Hi Hans,

> Hindemith, "Training…", indicates that 6/8 is always bipartite, so the 3/4 is 
> a metric shift in this music piece.

Correct.

> By contrast, 9/8 is tripartite, just as 3/4, so I do not see any obvious 
> difference here.

The difference is that each of the three big beats in 9/8 is subdivided into 
three eighth notes, while each of the three big beats in 3/4 is subdivided into 
two eighth notes… Writing it this way means that you don't have to write the 
tuplet notation on alternate bars.

Cheers,
Kieren.

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