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I would like to figure out how voice leading rules could be applied to non-vertical music (non-homophonic music), and when we are not using four-part harmony. I think that Chopin's study op. 25 #1 could be an example of this:

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How are met harmonical leading rules in these cases?

In this example, I can see that at the end of the third bar, the seventh note of the dominant goes to the third of the tonic and that the leading note goes to the tonic note. But the order of appearance of these notes along the arpeggio is not respected. Is therefore the order irrelevant, as if all the notes of the arpeggio were gathered and played at the time?

And what about parallel motion? If we gather the notes, I can see that the leading note is duplicated, making parallel octaves and that an inner voice jumps over the highest notes...

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These rules are derived from a strict 4 voices setting (in purpose that one line doesn't get lost).

So I wouldn't apply them for a voice leading of six or even eight voices, while it could even be explained by voice crossing: Bb -> Eb (3rd voiceand Db -> C). It is surprising how strict Beethoven also still repects the rules in 5 voices piano sonata, but I wouldn't break my head with Liszt and Chopin.

And what about parallel motion? If we gather the notes, I can see that the leading note is duplicated, making parallel octaves and that an inner voice jumps over the highest notes...

What do you expect? In an orchestration of a piece you will also find octav parallels of a voice in different instruments.

Is therefore the order irrelevant, as if all the notes of the arpeggio were gathered and played at the time?

I would agree and say yes. You can consider them as one chord and reduce them to a four part song, if you like.

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