Relationships behind Don Page commas

Looking at some 5-limit Don Page commas

http://xenharmonic.wikispaces.com/Don+Page+comma

I find the following factoids:

(5/3)^4/(4/3)^7 = 16875/16384, negri comma
(5/3)^3/(3/2)^4 = 20000/19683, tetracot comma
(32/25)^3/(10/9)^7 = |8 14 -13>, the parakleisma
(4/3)^7/(5/4)^9 = |32 -7 -9>, escapade
(5/4)^9/(6/5)^11 = |-29 -11 20>, gammic comma
(25/24)^7/(81/80)^23 = |71 -99 73>, raider
(128/125)^11/(81/80)^21 = |161 -84 -12>, the atom

These relationships lend themselves to an especially simple sort of comma pump, and in fact that is true of Don Page commas for higher prime limits as well. One question I have looking at this is to wonder why the exponent of the numerator is always smaller on this list than the denominator. Coincidence?