Danish: tonal suffices?

I want to ask here a few questions about Danish linguistics.

First I should clarify that I consider myself a "native speaker" of Danish,
even though I'm not Danish by birth. I lived in Denmark at the age of 9-11,
an excellent age for learning a "second native language".

The questions I ask are perhaps mostly directed to Lars from the U of
Copenhagen, though of course I'd like anybody with sufficient knowledge of
Danish to comment.

Recently, I've been considering Danish phonology and morphology.
Considering, not studying, that is; just thinking about it in my head,
pronouncing words to myself, etc.

What I'm thinking about is: Does Danish have a system of morphemic tones?
What I've usually read about tones in Scandinavian languages is "Swedish and
Norwegian have tonemes, Danish doesn't". But I'm not thinking about the
Swe-Nor tonemes, which differentiate between two words with different
meanings. The Danish use of tones I'm thinking about is this:

(note that this is all based on my examinations of my own Danish speech
(which is to be considered normal) and that of the few people I've spoken
native Danish with the past few days; I have read no books about the matter
and consulted no-one with linguistic knowledge; so if I'm discovering the
wheel, please bear with me :))

Stem + -e  =  RISING TONE
  (the -e is segmentally realized as either 0 or [@])
Stem + -er = FALLING TONE
  (the -er is realized as [a])
Stem + -   = FLAT TONE (either high or low)

Examples:
Sing. "dreng" (boy) has a flat tone, while its plural "drenge" is different
only in a slightly longer vowel (me thinks) and a _rising tone_. Sing.
"kvinde" (woman) also has a rising tone, while its plural "kvinder" has a
falling tone + suffix [a]. The infinitive "kende" (to be familiar with) has
a rising tone, while its present form "kender" has a falling tone + suffix
[a].

So it can be seen the tones have no semantic meaning or grammatical
association of any kind; they merely accompany the suffices -e and -er.

This is just what I've gauged today and yesterday, without thinking much
about it. I'm sure there's much more to the matter. Or am I completely
imagining this? Lars, I'm sure you have answers for me :)
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