This piece by Bach has confused musicians for years. It is exceptional in its complexity and has generated some bizarre approaches in trying to understand it. No, really.
There have been semiotic approaches, Shannon information theory (derived from thermodynamics - and measures uncertainty and disorder) and even entropic studies. I will leave the reader to research these fields of study if they wish. I am going to use The Modal Method to see if there are any underlying rules or patterns to this piece.
Now, whether or not Bach used this approach when writing is irrelevant. I am merely using it to understand the material in front of me. Here goes.
The piece is made up of predominantly 3 sequencies of scale changes. The one that is used most is the one I shall focus on for brevity.
The sequence in bar 3 - 4 is shown below, running from numbers 9 to 19. The changes are as follows:
9: C Harmonic minor
10: C Hungarian minor
11: Eb Major
12: F Melodic
13: F Harmonic Major
14: F Harmonic Major #4
15: F Hungarian minor
16: C Harmonic Major
17: C Harmonic minor
18: Eb Major
19: C Harmonic minor
Each alteration of the notes in the key implies a mode from another scale, and by analysing the changes the patterns in the music can be revealed. The 11 scales that are listed above, which occur in only 2 bars of music, appear in the exact order no less than 5 times. The first time is in C minor, then F minor, C minor, F minor and finally C minor.
So you can see that the Modal Method reveals hidden patterns within the music, here the 2 bar sequence, which Bach obviously bases this whole piece around, takes up 10 bars out of 34 bars, so almost a third of the music is this sequence. It is played, then another sequence, then the same sequence but back a fifth, then another sequence, then it returns forward a fifth, then back, then forward. Simple really. I sometimes approach music in much the same way, develop a set of changes that works well, however complex, and then base the piece around the sequence.
Now, this method seems to me to be far more useful in understanding complex music than entropic, semiotic or information theory studies. Let me know what you think.
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