Your study sounds very technical.

Most of us will just have 'practical' experience and a strong conviction that singing to and with young children is a good thing to do.
Parents and educators have always used song for teaching arithmetic - ten green bottles; 5 little speckled frogs; 1 man went to mow- etc etc.
And rhymes draw attention to sounds which may help with phonic spelling later (drat, the example in my head is - Five six, pick up sticks - so that idea doesn't work)

From my playgroup days I found that a music session (singing, listening or playing percussion) was a good way of getting the attention of the group, and developing concentration.