A recurrent feature of parallel techniques is exploitation of a proper name. Those performed on‘Wjlhelm Ernst’ and ‘Pachelbelivs’, the paragrams on ‘Daum und Thym’ and ‘Skt Egidien’ and Kuhnau’s puzzle on ‘Steffani’ have all been mentioned. This practice dates back to the earliest classical times when the Greek, Hebrew and Roman alphabets could be read as numbers as well as letters, and authors exploited the names of heroes.122 The Bach family name lent itself very neatly to a variety of parallel devices, which have led to many intriguing and fanciful claims about Bach’s use of his name. Although it is difficult to discern whether a parallel conceit was planned or a simple coincidence of numbers or music, it is essential to review the evidence, not least because I claim that Bach’s name appears in the bar total or key pattern as the third characteristic of proportional parallelism, in all collections that he published or left in autograph fair copy.
In 1732, under the entry‘Bach, Johann Sebastian’, Walther reports how the Bach family name can be adapted to musical usage:
The Bach family name is said to have originated in Hungary, and all those who have borne this name, so far as is known, are said to have devoted themselves to music; which perhaps springs from the fact that even the letters‘B’ ‘A’ ‘C’ ‘H’ are melodic in their arrangement.123
Among the annotations Walther made to his personal copy of the 1732 dic- tionary is a note that it was Johann Nicolaus Bach (1669–1753) from Jena who had told him about this.124Whatever the provenance, any member of the Bach family could have noticed the melodic parallel and used it.
B-A-C-H in melodies
Although it was the Jena Bach who reported to Walther that musical notation spelt out the family name, we know from an account by Johann Nikolaus Forkel (1749–1818) that Johann Sebastian used the melodic form of B-A-C-H at least once:
The last fugue but one has three themes; in the third, the composer reveals his name by B A C H. This fugue was, however, interrupted by the disorder in the author’s eyes, and as the operation did not succeed, was not finished.125
122 Tatlow, Bach and the Riddle, 37–9. 123 NBR, Doc. 304. 124Ibid., Doc. 305. 125 Ibid., 466. SeeChapter 9 §II.
Walther wrote that Johann Sebastian had published six partitas separately, giving the keys ‘B dur, C moll, A moll, D dur, G dur und E moll’.126 Devising a B-A-C-H signature in a large-scale key pattern is only a step away from the melodic B-A-C-H feature. The keys of the first three published partitas happen to be a permutation of thefirst three letters of the Bach family name, as Walther no doubt realised.
It is commonly thought that the letter ‘H’ instead of ‘B’ was used universally in Bach’s time in Germany for the note B natural, but this was not the case,127 as Riepel illustrated by citing the use of B instead of H by Fux and Mizler,128explaining that ABC was the old form, used by the Italians and French as well as some Germans. Later, when speaking of the use of ut re mi, Riepel comments that almost every music master has a different manner of teaching his students the note names.129 Because the letter B could read as both B and H, it gives an additional interpretation to the description in Walther: the four letters of the Bach family name could be equally well represented by three notes B/H-A-C.130
A century earlier Athanasius Kircher had used the letter‘H’. Had Bach used Kircher’s Alphabetum Steganographicum musicum, or his Alphabe- tum Musicum, his full name would have been created the melodies shown inFigure 2.5.
This begs the question of whether iconic themes, such as the opening of The Art of Fugue or the Ricercar à 3 of the Musical Offering, held any parallel meaning for Bach, and if so, whether being able to ‘decode’ the melody would add anything to our understanding of Bach’s music. Clari- fying the‘word’ might explain Bach’s starting point, the source of inspir- ation or Inventionsquelle.131
B-A-C-H in keys
When Bach published CÜ II in 1735 he chose to position the French Overture after the Italian Concerto, rather than publish it as the seventh
126
Walther, Lexicon, s.v.‘Bach, Johann Sebastian’. 127
Geßner, Buchdruckerei, 142 shows that the music printing standard was for‘B’ rather than ‘H’. 128 J. Riepel, Grundregeln zur Tonordnung insgemein. (Frankfurt; Leipzig, 1755), 3.
129
Riepel, Grundregeln, 11. 130
Unfortunately Bach rarely wrote the key name so we cannot know when or whether he used ‘H’ or ‘B’ interchangeably for the keys of B major/minor.
