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article: hidden symbols in the 14-th bach invention


EPTA

author: Tjako van Schie, pianist
c. July 6th 1999

contents:
Introduction The journey starts New Discoveries The Bonus: BINGO! Conclusion
Postscripts Comments Another article about the Goldbergs Appendix with comments


INTRODUCTION

You know how it goes. Sometimes you just pick up some musical score from your dusty bookshelves and find yourself browsing through the pages.Then suddenly you are fascinated by some strange things you encounter on a page... and you start to puzzle. This happened to me recently with the Inventions of J.S. Bach. As I have been reading a lot on Bach & Number Symbolism (see also my Goldbergs Article my eyes were attracted especially to the 14th two part Invention a few days ago. I made some remarkable new discoveries there! Now I think it is wise to publicize this, and to hear your reactions on it!

So I just was playing around a bit with the Bach Inventions. What I just have discovered is in my humble opinion really interesting! For understanding this I presume you have some knowledge of Kabbalistics. The Kabbalists had a way of encoding the alphabet, like a=1 b=2 c=3 etc.
The alphabet they used is the Pythagorean alphabet in which i and j are the same letter, just as u and v.:

a=1 b=2 c=3 d=4 e=5 f=6 g=7 h=8 i,j=9 k=10 l=11 m=12 n=13 o=14 p=15 q=16 r=17 s=18 t=19 u,v=20 w=21 x=22 y=23 z=24

LETS ROCK: THE JOURNEY STARTS!

Now take a close look at the 2 part Invention nr. 14 in B-flat.
(I do hope you have a score nearby: it is best to have it for you, to look for yourself!)

According to the above alphabet Bach can be represented by 14(=2+1+3+8). Bach often uses this number in his music to put a 'secret' signature in his work. Also small voices are heard by the Gods. Bach, being a devoted composer is humble, and doesn't show off with his name a lot, so he often hides it in his compositions.

There has been some investigations going on about Bach being a Rosicrucian, as (amongst other authors) is described in the book "Bach & the Number" by Kees van Houten & Marinus Kasbergen (1985, Walburg Press Holland). They have pointed out some things about this invention earlier already, by the way, which I have tried to intertwine in this article (their quotes are printed in italics).
The = sign in this article should be read as: 'can be seen as' or 'might represent'.

The 14th Invention is written in B flat - major.

  • (B flat= German B = the first and Capital letter of Bach's last name.)
  • This Inventio has 20 bars.
  • 20 can be split in 10+10 (=XX as symbol of Christ & Cross)
  • 20 can also be seen as 3+17=CR=Christian Rosencreutz.

The piece can actually be divided in these numbers: 3 bars form the main theme and the other 17 are a kind of variations on this theme group.
20 is also 9+3+8=ICH, which Bach often uses to point out that he wrote the piece, as a kind of second signature, according to K.v.H & M.K..

Now look at the whole piece:
K.v.H.& M.K.wrote (freely translated from Dutch to English by me):

"There is a 3 bar introduction=C
Then follows 8 bars development=H
(then a weak cadenza in c-minor)
Then the piece ends with 9 bars in another way of movement=I"


But now look at the theme:

It has 20 notes. We might suspect a correlation between the whole piece and the theme group, like the way Bach applied this as a principle in the Goldbergs with 32 pieces and a 32 note fundamental line, on which that piece is built. One could call this micro-macro correlation.

The theme can also be divided in 2 groups of 10 notes = X = Cross/Christ(Ichtus)

K.v.H. & M.K. continue in their book:

"8 (=H) are 32nd notes (those with 3 value lines)
3 (=C) are 16th notes (those with 2 value lines) which are attached to the 32nds
9 (=I) are other 16ths.(not attached to the 32nds)
This is repeated 14 (!) times in this whole piece. Therefore there should be 14 x 20 = 280 notes involved in this, but Bach has shortened the 13th entrance of the theme. This entrance has only 16 notes. Thus the total of notes involved in the theme is only 276. This can be split in 2x138 = B.ach!
When we count the number of 'Bach-notes' in which Bach could have put his signature in another way we see this: the notes B, A, C and H (H=B-flat in German notation!) all occur in this piece.

