Riemenschneider Bach Institute is collaborating with JSTOR to digitize, preserve and extend access to Bach. http://www.jstor.org Riemenschneider Bach Institute A Neglected Guide to Bach's Use of Number Symbolism — Part I Author(s): Randolph N. Currie Source: Bach, Vol. 5, No. 1 (JANUARY, 1974), pp. 23-32 Published by: Riemenschneider Bach Institute Stable URL: http://www.jstor.org/stable/41639913 Accessed: 22-10-2015 13:51 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. This content downloaded from 128.151.244.181 on Thu, 22 Oct 2015 13:51:54 UTC All use subject to JSTOR Terms and Conditions
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Riemenschneider Bach Institute is collaborating with JSTOR to digitize, preserve and extend access to Bach.
http://www.jstor.org
Riemenschneider Bach Institute
A Neglected Guide to Bach's Use of Number Symbolism — Part I Author(s): Randolph N. Currie Source: Bach, Vol. 5, No. 1 (JANUARY, 1974), pp. 23-32Published by: Riemenschneider Bach InstituteStable URL: http://www.jstor.org/stable/41639913Accessed: 22-10-2015 13:51 UTC
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].
This content downloaded from 128.151.244.181 on Thu, 22 Oct 2015 13:51:54 UTCAll use subject to JSTOR Terms and Conditions
BACH'S "Notebook for Students" will publish selected student articles on Baroque music as well as short papers of particular interest to music students. BACH welcomes queries concerning publication of such materials.
A Neglected Guide to Bach's Use of Number
Symbolism - Part I
By Randolph N. Currie Ohio State University, Newark
The Controversy
One of the most intriguing, yet controversial, developments in Bach research over the past few years has been the revelation of Bach's use of number symbolism in some of his compositions. Reaction to advance reports of this phenomenon has ranged from outright skepticism to enthu- siastic acceptance. The attitude of most scholars, however, has been a sort of polite reserve. ("Now isn't that interesting; but let's wait and see
Admittedly, the published studies devoted to Bach's use of number symbolism have been somewhat haphazard, and some of the arguments tenuous, to say the least. On the other hand, the difficulty of detecting and interpreting number symbolism is notorious and by no means limited to the works of J. S. Bach. In the words of Alister Fowler, a leading figure in the field of English literature, "numerical composition was an essen- tially arcane practice ... ; the last thing we should expect to find is an unveiled authorial exposition."1 Therefore, it should come as no surprise that the usually reticent cantor of Leipzig maintained absolute silence on the subject.
We do have a kind of "hearsay" evidence, by way of a debunking remark by Mattheson to the effect that C. L. Mizler (perhaps in private conversation) had claimed to have learned some "mathematical bases of composition" directly from Bach.2 Even Mizler, whose mathematical inter- est is well known, seems never to have written a word about numerical composition. Nor did he publish a rebuttal to Mattheson's snide remarks, thus contributing to our impression of secrecy and esotericism surrounding the subject. Perhaps this is to be expected, since, as Christopher Butler points out, "From Pythagoras onwards, knowledge of the properties of number had been regarded as a secret mystery."3 Butler goes on to quote Copernicus to show that such mysteries were revealed "only to initiates and friends, and then not in writing but by word of mouth."4 Thus, it stands to reason that most attempts at numerical analysis are open to
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charges that the critic is trying to find symbolic meaning where none was intended. Even when the same patterns occur repeatedly, skeptics can claim that such recurrence is simply a coincidence.
Bach's Overt Gesture
In view of these circumstances, even the slighest indication that Bach consciously engaged in numerical composition should be regarded as highly significant. It is the opinion of this writer that Bach made just such an overt gesture when he wrote the number "84" at the end of the Patrem movement of the B-Minor Mass (see Plate I at the end of this article).
Friedrich Smend, who discovered the number in the autograph score, assures us that the figures are in Bach's handwriting.5 Elsewhere, Smend has observed that "84" represents the number of measures in the move- ment and that it is the product of the important "holy numbers" 7 and 12. 6
Unfortunately, he did not choose to pursue the matter any further. Had he subjected the movement to the kind of detailed numerical analysis he used in his study of Bach's "Triplex Canon" ( BWV , 1076), he would, no doubt, have discovered that the total number of measures is just one aspect of a numerical labyrinth of monumental proportions. It is the author s sincere hope that the present study will chart a few of the larger passage- ways contained within this edifice.
Symbolic Associations of "84"
Before proceeding with an analysis of the movement itself, it seems advisable to take into account the numerical properties of 84, a number particularly rich in symbolic associations. As a point of departure, let us consider the relationship between the generating 7 and 12 mentioned above. To the medieval mind these two numbers were closely related, since both are the result of combining 3 and 4:
3 + 4 = 7 (Three symbolized the things of heaven; 3 X 4 = 12 four represented the things of the earth.)
