonder, what further insight the present considerations could reveal. To report still further, Dequevauviller observed that the Nachricht counts 76 words in total: for the title 1, and 75 words for the remaining body text. As is known, Bach gave a Tri-Unitary representation of the number 75 via 31+13+31 in the bar-wise structure of Duetto II (in bars, 149=37+75+37). The digits 7 and 5 of 75 may be related to the number of fifths in the unequal tuning system "wohltemperirt" of Werckmeister/

Bach.6 Let us now structure these 75 words via the unitas by writing 75=37+1+37 such that the central word upon which the text is pivoted emerges as bringen. Following this word, within this single rather long sentence, Dequevauviller mentions the partition by a semicolon.

Although the Nachricht comprising 76 words is somewhat long and continues via . . . bringen; . . . up to . . . wollen--knowing the baroque traditions, practice and procedures--it is tempting to convert that text into a number via Henk Dieben's alphabet and gematria.7 Summing up to the respective end of the words concerned, yields the result in Figure 2.

Here the gematria-sum of the last 37 words that follow after bringen, up to the final word wollen, amounts to 4466-2323=2143. It is striking that this sum 2143 is by only 5 too large, such as to yield 2138, corresponding number-letter wise to BACH. This "problem" suggests taking a closer look at the text of the Nachricht. Immediately a suspect word shows up, namely Stegereif (meaning a spontaneous improvisation). Certainly, this word, in modern German spelling would read Stegreif without the obtrusive letter E=5 that renders the sum too large by this amount. However, modern German is irrelevant in this historical baroque context and one ought to consult contemporary dictionaries to verify the spelling--or even better, texts of writers close to J. S. Bach. Provided one is familiar with those contemporary texts, one easily finds that Carl Philipp Emanuel Bach, in his treatise8 Versuch / über die wahre Art / das Clavier zu spielen, Volume 2, page 325, chapter 41, writes Stegreif, rather than Stegereif. (See Figure 3.) This succeeds in identifying the misprint of spelling within the Nachricht, first edition of Bach's Kunst der Fuga. The gematria-sum of the last 37 words can thus be corrected from 2143 to 2138, BACH--as expected.

What does this result signify? First of all, J. S. Bach's authorship of the Nachricht--in conformity with Dequevauviller--is corroborated and firmly established. Could it otherwise be imagined, that e. g., Carl Philipp Emanuel Bach--and for what reason--would have constructed that artifice? It is thus the composer's own authentic message. But in addition, one may realize that Bach has encoded here a profound personal theological statement into his last printed work. (See Figure 4.)

The composer, of faltering health, facing his death, shows himself in Christian creed aligned with and belonging to Jesus Christ. The correspondence of the initials J. CHR., 9+3+8+17=37 is "conventional," as shown frequently in several of my own papers and in the book of Harry Hahn as well.9

Dequevauviller presented the following example, Figure 5, in the context of the rupture of the unfinished fugue. In cantata BWV 106, Actus Tragicus, the choir's soprano, at the end of the second movement--final bars upon the words "Ja, komm Herr Jesu, Herr Jesu"--fades away into the last bar of--a pause! Associating with the termination of the second part of the Nachricht by 2138 = BACH with 37 meaning J. CHR., an allusion to rupture of life by death and transfiguration in Christ could be understood.

In this paragraph the firm connection linking the Nachricht to the unfinished fugue will be established. In fact, the study of Bach's message would remain incomplete, if after the count of the words and the application of Henk Dieben's gematria, the number of letters itself were not checked. Thus, the 76 words of the Nachricht, as printed, comprise 427 letters: 9 letters for the title and 418 letters for the body text. As the latter contains the misprint with the superfluous letter E, the length of the text of 75 words can be corrected to 417 letters, factorizing 3x139. On recognizes 1-3-9, the number of the circle of fifths 19, centered numerologically upon the 3 = Trinity. The number 417 depicts in juxtaposition the number of 4 well-tempered fifths, 1 tempering fifth and 7 perfect fifths of the system Werkmeister/ Bach. Converting 4,1,7 into letters yields D, A, G. My earlier article has shown that the first theme of the unfinished fugue is D,A,G,F,G,A,D. This accomplishes the proof of the connection between the unfinished fugue and the Nachricht via the number of 417 letters.

As there can be no longer any doubt about J. S. Bach's authorship of the prefatory message, this proves that according to his intentions, not only the unfinished fugue, but also the final chorale do indeed belong to the composition. Some editions omit the chorale, but future editions may take into account the present result and thus grant Bach--so to speak--the right to the architectonic structure he conceived for this composition and let the form of his last printed work be closed by the chorale.

