Toronto Chamber Choir Blog

July 18, 2021
Author: David W. Barber

Numerology and Other Symbolism in Bach’s Mass in B Minor

Bach portrait by Elias Gottlob
Haussmann in 1748


The great Mass in B Minor (BWV 232) of Johann Sebastian Bach (1685-1750) is an odd hybrid — a Catholic mass in Latin written by a German Protestant Lutheran composer. In part because of its length (two hours, more or less) and the large forces required, it’s impractical for performance in either a Catholic or Protestant church service. (And in Bach’s time, the tradition of a “concert mass” had not yet been established.) It’s also a work he began in 1733 but did not finish until 1749, not long before his death in 1750.

So for these and other reasons, it’s unlikely it was ever performed as a complete work in Bach’s lifetime. His son Carl Philipp Emanuel Bach conducted a performance of the Credo in Hamburg in 1786. C.P.E. had inherited the manuscript, and it remained in manuscript form, not very well known except among fellow composers, until Felix Mendelssohn conducted the first complete performance of Bach’s St. Matthew Passion in 1829 in Leipzig, helping to spark a wider revival of interest in Bach’s music. Although portions were given in read-throughs or concerts earlier, likely the first full public performance of the Mass in B Minor was also in Leipzig, under Karl Riedel, in 1859.

One of the first things to notice about the piece is that it’s not really in B minor. It does open with the first Kyrie in B minor (see image above), but most of the work is in the relative key of D major, with side trips into F# minor (e.g., the second Kyrie), E minor (e.g., Crucifixus), G major (e.g., Domine Deus), G minor (Agnus Dei, the only movement written in a flat key) and others. (The Credo opens in the mixolydian mode on A.) The various movements — whether choral, solo, or instrumental — are written in a variety of styles and combinations of voices and instruments. And much of it has deeply symbolic meaning, both musical and spiritual. (Bach was deeply religious.)

Bach’s Mass in B Minor began as a job application. In 1733, unhappy with his treatment (and underpayment!) by the town council of Leipzig, Bach began composing a work he called Missa for Friedrich Augustus II, Elector of Saxony, hoping to be appointed composer to the new elector’s court in Dresden. The Missa was not a complete mass, but comprised what we now have as the first two sections of the complete work, the Kyrie and Gloria. In its even distribution of parts for choir, soloists and instruments, it’s clear Bach intended it as a showcase both of his own talent and of the elector’s musicians. (In his groveling cover letter to the elector, he calls it a “slight product of that knowledge which I have attained in music.”)

For Bach, ever practical, it was also a typically ingenious solution: The elector, having in 1734 been also named King of Poland, had converted to Catholicism, and so would have use for music in Latin. And Martin Luther, although he’d rejected many things Catholic, had retained the Kyrie and Gloria in the form of the Missa. So maybe Bach thought he could also use it in a Lutheran setting. (There’s little evidence he ever did, though it’s possible the Missa was performed in 1733 at the Sophienkirche in Dresden, where Bach’s 23-year-old son, Wilhelm Friedemann, was organist — though scholars disagree on this.)

It’s likely many of the Bach family made the trip to Dresden: Portions of the instrumental parts are in the hands of Bach but also of his wife, Anna Magdalena, and sons C.P.E. and W.F. Despite all his efforts, Bach was not appointed Dresden court composer in 1733 (though he did later get the title in 1736), and the elector likely never heard it performed. Bach then put the work away for about 15 years.

In 1748 or so, Bach was in ill health and starting to go blind (in part from two unsuccessful eye surgeries by English oculist John Taylor, who went on to similarly harm Handel in 1758, though he’d had some earlier success with the historian Edward Gibbon). So Bach set out to complete the mass — mostly likely not with any particular performance in mind, but (like The Art of Fugue BWV 1080, which also dates from the 1740s) more as an abstract expression of his musical and spiritual ideals. In addition to various groupings of voices and instruments, the overall work includes a variety of older and then-current musical styles: the High Baroque fugal writing of the two Kyrie sections; the latest stile galant (elegant style) of the Christe soprano duet; the Palestrina-like fifth-species counterpoint stile antico (ancient style) of the Credo (with its modal harmony and basis on Gregorian chant); the Confiteor (old-fashioned styles to represent the foundations of faith); and more. Rather like a composer’s portfolio.

We should be grateful that, unlike The Art of Fugue, Bach was able to complete his B-minor Mass. The Art of Fugue stops abruptly just as Bach was about to complete a complex quadruple fugue, having introduced the theme of his own name, B-A-C-H (in German notation, B=b-flat and H=b-natural). Completing the mass was made somewhat easier because for so much of it Bach borrowed or reworked some of his own earlier music. (If you’re going to borrow, you might as well borrow from the best.)