Thus, as Vincent Foster Hopper stated, "from the triune principle of God and the quadruple principle of man are produced the universal sym- bols, 7 and 12. The addition of 3 and 4, spiritual and temporal, produces 7, which is, therefore, the first number which implies totality.'7 From Hugh of St. Victor, we learn that "12 signifies the universe, being a multiple of the corporeal 4 of the elements and the spiritual 3."8 It is noteworthy in this regard that the text includes the phrase
" factorem coeli
et terrae ." (See discussion of text below.)
To Bach, it was perhaps equally significant that 84 was the product
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of 14 X 6. It is surely well known by now that 14 stands for BACH by means of gematria.9 The number "6" is also interesting since it represents the number of days of Creation (another reference to God as "maker of heaven and earth"?) and is also a perfect number. (A perfect number is any number equal to the sum of its aliquot parts. Thus 6=1 + 2 + 3; the next three perfect numbers are 28, 496, and 8,128. Interest in perfect numbers dates back to Old Testament times; the concept is usually in- cluded in any thorough-going discussion of Christian number symbolism.
While 84 is an "abundant" rather than a perfect number, the sum of its aliquot parts is particularly interesting:
1+2+3+4+6+7+12+14+21+28+42 = 140 (10 X 14)
It will be noticed that the series of divisors includes the most im- portant "sacred" numbers (1, 3, 7, and 12), along with the first two perfect numbers (6 and 28), and, of course, the number 14. The sum of the parts, in addition to being the product of 14 and 10 (the number of law and completion), is also the sum of the first seven perfect squares.10 An even more striking property of 84 is the fact that its prime factors total 14 (2X2X3X7 = 84; 2 + 2 + 3 + 7= 14 - there are only ten such numbers).
As a final consideration, it might be instructive to examine the digits which comprise this number. It can be seen that both 8 and 4 are powers of two, as is their product (8X4 = 32), a fact which Bach seems to acknowledge during the course of the movement (see below). Even the quotient and the difference between the numbers are powers of two (8 -ť-4 = 2; 8 - 4 = 4). And finally, the sum of the digits (8 + 4 = 12) brings us back to one of the "universal" numbers with which this discussion began.
The Central Position of the Word factorem
From the preceding discussion, we can deduce that, from Bach's point of view, 84 might very well be a dynamic symbol with many important associations. If that is the case, he could hardly have picked a more rele- vant text than one which refers to God as the omnipotent creator of all things. The actual words used in the Patrem movement pose a bit of a problem, since Bach chose to include the words Credo in unum Deum, which had, of course, been set to music in the preceding movement.11 By incorporating these words, however, Bach brings the total number of words up to 14. A closer examination of the Latin reveals the rather astonishing fact that the text contains exactly 84 letters. The following chart tabulates the letters and syllables along with the gematria (and cumulative totals) for the segment of the Credo used in the movement:
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There are also many clues to be gleaned from Bachs treatment of the text. A cursory look at the full score is sufficient to make us aware of his special interest in the word factorem. Not only does Bach repeat the word frequently, he also exhibits a considerable variety in setting it to music, ranging from a simple syllabic treatment to rather extensive melismas. Referring to the textural analysis above (Table I), we find that this, the seventh word, results in a total of 41 letters from the beginning of the sentence. Since 41 is " J. S. BACH" in gematria, the composer s interest in the word is quite understandable. Notice also that when 41 is sub- tracted from 84, the remainder is 43 (gematria for Credo). In fact, the equation 41 + 43 = 84 becomes a dominant motive both in the structure and in many subordinate details of the movement. The symbolic meaning is clear: the composer proclaims his faith, saying "I (J. S. Bach) believe." One other detail supports a personal interpretation of the word factorem by the composer. Gematria for the word is 77, a number whose digits add to 14 (the third such number, the other two being 59 and 68).
The central position of this word in Bach's thinking can also be seen in the structure of the main theme. (See Example 1 at the end of this article.) This perfectly symmetrical melody can be analyzed as follows:
Words Patrem omnipotentem factorem coeli et terrae No. of Notes 7 3 7
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In the course of its 17 notes, Bach manages to incorporate all 11 diatonic pitches (in A major) which fall within the range of his unusually wide-ranging subject. The three repeated notes at the outset seem to refer to the triune God,12 while the shape of the final segment suggests a typi- cally Baroque visualization of the text at that point. The completion of the word meaning "earth" on the lowest pitch contrasts sharply with the word for "creator," which begins with the highest note, reading down- ward with a triadic motive which is, in all probability, symbolic. It is with some difficulty that we recall that this melody, in a slightly different form, was once associated with the words Gott, wie dein Name, so ist auch dein Ruhm bis an der Welt Ende, the text of the opening chorus of Can- tata 17 1.13 (See Example 2.)
