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Ich muss - wir müssen

Ich mag - wir mögen

Ich kann - wir können

Ich darf - wir dürfen

Why are the singular persons so different from the infinitive form, for these verbs? It's clearly not umlaut, at least not in the usual sense. (It could be for "muss/müssen", but not for the other three.) Is there an explanation, analogous for example to "i-mutation" for "fahren/fährst"?

In Dutch ("kan/kunnen") and Swedish ("kan/kunna") there is something similar, so I guess it's something quite "old", linguistically speaking. But what is it?

Vielen Dank!

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As rogermue already pointed out, these verbs once were past tense forms:
Verbs that had a shift were past tense forms gained a present tense meaning like muss/müssen are called preterite presents or Präteritopräsentien and most of these verbs are the modals that you gave.

In former times, there was a difference in singular and plural for strong past tense forms. You may know that the verb werden has the past tense

er wurde - wir wurden.

However, formerly these forms were:

er ward - wir wurden

so back then, the past singular and past plural had different vowels. This is a subset of a phenomenon called Ablaut. One more example:

today: er band - wir banden (verb binden)
formerly: er band - wir bunden

This vowel difference between singular and plural disappeared for "normal" strong verbs. However, this vowel difference was preserved for the preterite presents (that is the strong verbs that had a tense shift).
The infinitives for the preterite presents are derived from the plural forms.

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  • Compliment for these details of historic evolution.
    – rogermue
    Commented Oct 27, 2014 at 19:39
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Historically the modal verbs derive from the perfect tense which took over a meaning referring to present time. That's why the forms of the modal verbs don't follow the normal pattern.

German wissen, not exactly a modal verb, has a similar conjugation in present tense. It is connected with the Latin perfect vidi - I have seen. If you have seen something then the consequence is that you know something. So some perfect forms have taken over a meaning in present tense. German ich weiß means I know.

The term for such verbs which have changed tense is preterite-present verbs. See wikipedia http://en.m.wikipedia.org/wiki/Germanic_verb#Verb_types

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  • "the modal verbs derive from the perfect tense"? I don't understand that. As far as I know, modal verb were there long before Germanic languages started tinkering with a perfect tense. I'm probably misunderstanding the sentence but I think it could be expressed differently.
    – Emanuel
    Commented Oct 27, 2014 at 12:57
  • Latin vidi is perfect tense.
    – rogermue
    Commented Oct 27, 2014 at 13:09
  • Latin vidi,I have seen, is connected with ich weiß. Latin vidimus, we have seen, is connected with wir wissen. The vowel change in the German present tense is due to different forms of the Latin perfect tense.
    – rogermue
    Commented Oct 27, 2014 at 13:14
  • @Emanuel you can see that they derive from perfect tense, for example, because they don't get a "t" at the third singular person. Analogously, in English they don't take an "s".
    – geodude
    Commented Oct 27, 2014 at 15:54
  • @rogermue Oh wait, considering PIE ablaut, they do.
    – geodude
    Commented Oct 27, 2014 at 16:00

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