131 G. P. Harsdörffer, Poetischer Trichter. 3 vols. (Nürnberg, 1651–3), vol. III, 72.
Partita, or as thefirst work in CÜ II. He originally composed and revised the French Overture in C minor,132 but transposed it to B minor for the 1735 publication. This transposition created a large scale B-A-C-H signature across the two parts of these two keyboard publications (Table 2.1) and speaks of a changed plan from the B-A-C pattern in the
Figure 2.5 ‘Johann Sebastian Bach’ in Kircher’s musical alphabets
132 The manuscript of the C minor version in Anna Magdalena’s hand (P 226: 41–65) “Ouverture pour le clavecin par J. S. Bach” is extremely neat, suggesting that it was copied from a revised autograph source.
first collection, highlighting the new unity between the two collections, with all this implies for proportional parallelism. Transposing and inverting the B-A-C-H motif naturally gives many other possible‘signa- tures’: at the fifth this would be F-E-G-F♯ and at the fourth E♭-D-F-E. An inverted F-E-G pattern can be seen in Table 2.1 column 5, with Partitas 5 and 6 and the Italian Concerto; the D major of Partita 4 standing outside this ‘self-referential ‘scheme. Although tonal trans- positions and inversions would regularly occur in fugal treatment of the B-A-C-H theme, I wonder if the transposition of a name would have been as compelling a conceit to Bach and his contemporaries as the name in ‘normal’ order.
A signature in its B-A-C form can be seen in the Six Solos for violin (BWV 1001–6) and in the Six Sonatas (BWV 1014–19),Table 5.4. The dual use of the musical letter‘B’ facilitates the formation of a B-A-C signature in the keys of a collection. One could reasonably object that there are only seven or eight musical letters from which to choose, and that therefore early eighteenth-century composers writing a collection of six or eight works in different keys would naturally choose a combination of the keys A, B and C. Strangely enough, I have not found this signature combination in many other collections. The ordering of keys across CÜ I and II (Table 2.1) has recently been remarked upon.133 Bach’s contemporary Meynrad Spiess (1683–1761) included keys among his list of features to be ordered in a musical composition.134 Perhaps he too had noticed the pattern of keys in Bach’s collections.
Table 2.1B/H-A-C key pattern across CÜ I and II
Title BWV Keys Bach allusion Partita 1 825 Bflat major B
Partita 2 826 C minor C Partita 3 827 A minor A Partita 4 828 D major
Partita 5 829 G major G Partita 6 830 E minor E Italian Concerto 971 F major F French Overture 831 B minor H
133 Wolff, Essays,‘The Clavier-Übung Series’, 189–205; Learned Musician, 378–9. 134 M. Spiess, Tractatus Musicus Compositorio-Practicus (Augsburg, 1746), 134, col. 1.
B-A-C-H and other forms in number alphabets
In his celebrated essay Bach bei seinem Namen gerufen, Friedrich Smend announced that he had found Bach’s signature embedded in music.135
With the numerical equivalents to‘J. S. Bach ‘(41), ‘Bach’ (14) and ‘Johann Sebastian Bach’ (158) and using the simplest of all number alphabets, A=1 to Z=24, he noted the mirror image of 14 and 41 and isolated many occurrences of these numbers in Bach’s music.136Although Smend’s lack
of documentary evidence made his experimental results easy to dis- credit,137he had discovered something very important about the creative possibilities of this time. Bach and his contemporaries could have used many different lusus ingenii and hybrid parallel techniques involving number alphabets and names. The name ‘Bach’ could be represented in the numbers suggested, but the variables were far greater than Smend had imagined. Bach signed his name in many different forms while thirty or more number alphabets and at leastfive different music alphabets were regularly used. And that is without allowing a composer to process the numbers using different parallel techniques. Translating a name to numbers through a number alphabet is an exact science, but working in reverse as Smend did, from numbers to their meaning, is far more hit and miss.
In 1968 the compilers and editors, Werner Neumann and Hans-Joachim Schulze, of thefirst volume of Bach Dokumente grouped together all the surviving documents in Bach’s hand available at the time. In 2007 a supplementary fifth volume of more recently discovered documents was published. In BD I and V 185 documents are signed by Bach, in one of his many different signatures. Because the editors transcribed the exact signa- ture form, it has been possible to make a statistical comparison of the signature forms Bach used.138Even though far from complete, and ignor- ing conventions that may have motivated a particular signature type, Table 2.2shows some important trends. When Bach signed a receipt he usually did so as‘Joh: Seb: Bach’. By far his favourite form for title pages was‘Johann Sebastian Bach’, with ‘J. S. Bach’ used less frequently and ‘Joh:
135
Smend, Johann Sebastian Bach bei seinem Namen gerufen (Kassel; Basel: Bärenreiter, 1950), reprinted in Bach-Studien: Gesammelte Reden und Aufsatze. Friedrich Smend zum 75. Geburtstag (Berlin, 1969).