In scheme:

  b a c h  
'' octave  5 1 35 - = 41 J.S. Bach =(9+18) +(2+1+3+8)
'  octave 34 19 27 - = 80 158 Johann Sebastian Bach
small octave 27 23 27 1 = 78

big octave

24 12 3 2 = 41 J.S. Bach  


The 80+78 remaining make up 158 = Johann Sebastian Bach

Then it is funny that this scheme (because h doesn't occur in '' and 'octave) doesn't contain 16 explicit note names, but only 14!"

NEW DISCOVERIES!

Now back to some of the discoveries I did during the last days:

  • The h notes, there are 3 (!) of those, occur in bar 11 (remember: h is the alteration of B-flat, or B-flat with a  )
  • So we also have a division of 10 bars / 1 bar, with the 3 h's / 9 bars.
  • 10 = X
  • 1 = God (or: Principle, Initial Power)
  • 9 = 3x3 symbol of Holy Trinity

Also funny is that 27 occurs 3 times in the scheme above:

  • 27 = 3x3x3.
  • (And 27 = 9+18 = "JS" being the initials of his first name.)
  • By the way: 9 = "I" can also be understood as a symbol of Christ = (Ichtus) or "J" = (Jesus). Remember: in the Pythagorean alphabet Bach was familiar with, the I and J had the same number value.

Another remarkable thing I discovered with these #,b and  signs in this piece:
Some notes are altered with a b or # or are been set to 'white key' with  (eg. e-flat becomes e in bar 8).

There are

  • 11x b
  • 7x 
  • 2x #
  • Total: 20 again!
  • And we can divide them in 2 x 10!
  • There are 10 (= X) of these alteration signs in the upper voice
  • There are 10 (= X) of these alteration signs in the lower voice

Heaven & Earth in perfect balance?

Scheme:

  • Uppervoice: 2b  1   1#  2b       1    3b
  • Lowervoice: 2   1#  1b  1 1b    1    2b 1

The two #'s are in bar 9 = 3x3... And the # might represent a "Cross" too.

Now we group them in the upper voice circular:

  • Uppervoice: [2b 1 ] 1# [2b 1 ] [3b]

Isn't this amazing? The # divides the upper voice in 3 groups of 3 accidentals.
Lowervoice circular reading (see the place of the [brackets] ) gives almost the same dividing in 3 groups as follows!

  • Lowervoice: 2 ] 1# [1b 1 1b] [1 2b] [1

Taking the last and the first together gives:

  • Lowervoice: [3 ] 1# [1b 1 1b] [1 2b]

And taking the 2nd[] together gives:

  • Lowervoice: [3 ] 1# [2b 1 ] [1 2b]

The uppervoice was:

  • Uppervoice: [2b 1 ] 1# [2b 1 ] [3b]

So now we have:

  • Uppervoice: [one pair +1 or 2+1] x2, # , and [3 of the kind]
  • Lowervoice: [3 of the kind] , #, and [one pair +1 or 2+1] x2

Excuse the poker-terms...) Or shorter:

  • U: [2/1] 1 [3]
  • L: [3] 1 [2/1]

Do you see the beauty of this pattern/construction? It is in cross form too!
Lower and upper voice both seem to have the same underlying accidental-structure!

And finally notice this:

  • Bach uses 3 b-notenames including the 2 on the left of each staff: b-flat, e-flat, a-flat.
  • Then 3  notes: e, b and a.
  • And only 1 # note: f-sharp.
  • We see the correlation between the 3 b notenames and the 3 notenames.
  • The f-sharp is litterally as well as metaphorically speaking a 'solo-alteration'.
  • Obviously he emphasizes on the numbers 3 (= Holy Trinity) and 1 (= God) again!

THE BONUS: BINGO!

And it doesn't stop here: another discovery! Now we look at the German note names!!
I need more exclamation marks!!!
Remember: in Germany they use these names (as Bach did too):
B-flat=B, A-flat=As, E-flat=Es, normal B=H, F-sharp=Fis.
Now we put our Kabbalistic alphabet into the job again:

-> the Flat notes:

  • B = 2
  • As = 1+18 = 19
  • Es = 5+18 = 23
  • total: 44 = 30+14 (= 3*10+14 = XXX+14) (or maybe 41+3 = J.S.Bach+Holy Trinity)

-> the 'normal' notes:

  • H = 8
  • A = 1
  • E = 5
  • total: 14 (!)