The unfinished fugue: midpoint and length according to the unitas

The following section investigates the unfinished fugue in more detail, the first theme of which my preceding article in The Diapason (March, 2000, p. 13) associated with "wohltemperirt," as described above. Dequevauviller presents convincing arguments that Bach intentionally and expressly left the fugue unfinished! Musically, the ensuing rupture of flow depicts death dramatically and in a macabre fashion. However, Dequevauviller sees an ambiguity and remains undecided, whether there are 238 complete bars to be terminated by 38 further bars or 239 bars for which 37 bars are lacking. For details, his original paper ought to be consulted. On the contrary, it will now be shown that the rationally admissible viewpoint is that the manuscript of the fugue holds 239 bars terminating at the last bar-line Bach put there. (See Figure 6.) There are 37 bars missing.

From bar 238 to bar 239, the bass descends by a fifth A-D. In numbers, as A=1, D=4; there follows 14=BACH in juxtaposition. Why should this "signature" within these two bars of the autograph be truncated and discarded by assuming only 238 bars? As concerns this signature AD=14, see also the 8th and 9th keystroke of Fugue N° 1, C-major, Das Wohltemperirte Clavier 1. 10 Furthermore, in bar 239 itself, following the quarter note D of the bass, Bach's manuscript notates a single eighth-note of the tenor upon A, into the system of the bass. Juxtaposing again within bass-system, there now holds DA=41=J. S. BACH, representing a further and ultimate signature in bar 239 at the termination of the unfinished fugue. Its manuscript--contrary to the printed version--is written into the two systems of soprano and bass-key. Had the tenor been written, as in the edition, into its system of the tenor-key, such a signature would not have been feasible. It is incoherent to recognize on the one hand via the digits of the partition 239=1+238 the letters of 2138=BACH and on the other hand, assume the factual last bar of the fugue were 238. There is no way out: the fugue, as it exists, logically extends over 239 bars; the completed one totaled 239+37=276 bars. It may be worth noting, and must have been known to Bach, that the number 239 also corresponds to Vom Himmel hoch da komm' ich her.

How can the ideal extension of 276 bars for the fugue be made plausible, or corroborated? For this purpose, let us now evoke the principle of the baroque unitas with this even number. Thus, 276=138+138, showing that the complete ideal fugue would be pivoted upon the two central bars 138 and 139. (See Figure 7.)

Incidentally, upon separating the two syllables of NACH-RICHT (13,1,3,8-17,9,3,8,19), its first half terminates letter-numberwise as (13)138, but this observation is numerology and means nothing in itself; nor, that the letters, except the last one of the second syllable, yield 37. These midpoint-bars, at first sight, appear somewhat inconspicuous. Nevertheless, four characteristic and pertinent features will be identified therein. The literally exact midpoint (bar-wise) of the completed fugue clearly would be the bar line between 138 and 139.

* Regarding the voice of the alto, the bar-line 138/139 separates the note C from the note A: Henk Dieben's number alphabet yields C=3 - Trinity, and A=1--Unity. Hence, the completed fugue of 276 bars appears to be appropriately centered upon the Tri-Unity. This is as well the basis and principle for the tuning "wohltemperirt." At this point, a correlation with the 75 words of the Nachricht emerges. The representation 75=37+1+37 showed the midpoint, the word bringen, pivoted itself upon the letter N. (See the appendix for the details of the relation with tuning.) The letter N converts to 13--the juxtaposition unitas-trinitas. The Tri-Unity can be represented by a single letter N=13--but not its form 31. In the alto voice, flanking this bar-line, the notes C, A transform to 3, 1. Incidentally, that alto voice reminds us that J. S. Bach is told to have played himself in the orchestra the part of the viol.

*In the first central bar, 138, the two lower voices of bass and tenor attack 7 and 5 notes, respectively. These numbers correlate with the tuning system Werckmeister/Bach. It comprises 7 perfect fifths and 5 fifths "wohltemperirt." The Nachricht counts 75 words plus its heading.

*In the second central bar, 139, the tenor attacks 5 notes, and the alto 3. The system Werckmeister/Bach derives from the triad of C-major--center of tonality--wherein third and fifth beat in unison. In thoroughbass, these numbers 5 and 3 represent the intervals of fifth and third.