136
Smend, Johann Sebastian Bach: Kirchen-Kantaten, vol. III, 8. 137 Tatlow, Bach and the Riddle, 6–36.
138 W. Neumann, Johann Sebastian Bachs Unterschriften (Leipzig: Bach-Archiv, 1972), a facsimile collection of thirty-six of Bach’s signatures.
Table 2.2Statistical survey of signatures Bach used. Data from BD I and IV
Form of Signature I Letters II Testimonial III Organ IV Legal V Receipts VI Title pages Totals Joh: Seb: Bach 1, 4, 5, 16, 20,
22, 38, 42, 43, 50 61, 62, 67, 69, 71, 73, 75, 79, 82 87 94, 95, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 109, 112, 113, 114, 115, 117, 120, 124, 126, 127, 128, 129, 146 (4 ex), A111b, A111c, A112 A119a, A120a, A129a, A134
153, 157, 167 58
Joh: Sebast: Bach 27, 14, 15, 17, 18, 23, 29, 30, 32, 34, 48, A13 57, 60, 63, 66, 68, 78, 81, A82a, A82b 84, 85, 89 96, 110, 119, 123, 125, 130, 131, 132, 135, A111a, A133, A135a, A139
147, 161, 164 40
Johann Sebastian Bach 10, 11, 12, 19, 27, 28, 31, 33, 35, 39, 40, 41, 54
80, A70 86, A90a 91, 92, 93 104, 108.122, 146 (1 ex) 152, 155, 156, 159, 160, 162, 164, 165, 168, 169, 172, 173, 175, 176 38 J. S. Bach 36, 49 65 146 (23 ex) 151, 154, 158, 166, 174 31
Johann Seb(ast) Bach 74, 77 111, 121, 146 (2 ex) 6
Joh. Sebastian Bach 47 90 2
Joan(ne) Sebast: Bach (Joan) 146 (1 ex) 148 2
Jean Sebastian Bach 150, 177 2
Bach 22 155 2
J. S. B 44 118 2
G. S. Bach 170 1
Sebast: Bach’ and ‘Joh: Seb: Bach’ in third equal place. When signing letters he seems to have used three forms fairly equally:‘Johann Sebastian Bach’, ‘Joh Sebast Bach’ and ‘Joh Seb Bach’. Extant documents show that on the whole ‘Joh: Seb: Bach’ was Bach’s favourite signature,139with regular, but significantly
less frequent, use of‘Joh: Sebast: Bach’, ‘Johann Sebastian Bach’ and ‘J. S. Bach’. Table 2.3shows the numerical value of these four signature forms. I have added the forms ‘Bach’, because of the contemporary evidence that the surname ‘Bach’ was used in a musical alphabet, and ‘Sebastian Bach’ because tradition suggests that this was the name Bach went by. All six forms are given their numerical values according to the three most com- monly used number alphabets in Bach’s time: the natural order,140 tri-
gonal141and milesian.142
The six signature forms generate eighteen possible numbers for Bach’s name. Although there is a high probability that composers in Bach’s time and location knew number alphabets and would have thought of using a signature as a parallel form, it is still a large jump to claim that a composer actually embedded his signature in a composition. Nevertheless, if one is intent on investigating the possible usage, the safest method is to note any recurring number in obvious musical units, and then assess its plausibility by weighing the result against external documentary evidence. Each occur- ence of a number I have tentatively isolated as an allusion to Bach’s name Table 2.3Bach’s signature forms in three common number alphabets
Signature form Natural Order Alphabet Trigonal Alphabet Milesian Alphabet Joh: Seb: Bach 31+25+14 70 186+189+46 421 67+97+14 178 Joh: Sebast: Bach 31+63+14 108 186+551+46 783 67+288+14 369 Johann Sebastian Bach 58+86+14 158 369+688+46 1103 148+338+14 500 J. S. Bach 9+18+14 41 45+171+46 262 9+90+14 113 Bach 14 14 46 46 14 14 Sebastian Bach 86+14 100 688+46 734 338+14 352 J.S.B 9+18+2 29 45+171+3 219 9+90+2 101
139 I.e., Letters, Testimonials, Organ Testing, Legal Documents, Receipts and Title pages. 140
Natural Order Alphabet: A=1, B=2, C=3, D=4, E=5,F=6, G=7, H=8, IJ=9, K=10, L=11, M=12, N=13, O=14, P=15, Q=16, R=17, S=18, T=19, UV=20, W=21, X=22, Y=23, Z=24.