-> the sharp note:

  • Fis = 6+9+18 = 33
  • (Notice the two 3's here again! A nice coinicidence? And 33 = 3x10 + 3 too...)

We end up with

  • the 3 b-names = 2+19+23 = 44, plus Fis = 33, plus 14 = Bach

Put in scheme:

  • 3 bbb names  = 44 (= 30+14 = 10x3 +14)
  • 1#name         = 33 (= 30+3 = 10x3 +3)
  • -----------------------------------------------------------
  •              total  = 77 = (and these two 7's also add up to 14)
  • remaining: the 3  names = 14 = Bach

In another formulation we might see it this way:
Bach is encoded in white accidentals, hidden (as he usually is) between 'normal' white keys.
Bach's relation to the 'divine' is visible in the 'real' alterations or real black keys.
And so we keep wondering about the (left-out) other notenames in the piece (in between which Bach has 'hided' his name), being the mentioned 'normal' white keys:

We shall encode them also:

  • c+d+f+g = 3+4+6+7 = 20 = 10+10 again!

BINGO! Bach between the divine powers again!
What remains further is the one black key which Bach doesn't use in this piece: the c-sharp (or d-flat).
We shall see what happens when we translate this notename into numbers:

  • Cis = 3+9+18 = 30 = 3X10 = Holy trinity and the X again.

As we don't know if Bach omitted the C-sharp or D-flat we do the same on the D-flat name:

  • Des=4+5+18=27=3x3x3!

So both these values give hints towards the unspoken Holy Symbols of Christ and the trinity!

CONCLUSION:

WOW! That was my first reaction! I was really speechless as you can imagine.
Then I thought this stuff is soo beautiful that I should tell about it.
Maybe you think right now that I am 'nuts'.
But I simply cannot resist the beauty of these metaphysical/compositional aspects!
I see them over and over again in Bach's music.
And this is such a beautiful example again! It is so fascinating!
This kind of discoveries prove to me at least the unbelievable magnitude of Bach's geniality.

Please feel free to react on this article. All reactions will be considered seriously.
Also if you have your sincere doubts, please let me know!
If you want to see more of these beauties I urge you to read my Goldbergs Article too!

Tjako van Schie, pianist
8th of July, 1999

Mail your reactions please!

POSTSCRIPTS

P.S. Read more on Bach & Symbolism in my other article on the Goldbergs.
There you can learn more about how Bach is a Master of Architecture and has such a superior control over both form and contents!

P.P.S.: Ioannis Galidakis: thanks a lot for your encouraging opinion to publicize this.
I made some modifications to the original text I have sent you, in order to justify some of my sources and to enlarge readability.
And I did some more discoveries since I mailed you the first time, which are also included now.

P.P.P.S. Some other interesting numbers:

  • There are 15 pieces in the 2 part inventions.
  • This makes a total of 30 voices.
  • This can be seen as 3x10 as well!
  • Besides: Bach signs the 14th Invention with his name in many ways.
  • There are 14(!) other inventions left.
  • So we might consider the 15 Inventions as being 1+14: a close bond between Bach and God is the most obvious explanation for this phenomenon.
  • Another possible clue: the number of 15 inventions can be seen as 15=P=Pesces, another symbol of Christ.
  • As we take the 15 2 part inventions together with the 15 3 -part inventions (Symfoniae) we end up with 30(=3x10) pieces.
  • Another note: in bar 14 of the 14th Invention we see a rhythmical unisuono between upper and lower voice. This is done with the head of the theme and it occurs 10 times. Here also we might see a connection between Bach and Christ!

COMMENTS

It is obvious that there is a strong debate about the issue of 'deliberate' insertion of hidden symbols in Bach's music.
That is why I place reactions I receive also on my site. They can be read on: appendix.htm .
I do not claim that my findings are above all true.

But to me the finding of these kind of patterns in Bach's music is just big fun.
Even if could be proven that Bach did not intentionally coded his name and other symbols in his music (I am convinced however that he did it deliberately) the music itself remains a source of big joy and a pointer to even more beauty.