it was the old way of thinking.
you see - back then, peeps had a different way to approach all that artsy stuff. Architecture, Paintings, Music.. it all followed the same rules. Cathedrals for example - they are build the same way that composers like bach wrote his compositions. it is said, that cathedrals are a frozen piece of music. you can trace that back till you reach the writings of the bible (to which the music was is cosely related). there also was alot of mathematics involved (not exclusively though - they also had some feel of course). if you analyze bach´s music for example you can see a breathtaking amount of number-mysticism, symmetrical note-arrangements, golden section, fibunacci-rows, etc.
like ein "the art of the fuge" for example.

For those who dont know what the golden section is:



The whole piece 'a' is divided in 2 smaller pieces. the bigger of those pieces 'b' (the Major) has the same proportion to 'a' as the smaller piece 'c' (the Minor) has to 'b'. In numbers that is 0.382 : 0.618 (aprox used as 3:5). This ratio comes pretty natural and harmonic to the mind of the human because this ratio often occurs in nature itself. and since we are part of the nature, we find that ratio pretty pleasurable. alot of artists have used that golden section in their art as stated before. the golden section is always a place where something rather special occurs like the highest note of a piece, or the eyline of a face in a painting, etc

"Musica est disciplina, quae de numeris loquitur" - Music is a discipline, that talks through numbers.

Bach managed it, to code his name B-A-C-H into the Art of the Fuge.

Here´s a short glimpse of how he constructed his art of fuge:

From the whole piece, the golden section is exactly at measure 1373. if you count those digits together, you get the number 14 - 14 is the code for the name BACH (in an alphabetical order the letters B=2 (second letter), A=1, C=3 and H=8 --> 2+1+3+8=14). Measure 1373 is in the octave-canon (its measure 64 in that piece) - that measure is - without a reason in the sense of a counterpoint kept single-voiced.

the golden section if you count the number of the pieces of the art of the fuge which is 18 (mirrorfuges-pairs counted as one) is after the 11th piece. and that exactly where the axis for the whole symmetry of the piece lies.

and a small example or the relation to the bible:

in Corinthian 13 the word MIRROR (he used alot of mirrorimages n his music) is in the 12 sentence - so you have the numbers 12 and 13. the two mirrorfuges have the numbers 12 and 13.

after the general-rest in CP 13 there are 12 more measures to come

Cp 9 has exactly 130 measures while CP 10 has 120

(theoretically) in the last 21 measures of the last fuge there would be 13 theme-entries.

13 theme-entries in CP. 2 and 12 theme-entries in Cp.3

plus - the first Corinthian letter is in the 7th book of the new testament. the word mirror in german has 7 letters (Spiegel). the first 7 Cp (CP=Counterpoint) are symmetrical and the first theme of the finishing fuge has 7 notes.

the 3rd theme of the last fuge consists of the notes b-a-c-h (it has to be said that a B in germany is a B-FLAT in the rest of the world and an H in germany is a B in the rest of the world - that is because some stupid monk has written a b that looked like an h and all the other monks copied that mistake)

this is only a VERY SMALL glimpse into bachs music and his way of thinking. his works are FULL if such spectacular number-magic and relations, that one can only stand in awe at what this dude (and alot of other guys back then) did.

[Edited by Azrael on 09-08-2003 at 01:40 AM]