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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

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  • Notizbuch fr Studenten

    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 --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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  • Table I: Numerical Analysis of the Text Used by Bach in the Patrem Section of the B-Minor Mass

    # LETTERS # SYLLABLES GEMATRIA TEXTURAL WORD (TOTAL) (TOTAL) (TOTAL) REPETITIONS

    1. Credo 5 - 2 43 12 2. in 2 (7) 1 22 (65) 9 3. unum 4 (11) 2 65 (130) 9 4. Deum 4(15) 2 (7) 41(171) 9 5. Patrem 6JT) 2 69 (240) I 6. omnipotentem 12 (33) 5 (14) 150 (390) 10 7. factorem 8 (41) 3 (17) 77 (467) 32 8. coeli 5 (46) 2 42 (59) 33 9. et 2 (48) 1 24 (533) 34

    10. terrae 6 (54) 2 (22) 64 (597) 34 11. visibilium 10 (64) 5 119 (716) 22 12. omnium 6 (70) 3 80 (796) 22 13. et 2 (72) 1 24 (820) 24 14 invisibilium 12 (84) 6 (37) 141 (961) 25 (285)

    There are also many clues to be gleaned from Bachs treatment of the text. A cursory look at the full score is s