*The last manifestation of the central pivot point is perhaps the most esoteric, profound and comprehensive one. Going from bar 138 to the onset of bar 139, the tenor holds a suspension on E, whereas the bass, figure of a catabasis, falls into the F. This reminds about "Fa mi et mi fa est tota musica,"11 Bach set to his Canon BWV 1078. Here, at the partition point via the unitas of his "last fugue," Bach addresses, what represents for him "the totality of music"! Unfortunately, the utilization of this suspension, in particular at central points (unitas) has not yet been systematically investigated within Bach's compositions, such as cantatas as well. A different most characteristic setting, simply the sequence of the notes F-E within a descending scale, occurs at the exact center of the Four Duets,12 wherein Bach had musically and mathematically specified the tuning "wohltemperirt."

At this stage, of course, one might start searching across the unfinished fugue, to find further passages where the four aspects above occur simultaneously. Or else, define different criteria for midpoint-characteristics and check whether there are possibly other candidate-midpoints under such criteria. At about twice the bar number of such places identified, the completed fugue would terminate. However, I have not yet succeeded in finding any different midpoint more convincing and significant than the one indicated within the existing part of the unfinished fugue, bars 138/139.

For completing the fugue it is thus confirmed that 37 bars are missing, related to the number of the 37 final words of the Nachricht, that succeed the semicolon. The ideal length of the complete fugue amounts to 276 bars--in agreement with the outcome of Dequevauviller's ingenious intuition and despite his ambiguous reasoning.

The autograph manuscript terminates with: "NB Ueber dieser Fuge, wo der Nahme// BACH im Contrasubject// angebracht worden, ist// der Verfasser gestorben" (Upon this fugue, where the name BACH is applied in the contrasubject, the author passed away). Whilst keeping in mind the 37 final words of the Nachricht, together with the 37 missing bars of the fugue, this sentence converts via Henk Dieben's alphabet to 867, factorizing 17x3x17. On the way to this total, when summing the text across its word BACH, up to and including the letter C--center of tonality--the intermediary result becomes 266 = Das Wohltemperirte Clavier. Alternatively, according to the triangular alphabet, the factors of the total are 6657=3x7x317. Herein, 317 may be seen as 37=J. CHR., centered upon 1=unitas.

Conclusion

Having established the corrected sum 2138 via the number alphabet for BACH in the second part of the Nachricht now proves beyond doubt that the composer himself was its author. As a consequence, that message--as concerns the contents and extension of the composition--can be trusted and taken literally. Thus, the unfinished fugue does, of course, belong to the composition and the complete work terminates with the chorale. The parallelism between the 37 words of the message's last part (37=J. CHR.) and 2138 meaning BACH, can be interpreted as a profound theological statement within his last printed work--did Bach take the last 37 bars with him when rejoining Jesus Christ? Finally, again numerous allusions or references to the tuning system Werckmeister/Bach could be identified within Die Kunst der Fuga.

For its second edition, Marpurg replaced Bach's authentic Nachricht by a "Vorbericht." The latter, although not without praise, admiration and meritorious commercial and sales intentions, can be dismissed as gibberish if compared to the significance of the composer's own message: Bach's work and concepts cannot easily be improved upon! Fortunately enough, the first printed edition has survived.

Epilogue and outlook

Contemplating this article on Die Kunst der Fuga, I realize and admit that I am myself most and principally interested in the psychology--the obvious one and the one implied--of this personality of a composer/mathematician. It is hoped that by presenting paradigmatically these results, the psychological approach apt for studying musico-mathematical baroque mentality, not only Bach, but e. g., Werckmeister and Zelenka as well, is initiated. And thus, that the official and institutionalized European Bach-research can be relieved from its present deadlock.

Appendix

Applying the gematria between the semicolon at the midpoint of Nachricht to its end yielded 2138. The body text of Bach's message counts 417 letters. These digits specify the three types of fifths in the system. Therefore it is tempting to apply gematria from the onset of the 75 words--excluding the title--and check the sum up to and including the central tri-unitary letter N=13 of BRINGEN. The result is 2217. Rearranging digits will make identification obvious: 1722. This is the year Bach has dated Das Wohltemperirte Clavier, showing 1 tempering-fifth (B-F#), 7 perfect fifths and two pairs of fifths wohltemperirt (C-G, G-D and D-A, A-E). As to the factorization, 2217=3x739. Obviously, 3 means the Trinity, and writing the other factor as 7-3-9, centers 79 upon the Trinity; whereas Johann Sebastian Bach corresponds to 158, its half is 79; a representation investigated already a long time ago.13 It is worthwhile to stress that BRINGEN has at is center the letter N and this was the word at half the length of the message.