A detailed analysis of Bach's deployment of this pivotal word is of- fered below (see Table II):
Table II: Repetitions of the word FACTOREM in the Patrem Section of the B-Minor Mass MEAS. NO. OF NOTES MEAS. NO. OF NOTES
The preponderance of 3 s and 7 s is arresting, particularly in view of the symbolic associations of those numbers. Even more striking is the fact that there are exactly 14 statements with 3 notes each,14 while the 7-note statements occur 10 times (7 X Ю = 70 == 14 X 5). 15 Bach even seems to "count" the number of statements at times, as in the case of the eleventh and sixteenth statements, which have 11 and 16 notes respec- tively.16 Even the 32 words rendered in gematria (32 X 77) yields 16 as the sum of the digits (2, 4 6 4).
Bach marks the midpoint in the repetitions of factorem with a par- ticularly intricate design. Not only are there 16 notes in the sixteenth statement, but we also find a total of 16 notes in the 3 accompanying presentations (17, 18, and 19 in Table II). The resulting 32 notes are bisected by the barline which begins the thirty-second measure of the movement. With a sense of wonder, we discover that the 16-note factorem is the 32nd word in the alto part! To cap it off, Bach constructed a bril- liant 16-note canopy in the portion of the high trumpet part which lies over the long alto statement.
As a final touch, the composer introduced the only two sixteenth- notes in the entire movement at this very moment ( trumpet part, measure 32; see Example 3 at the end of this article). As noted above in the dis- cussion of the properties of 84, 32 is the product of the 2 digits, and, like 16, it is a power of 2. Looking further, we find that Bach was as thorough in his use of numbers as he was in other aspects of his art. Counting the instrumental parts in the segment delineated by this group of factorem statements, we arrive at a total of 119 notes. That number would seem to imply that the Maker of the Universe is visible everywhere in creation. This interpretation is supported by two facts: first, 119 is gematria for visibilium; and second, that word is the only complete word in the soprano part while the other voices sing factorem (see Ex. 3). Also notice that in the 3 lower parts, the 32 notes on factorem are augmented by 9 notes (bass and tenor, m. 32-33), bringing the total in those parts to 41 notes.17
If the reader has begun to suspect multiple meanings for the word "Maker," he might find the evidence presented by the twentieth repetition illuminating. Here, in measure 41, the word factorem appears in isolation in the soprano part, bringing the total number of notes on that word up to 123 (41 X 3). This occurs just prior to the recapitulation of the Credo in unum Deum in measure 42. In fact, the absence of the other voice parts after the first note in measure 40 serves to throw the soprano text into sharp relief: - potentem factorem. Once again, the pattern of notes in the other parts is highly significant (see Ex. 4). The following chart tabulates the notes in each of the four sounding parts:
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Table III: Tabulation of Notes in Each Notated Part
Part No. of Notes Interpretation Trombai 14- BACH
Ob I & Violin I18 6 ( days of creation; 12 21 <
Soprano I and II (3x4) 6 (3x7) ( perfection
Continuo 7 - the spiritual ( 3 ) -f the physical (4)
Total: 33 (3x11) Christ (or Holy Spirit?)
The total of 33 is underscored as an important and intentional num- ber, since factorem is the thirty-third word in the soprano at that point. Of the several possible Trinitarian meanings of this number, the most likely seems to be "God the Son" because of the numerous 33's associated with Christ in the Bible. Thus, even though Bach identifies himself as the "powerful creator" of this musical work, he implies that his faith in Christ is the ultimate source of his creative strength. Also, 33 is the first number whose prime factors total 14 (3 X 11 = 33; 3 + 11 = 14).
It would seem that Bach felt that he was following the true example set by the Maker of all things by incorporating numbers in his own crea- tive process. The composer seems to have accepted without question the tenet that God "arranged all things in number and measure" (Wisdom 11:20). Certainly Bach would easily have joined Copernicus and Kepler in thinking that "the universe was ordered in a mathematically satisfying way" and that it "carried upon it the 'signature' of its creator."19 Thus, even in the act of "signing" this and other works by way of numerology, Bach could have felt he was following the model of the "Almighty Father, Maker of all things, visible and invisible."
(Note: Part II of this article will discuss some of the layers of 84's woven into the Patrem along with other examples of number symbolism. The author will explore some of the implications of his findings and offer some opinions on the meaning of Bach's use of numbers.)
Footnotes 1 Alister Fowler, Spencer and the Numbers of Time (London, 1964), p. 238. 2 Bach Reader, rev. ed. (New York, 1966), p. 440. The passage is quoted from Mattheson's Ekrenforte (1740).