Of the some 2,300 bars in the B-minor Mass, we know for sure he borrowed about 600, though the revered Bach scholar Joshua Rifkin and others say that number is likely much higher, but we just haven’t found the original sources. We infer this in part because, with the exception of the opening four bars of the first Kyrie and portions of the Confiteor, which show signs of reworking and erasures, the original manuscripts are remarkably clean and error-free. (Even the great Bach made mistakes or at least changed his mind sometimes.)

The practice of borrowing or parody, by the way, was accepted — even prized as a skill — as it had been for centuries. In Bach’s case, since he was reusing some of his own music, this was likely also a means for him of preserving and displaying music he was proud of. Any given cantata was likely performed once or only a few times (not repeated year after year, as we do now), whereas a mass setting could or would be performed multiple times.  

Musical and number symbolism in the B-minor

Though there’s much scholarly debate as to the extent of it, there’s no doubt Bach’s music shows the influence of his interest in the mathematics of his chosen art form — among other things an attention to form and symmetry and a fascination with numbers and number symbolism that seems too precise to be merely coincidental.

The Hebrew writers of the Bible or Tanakh (the Old Testament) and Talmud often employed number symbolism called gematria (which through Greek gives us our word geometry — and possibly grammar, though scholars disagree on that, too), where the 22 letters of the Hebrew alphabet (aleph, beth, gimel, etc.) and certain words are assigned number values. (In the simplest English version, imagine a cipher where A=1, B=2, C=3, etc.) This later moved to New Testament Koine Greek (for example, 666, the “number of the beast” in the book of Revelation, is often cited as a veiled reference to the hated Roman emperor Nero) and by Bach’s time to German as well. Some numbers were also considered to be mystical or sacred on their own merit, such as 7 (the 7 days of Creation, Jesus suggesting forgiveness 70 times 7) and 12 (the 12 tribes of Israel, 12 disciples).

Bach was obviously familiar with this practice, as evidenced, for example, by his frequent references to 14 (2x7) and its inverse, 41. In addition, the letters BACH total 14 (2+1+3+8=14) and JSBACH total 41 (9+18+2+1+3+8=41). (By tradition from the Greek, I and J are the same letter, counting for 9.) There’s a real danger, of course, in taking this too far or in looking for such symbolism where it may be just coincidence (the gematria of the great humanitarian Albert Schweitzer also equals 666), but there are enough examples in Bach’s music — and not just in the B-minor — to make the case. Maybe for him it was little more than an intellectual game, although there also seems to be some spiritual symbolism at work.

The Mass in B Minor opens with a grand, slow, four-bar introduction (that seems to be freshly composed) for the first Kyrie. Then the orchestra sets up an elaborate five-part fugue for the choir, working its way around the fugal clock, TASSB. Scholars believe Bach based this on one of his earlier four-part church cantatas (now lost), to which he added a fifth voice, most likely one of the sopranos. The Kyrie fugue figure (ignoring a few passing ornaments) is a theme of 14 notes. The fugue remains in the opening key of B minor until bar 41, where it begins to modulate and develop. (There are those numbers again!)

The Christe eleison section is a duet for two solo sopranos, the first of only three duets in the whole mass, each of which reflects on the nature of Christ. The others are the soprano/tenor duet Domine Deus (Lord, God) in the Gloria and the soprano/alto duet Et in unum Dominum Jesum Christum (And in one Lord, Jesus Christ) in the Credo. In each duet, the two voices weave around each other in close imitation (sometimes even in strict canon), blending like the human and divine natures of Christ. (Compare also John 10:30, “I and the Father are one.”)

The second Kyrie is another fugue, using a four-note musical figure called circulatio, with a rising interval followed by a descending interval and a return to the home note, or sometimes for the harmony to fit, a note nearby. In this case, it starts in the basses with F#, G, E#, F#. Bach often used this kind of figure in his music (and indeed the B-A-C-H theme is an inverted circulatio), most often in reference to Christ or the cross or the crucifixion (the figure itself forms a sort of cross). Echoes of this pattern return in the Crucifixus of the Credo, another reference to Christ on the cross.

One section of the Gloria, Gratias agimus tibi (We give thanks to thee), Bach based on his 1731 cantata setting of the same words in German, Wir danken dir, Gott (BWV 29). The music from the Gratias will return at the close, for Dona nobis pacem. The setting of Quoniam tu solu sanctus (For thou only art holy) is for bass solo and French horn — the hunting horn suggesting royalty and, in Bach’s day, a “natural” horn suggesting the natural perfection of God. (And please have some sympathy for the poor horn player, who must enter with a dramatic D octave leap after sitting silent for about 45 minutes.)

