New answers tagged counter-words
Unless you are looking for some deep meaning I cannot think of, I would say it is applicable because the song is played by 6 guys --- 4 from Monkey Majik and 2 from the Yoshida Brothers. That is 12 arms all together instead of saying "the 6 of us".
The changes you're talking about are actually pretty regular. There are some irregular ones (一人【ひとり】、二人【ふたり】、三階【さんがい】), but what you're looking for is pretty straight-forward. Wikipedia has a pretty good summary of the sound changes.
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