141 Trigonal Alphabet: A=1, B=3, C=6, D=10, E=15, F=21, G=28, H=36, IJ=45, K=55, L=66, M=78, N=91, O=105, P=120, Q=136, R=153, S=171, T=190, UV=210, W=231, X=253, Y=276, Z=300.
142 Milesian Alphabet: A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, IJ=9, K=10, L=20, M=30, N=40, O=50, P=60, Q=70, R=80, S=90, T=100, UV=200, W=300, X=400, Y=500, Z=600.
will be discussed in Part Two. My observation of the strategic positioning of many proportional units based on the numbers 70, 158, 41, 14 and 29 appears to confirm Smend’s theory that Bach used the natural order alphabet.
An uncanny recurrence of various permutations of the numbers 1, 2 and 3 in strategic large-scale units, or as thefinal bar total of complete collections, drew my attention, and, together with a later discovery of the parallel total 3120 : 3120 bars between hisfirst four keyboard collections and the 1032 total of Aufrichtige Anleitung,143 forced me to consider the possibility that his use of the numbers 1, 2, 3 might have been intentional. Both 3120 and 1032 are permutations of the number-letters for B-A-C or 2-1-3, which raises the question of whether Bach might have intended it to refer to himself, or to the perfect number 6, with its 1+2+3=6 and 123=6.144 Permutation was a subject that fascinated mathemat- icians, philosophers and musicians. As Bach was able to generate and mentally retain endless possibilities to solve the technical challenges of his canons and fugues, I can see no reason why he would not have considered any combination of the numerals 2-1-3 as an allusion to his family name.
14-41 and 29 as family number names
There is a neat symmetry in the numerical value of the initials of Bach’s name in the natural order alphabet Bach=14, J. S. Bach=41, and that of his first wife. This may be a simple numerical coincidence, but its recurrence in the names of theirfirst- and second-born sons suggests deliberate design.
Maria Barbara Bach, Johann Sebastian’s cousin and his first wife, retained her surname‘Bach’ (=14) when they married. Her middle name Barbara (=41) created the same 41 : 14 as the value of her future husband. Her name as initials also contains a happy 1 : 1 symmetry: M.B.=14; Bach=14. Were the couple conscious of this numerical and harmonious match? Coincidentally, or deliberately, they chose names for their two eldest sons that also conform to this 41 : 14 pattern: their first-born son W. F. Bach=41; and their second son Carl Philipp Emanuel (Immanuel), using the initials given at his baptism,145was also 41– C. P. I. Bach=41. The pattern continues with parallels between the full initials of the father and 143
SeeTable 7.4.
144 SeeChapters 1and4for‘numerus perfectus’ and interpretations of the number 6. 145 BD II, Doc. 67‘getauft den 10ten Martij Nahm[en] Carolus Philippus Immanuel’.
the two sons: J. S. B.=29, W. F. B.=29, and C. P. I. B.=29.146Their daughters and younger sons fall outside this pattern. So does the name of Bach’s second wife, Anna Magdalena Wilcke (Wülcke), whose disappointing numbers A. M. W.=34, A. M. Wilcke (Wülcke)=72 (83), Magdalena=55 became an equally unsatisfactory A. M. B (15) and A. M. Bach (27) when they married on 3 December 1721, although had it been a serious issue, the harmonic perfection of 28 : 14 (Anna:Bach), and 27 : 27 (J. S. :A. M. Bach) would have more than compensated.147 Contrary to earlier Bach family traditions, Johann Sebastian Bach did not choose Johann as the name for either of his older sons. Although it is not possible to prove that they chose their sons’ names and godparents on account of their numerical value,148
the avoidance of ‘Johann’ and the recurring coincidence of 41 and 29 strongly suggests that Bach and his first wife had an eye on numerical unity within the male line.149 As if by design, Bach also became the fourteenth member of Mizler’s corresponding society.150
B-A-C and 2-1-3
The number letters of the word BACH in both the natural order and milesian alphabets are 2 1 3 8. In paragrams the numerical value of each letter was added to make a total for the whole word, so that Bach would become 14, as the sum of 2+1+3+8=14. Sometimes, however, the number letters were not added together, but remained separate, each number substituted for a letter in the solution word, such as in Kuhnau’s Steffani puzzle and in the algebraic problems Bach would have met at school.151
The coincidence of the letters B-A-C with the first three letters of the alphabet and the note-names of thefirst three notes of the musical scale would not have escaped the attention of any young, literate and numerate