We presume the remaining sections of the work — Symbolum Niceum (the Nicene Creed, or Credo), Sanctus, Benedictus, Agnus Dei and Dona Nobis Pacem — come from the later period in Bach’s life, when he set out to complete it.

The Credo is where Bach uses the most musical and number symbolism. Like the Confiteor una baptisma (“I acknowledge one baptism”) that comes later, he writes the opening Credo in strict Palestrina-like fifth-species counterpoint, a traditional musical style symbolizing the traditional foundations of the faith. He bases the opening movement on a cantus firmus (“fixed song”), an elongated version of a Gregorian chant melody on Credo in unum Deum (“I believe in one God”). Composers leading up to Bach’s time would often begin the Credo with just this Gregorian melody or one like it, called an incipit (Latin for “it begins”), with the choir entering on Patrem omnipotentem (“Father Almighty.”)

The whole Credo has nine movements (3x3, representing the Trinity). The central three movements encapsulate the faith — Et incarnatus/Crucifixus/Et resurrexit (incarnation/crucifixion/resurrection) — the centre of the centre of which is the Crucifixus (movement five of the Credo, perhaps representing the five wounds of Christ). The gematria of CREDO gives us the number 43. In the full Credo, Bach sets the word “credo” 43 times.

The Crucifixus contains music that’s the oldest of Bach’s borrowings (that we know so far), his 1714 cantata BWV 12, Weinen, Klagen, Sorgen, Zagen (Weeping, Wailing, Sorrow, Trembling), a suitably dark reference for the crucifixion. It has a passacaglia bass figure in the orchestra, a chromatic descending lamento figure similar to the one Purcell used in Dido’s Lament (written in the 1680s, though it’s unclear, but probably unlikely, that Bach would have known this particular music — the lamento melody was widely used). This bass figure appears 13 times (12 disciples plus Christ at the Last Supper, which also gives us the tradition of 13 being an unlucky number, with 13 steps to the gallows and 13 coils on a noose). At some settings of the Crucifixus text, a cross-like circulatio figures, similar to the second Kyrie. Notice the many entries at the tritone — the interval of the augmented fourth or diminished fifth that was considered diabolus in musica, “the devil in music.” Notice also the setting of the final bars, passus et sepultus est (he suffered and was buried), where the melodic line gradually descends and the voices are generally lower in their vocal ranges. And, in the next movement, the rising figure (in most voices) of et resurrexit (he rose…). Granted, this sort of word painting is not unique to Bach, but a convention he does follow here.

The Sanctus contains music from Bach’s Christmas cantata of 1724 (BWV 91), with six-part writing of three “choirs” (two vocal choruses plus orchestra) representing the “Holy, Holy, Holy” of the text, allusions to the Trinity and, mostly likely, the vision of six-winged seraphim that King Uzziah has in Isaiah 6. (It’s written in common 4/4 time, but the many triplets in the first section give the feel of a triple-metre 12/8, and the Osanna that follows is in triple-meter 3/8.)

The Benedictus, for tenor solo and flute obbligato with continuo, is peaceful and pastoral, befitting the text (“Blessed is he that cometh in the name of the Lord.”

The Agnus Dei solo for alto is likely from a lost cantata Bach wrote for a wedding in 1725. Aside from being heart-achingly beautiful, it’s the only movement of the whole mass that’s in G minor, in fact the only movement in a flat key. The G-minor tonality sets up the return to D major for the closing movement.

Even by Bach’s time there was a long tradition in mass writing of reusing earlier material for the closing Dona nobis pacem (Grant us peace). Often this would be from the Kyrie. But, in Bach’s case, the B-minor tonality was presumably the wrong feel for a positive, if restrained, close. So Bach provides some symmetry and closure with a return (in D major) of the Gratias agimus tibi (We give thanks to thee) music from the Gloria in a final prayer for peace.

© David W. Barber (SOCAN) 2001, rev. 2011/2021

Select bibliography

Jenkins, Neil. Bach B Minor Mass. Programme Notes and Prefaces, 2001
Keller, Herbert Anton. "Was Bach a Mathematician?" English Harpsichord Magazine 2(2), 1978
Szeker-Madden, Lisa. "Topos, Text, and the Parody Problem in Bach’s Mass in B minor, BWV 232." Canadian University Music Review, 1995
Tatlow, Ruth. "Collections, bars and numbers: Analytical coincidence or Bach’s design?" Understanding Bach, 2007





David W. Barber has sung with the TCC for more than 20 years, and the choir has performed several of his compositions. He's a journalist, composer, and the author of more than a dozen books of classical music history, literature, and other fields, including the bestselling Bach, Beethoven and the Boys: Music History As It Ought To Be Taught.



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