Finally, the word BRINGEN itself, at the midpoint of the Nachricht, has several remarkable properties that can best ited in form of a table. (See Figure 8.)

The seven letters of BRINGEN, according to 3+1+3=7, are centered upon the Tri-Unity, N=13, the juxtaposition of unitas-trinitas, the basis of the system wohltemperirt. The sum of the first three letters, BRI, yields 28, secundus numerus perfectus. Such numbers are made up by the sum of its parts, 1+2+4+7+14=28. Or else, 6=1+2+3, primus numerus perfectus. Werckmeister, in his treatises, quotes perfect numbers up to 33550336(!). Looking now at 28 and at the midpoint 13, permits the numerological contraction and juxtaposition to 2813, a permutation of BACH = 2138.

The group of letters GEN, 7,5,13, obviously can encode the 7 perfect fifths together with the 5 well-tempered ones by a procedure14 I have called "appearance method." Otherwise, the final letters EN, appearing as 5-13, show 53 centered upon the 1 = unitas. This may be associated with 5 = fifth in thoroughbass and 3 = third. In the C-major triad of the system Werckmeister/Bach, third and fifth beat at the unison. In analogy, similar to the exercise of this appendix, the title-word NACHRICHT itself may undergo further numerological interpretation, but this is left to the reader.n

Notes

                  *               In commemoration of the 250th anniversary of J. S. Bach's death on 28 July 1750.

                  1.              Kellner, Herbert Anton, "Johann Sebastian Bach and Die Kunst der Fuga." The Diapason, March, 2000, p. 13.

                  2.              Kellner, H. A., "How Bach encoded his name into Die Kunst der Fuge together with his tuning."     The Diapason, May, 1999, 14-15.

                  3.              Dammann, Rolf, Der Musikbegriff im Deutschen Barock Laaber 31995.

                  4.              Kellner, H. A., The Tuning of my Harpsichord. Schriftenreihe 18. Verlag Das Musikinstrument, E. Bochinsky, Frankfurt/Main 1980.

                  5.              Dequevauviller, Vincent, L'art de la fugue, un "problème algébrique." ISBN 2-9513089-0-6. Association pour la connaissance de la Musique Ancienne, 75005 Paris, 10, rue Guy de la Brosse. 1998.

                  6.              Kellner, H. A., "A Mathematical Approach Reconstituting J.S. Bach's Keyboard-Temperament." BACH, The Journal of the Riemenschneider Bach Institute, Berea, Ohio. Editor Melvin Unger. Vol. 30/1, Spring-Summer 1999, 1-10

                  7.              Kellner, H. A., "Le tempérament inégal de Werckmeister/Bach et l'alphabet numérique de Henk Dieben." Revue de Musicologie Vol. 80/2, 1994, 283-298.

                  8.              Bach, Carl Philipp Emanuel, Versuch über die wahre Art, das Clavier zu spielen. First edition I/II 1753/1762; Facsimile, Ed. Lothar Hoffmann-Erbrecht 1958, 71986.

                  9.              Hahn, Harry, Symbol und Glaube im 1. Teil des Wohltemperierten Klaviers von J. S. Bach.  Wiesbaden 1973.

                  10.           Kellner, H. A., "Review of Musique et Tempérament by Pierre-Yves Asselin." Revue de Musicologie Vol. 72/2, 1986, 294-296.

                  11.           Duparcq, Jean-Jacques, personal communication, drawing my attention to this canon's text, and that the number alphabet converts "est tota musica" to 158--as well as Johann Sebastian Bach, equal to the value for Die Kunst der Fuga.

                  12.           Kellner, H. A., Barocke Akustik und Numerologie in den Vier Duetten: Bachs "Musicalische Temperatur." In "Bericht über den Internationalen Musikwissenschaftlichen Kongreß Stuttgart 1985," Ed. Dietrich Berke and Dorothea Hanemann, Kassel 1987, p. 439-449, as well as Kellner, H. A.: "How Bach quantified his well-tempered tuning within the Four Duets." English Harpsichord Magazine, Vol. 4, No. 2, 1986(87), 21-27.

                  13.           Kellner, H. A., "Das wohltemperirte Clavier" --Implications de l'accord inégal pour l'œvre et son

autographe. Revue de Musicologie Vol. 71, 1985, 143-157.

                  14.           Kellner, H. A., "One typographical enigma in Werckmeister, Musicalische Temperatur." English

Harpsichord Magazine, Vol. 3, No. 8, 1985, 146-151; in particular p. 148.