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Your post is slightly inaccurate. It says that the meter does not change and this is false. In this song the meter changes from duple to triple. The time signature is 6/8 and this is the thing in this song's rhythm that does not change.

It may be that what needs to be is the distinction between "meter" and "time signature." In the example posted here, both yours and mine, there is ONE time signature and TWO alternating meters in alternating measures.

Flatfoot sez: Call me when 'Talent-in-a-Box' is ready to ship! -- [8{>

Got some tunes on You Tube:
http://www.youtube.com/user/flatfoot50
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My BiaB lesson site:
http://jdwolfe0.wixsite.com/learnbiab