3 Christopher Butler, "Numerological Thought" in Silent Poetry, ed. Alister Fowler (London, 1970), p. 16.
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4 Ibid. The passage is from Copernicus' prefatory letter to Pope Paul. 5 Friedrich Smend, Kritischer Bericht, NBA Ser. II, Bd. 1 (Kassel and Basel, 1956), p. 333. 6 Smend, Kirchen Kantaten: Ende des Kirchenjahres (Berlin, 1947), p. 14.
7 Vincent Foster Hopper, Medieval Number Symbolism (New York, 1938), p. 84 {sic.). Hopper is abstracting from several sources, most importantly, St. Augustine ( Civitas Dei). He cites many examples to support this interpretation of 3 and 4 (pp. 68-86). 8 As summarized in Butler, op. cit., p. 20. The special significance of 7 and 12 is indeed a universal phenomenon as can be seen by comparing various calendrical and timekeeping systems (12 months, 7 days, etc.).
9B + A + C + H = 2 + l + 3 + 8=14. The word "gematria," dating from c. A.D. 200, refers to the practice of "assign- ing numerical values to the letters of the alphabet." ( Hopper, op. cit., p. 62 ) . Since the word is an accepted English term, it will be used in place of the some- what awkward phrase "letter-number system."
10 This property of 140 seems related to the fact that 14 = l2 -f- 22 + 32. 11 The inclusion of these words was evidently the result of a reworking of the move- ment after at least part of it was written. As Smend points out ( K.B. , p. 135), vestiges of the words Patrem omnipotentem can be seen underneath changes in text in the soprano part, meas. 1-3.
12 The three repeated tones at the head of a seven-note phrase is strikingly similar to the bass melody at the outset of the chorale prelude Wachet auf ( BWV , 645). (See this author's discussion of that passage in BACH , Vol. IV, No. 2, p. 26.) In the present example, the Trinity lies at the heart of an enfolding 14 (7 + 7). The total 17 ( 10 + 7 or 14 + 3) holds a tremendous symbolic potential.
13 "As thy name, О God, even so thy praise, unto the ends of the earth." The cantata was probably first performed on New Year's Day, 1729. As Smend has observed, the theological implications of both texts are quite similar (K.B., p. 134). The reworking of the movement was extensive; however, the details of the parody tech- nique lie beyond the scope of this study.
14 A similar pattern occurs in the organ Passacaglia (BWV, 582), where the theme appears in its original form 14 times and is varied 7 times for a total of 21 state- ments, which are then mirrored by the 12 statements of fugue subject. (See also the discussion of Ex. 4 above, where the outer voices totaling 21 notes enfold the 12 notes of the middle parts.) The number of repetitions of the other words in the present work are doubtlessly symbolic also: Credo x 12; in unum Deum x 9; Patrem omnipotentem x 10 (God as the Law Giver and Judge?) ; and coeli x 33. There may be a pun involved with the second et , since the 24 repetitions refer to the gematria for that word. A curious detail of the text in gematria relates these "unimportant" words for Bach: the cumulative total in both cases (and no place else) is a multiple of 41. (533 = 41 x 13; 820 = 41 x 20).
15 Perhaps of equal importance is the fact that 70 is the third of the 10 numbers whose prime factors total 14 (2 + 5 + 7). The number "32" itself is something of a mystery; if it has a personal significance for Bach beyond the fact that its digits (like 14, 23, 41, and 50) add to 5, this writer has not uncovered it. There is the possibility, however, that the symbol "32" is another way in which Bach signs his name numerically, since "S. Bach" = 32. Notice, also, that Bach has used it elsewhere - e.g., in the Goldberg Variations.
16 Notice that the eleven presentations from 11 to 21 comprise 84 notes; also note the way Bach has "framed" the seven statements from 14 to 20 (m. 41) with two identical groups of 67 notes:
Statement: 1-13 14-20 21-32 Notes: 67 56 67 Numerical Property: Prime 14x4; 7x8 Prime
factors total (6+7=13) 13(2+2+2+7) 6+7=13
17 The total of all the notes is 175 (119 instrumental + 56 voice). (See note 16 for another bracketed 56.) 175 = 7x5x5; 7 + 5 + 5 = 17.
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18 The oboe and violin are compressed into one line in the holograph at this point (p. 102), as are the soprano parts throughout. The entire movement has a some- what crowded appearance, which may result from the composer's attempt to make the format of the score fit a numerical scheme.
19 Butler, op. cit., p. 12.
PLATE I
Concluding Page of Bach's Holograph, Patrem Movement, B-Minor Mass (from Faksimile- Ausgabe [Leipzig, Insel Verlag, 1924, p. 105]; re- printed with the permission of the publisher.)
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