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Is this a certain progression in both pieces? Both parts are here slowed down: https://sndup.net/7w6t

The first part is from that piece

(2:18)

The second piece:

(18:51) Is Bach doing here something which can be classified in terms of music theory? It sound very similar to my ears.

EDIT: something very similar happens here too

(20:48) What is this? Does it have a name?

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I think you are hearing the sequence musical device where a short segment of music is repeated but transposed up or down usually by step. Sometimes the transposition is diatonic other times it is chromatic.

You can refer to either harmonic sequence or melodic sequence. Often a sequence is both harmonic and melodic which is what these Bach examples sound like.

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