146 JSB=9+18+2=29; WFB=21+6+2=29; CPIB=3+15+9+2=29.
147 Anna=28, Magdalena=55, Wülcke=70. Anna Magdalena=83 and A. M. Wülcke=83. 148
Although traditionally a child took the name of a godparent, one cannot exclude the possibility that a godparent was chosen for their name. BD II, Doc. 51 Friedemann’s godparents include Wilhelm Ferdinand von Lyncker, and Friedemann Meckbach. BD II, Doc. 67 C.P.E’s godparents included Adam Immanuel Weltig and Georg Philipp Telemann. There was no Carl.
149 Theirfirst-born, Catharina Dorothea, does not conform to the pattern. 150
Musicalische Bibliothek, vol. IV (Leipzig, 1754), 107. In 1746 there was only one new member. Clearly he would not have been able to influence his position in the Eisenach Latin school register, BD IV, Image 20.14. Joh: Sebastian Bach; 15. Joh: Jacob Bach.
member of the Bach family. The further coincidence of Sebastian’s birth- day would have been noticed by the bright schoolboy. He could not choose his birthday. It just happened to fall on the twenty-first day of the third month of the eighty-fifth year of the seventeenth century: 21385. This day and month was the official date of the spring solstice, although in reality the solstice fell days earlier for thefirst fourteen years of Bach’s life due to an error built into the Julian Calendar. The Protestant states corrected the error by losing 10 days in 1700, when the day after 18 February became 1 March, and not 19 February. The spring solstice finally coincided astronomically on Bach’s fifteenth birthday, 21 March 1700. Irrespective of the position of the sun and moon on 21 March, and whether he liked it or not, his birth date when written in the customary order Day-Month- Year152 21.3.85 translated into letters B-A-C-H-(E) and was numerically parallel to the numerical value of his surname, B-A-C-H=2-1-3-8. In its simplified form his birthday fell on 21.3, parallel to 2-1-3, B-A-C, and parallel to the musical notes 2-1-3, B-A-C.
Bach’s name in parallel imagery
The name‘Bach’ means ‘brook’ or ‘stream’ in German and this parallel was an obvious image to exploit in poetry. Johann Gottlob Kittel (1732–1809) (alias Micrander) composed the emblematic poem below when reviewing a concert given by Bach on the Silbermann organ in St Sophia’s church, Dresden on 14 September 1731.
Ein angenehmer Bach kan zwar das Ohr ergötzen,
Wenn er in Sträuchern hin durch hohe Felsen läufft;
Allein, den Bach muß man gewiß weit höher schätzen,
Der mit so hurtiger Hand gantz wunderbahrlich greifft.
Man sagt: Daß wenn Orpheus die Laute sonst geschlagen,
Hab alle Thiere er in Wäldern zu sich bracht;
A pleasant brook may well the ear’s delight inspire,
As through the woods, between high cliffs, itfinds its way;
But surely one must rank that other Bach far higher,
Who with his hurrying hand so wondrous sure doth play.
’Tis said, when Orpheus did his lyre strings awake,
All creatures in the forest answered to the sound;
152 Bach used the order Day, Month, Year, e.g. 14 Jan 1714. BD I, 33.
Gewiß, man muß diß mehr von unserm Bache sagen,
Weil Er, so bald er spielt, ja alles staunend macht.
But sure,’twere better that such praise of Bach we spake,
Since he, whene’er he plays, doth each and all astound.
In 1732 Ludwig Friedrich Hudemann published a poem dedicated to Bach in a collection of poems and translations. The poem is full of common musical imagery– Orpheus, his harp, Bach’s ability to sway the souls of the righteous, the choir of the Muses, the organ, the serpent’s tongue, Apollo, the laurel crown, marble edifice, living strings, and the perfection of Bach – as if Hudemann was designing an emblem for Bach.153 It is thought Hudemann wrote the poem in gratitude to Bach