Bach passage spectrogram - piano arrangement

The spectrogram for the Bach passage is shown below.  This spectrogram confirms that the Bach passage does not exactly produce a consistently rising pitch, but interweaves a descending pitch, the overall effect is like ascending a spiral upwards in pitch.  (It is interesting to note that Shepard proposed a double helix representation of pitch perception:  perhaps Bach is showing us how to ascend one spiral of this double helix!)

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Here is a portion of the first seven measures of the score of this piano arrangement.  We show in the three red trapezoids that there is a partial exhibition of the Shepard tone arrangement in the first three bars, and a similar sequence can be discerned in the following four bars.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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