Why does “missmutig” lack an umlaut when every other “-mütig” adjective has one?

Question

There are lots of nouns ending in ∙mut

Schwermut, Wehmut, Langmut, Grossmut etc.

and lots of adjectives ending in ∙mütig

gutmütig, kleinmütig, wankelmütig, freimütig, reumütig.

So far as I can tell, every adjective constructed this way has an umlaut in ∙mütig except missmutig.

Why?

Answer 1

The German word Mut has the meaning courage, boldness, bravery:

Er bewies Mut und nahm die Herausforderung an.
He showed courage and accepted the challenge.

But it also can mean mood:

Frohen Mutes machte er sich auf die Reise.
He embarked on the journey in a happy mood.

You find the second meaning even more often in compound nouns:

• Sanftmut = meekness
• Schwermut = gloom
• Edelmut = generosity

Adjectives, that are derived from words of this second meaning end in »∙mütig«:

sanftmütig, schwermütig, edelmütig, gutmütig, demütig, wehmütig

Adjectives, that are derived from the courage-meaning end in »∙mutig«:

mutig, wagemutig, todesmutig, kampfesmutig

But there are also two exceptions:

• Anmut = grace, charm; anmutig = graceful, charming
• Missmut = displeasure; missmutig = morose, grumpy

(anmütig and missmütig do not exist)