There aren't any specific rules about emanations that override the normal interaction between a spell's range and its area.
As far as I'm able to tell, the rule mentioned in the question is the only mention in the game of how a spell's range and area interact, and it says:
If any portion of the spell’s area would extend beyond this range, that area is wasted.
This rule appears both in the SRD, and again in the Rules Compendium, p. 126.
Nothing about the rules for emanations appears to contradict this text:
A burst spell affects whatever it catches in its area, even including creatures that you can’t see. It can’t affect creatures with total cover from its point of origin (in other words, its effects don’t extend around corners). The default shape for a burst effect is a sphere, but some burst spells are specifically described as cone-shaped. A burst’s area defines how far from the point of origin the spell’s effect extends.
An emanation spell functions like a burst spell, except that the effect continues to radiate from the point of origin for the duration of the spell. Most emanations are cones or spheres.
...and many emanation spells have ranges that make no sense, except in terms of interaction with this rule. For instance, Antimagic Field's area is a 10-foot emanation centered on the caster (i.e., the caster doesn't decide its point of origin). The only reason for the spell to also have a 10 foot range is because, if it didn't, the spell wouldn't work properly due to its area falling outside of its range and therefore being "wasted," per the rule already quoted.
...that said, spell authors definitely forgot this rule sometimes when writing spell descriptions.
The example from the OP, where the spell's area is vastly larger than its range until rather high caster levels, is probably an example of such an oversight, but it's hardly the worst case. At least the spell still does something, even if it ends up with a smaller area than was probably intended.
If you really want to bang your forehead against something, take a look at the spell False Vision, whose area is a 40-foot emanation, and whose range entry is...touch.
Yes, I believe this means that by strict RAW the spell doesn't do anything. Yes, this is stupid.
My recommendation: Just houserule the obvious cases.
Most spells (like Antimagic Field above) were written properly with this rule in mind. They can be run RAW with no ill effects.
When you run across a headscratcher like Dissonant Chant or False Vision, where it seems pretty obvious that the authors just forgot this rule, I recommend simply houseruling the spell's range to equal the radius of its area. This is probably what the spell should have said in the first place.